Abstract

Damage to radar absorbing materials (RAMs) reduces the stealth capabilities and battlefield survivability of the equipment. Research on RAM damage detection technology is key to outfield equipment maintenance. In this paper, an intelligent RAM damage detection method based on visual and microwave modalities is proposed. A compressed sensing planar-scanning microwave imaging method based on a range migration algorithm (RMA) imaging operator and fast Gaussian gridding nonuniform fast Fourier transform (FGG-NUFFT) is proposed, achieving high imaging quality and speed. A dual-modality, curved RAM dataset (DCR dataset) is constructed, composed of visual images and microwave images showing two kinds of damage: round shedding and strip cracks. A new dual-modality target detection model, the visual-microwave fusion network (VMFNet), is designed to detect RAM damage. Its mean average precision (mAP) reaches 81.87%, and its inference speed reaches 35.91 fps. A visual network (VisNet) and microwave network (MicNet) are designed as the backbone of VMFNet for extracting the visual and microwave features of RAMs. A path aggregation network (PANet) unit is designed to fuse the multiscale features of the two modalities, resulting in good retention of shallow-level features and high detection accuracy. The head contains different receptive fields and outputs three scales of detection results, effectively detecting damage of different sizes.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Radar stealth technology is used to effectively improve the survivability of weaponry. Because they are lightweight, easy to paint, and do not change the aerodynamics of the equipment, radar absorbing materials (RAMs) have been widely used in developing stealth weaponry [1]. However, during the normal use and maintenance of stealth equipment, RAMs may undergo local structural damage or performance degradation due to environmental and human factors such as collisions, scratches, natural aging, and salt spray-induced corrosion, further reducing the penetrability and survivability of the equipment. Therefore, the maintenance of stealth equipment substantially relies on the detection of RAM damage.

Scholars have mostly focused on the development and performance testing of RAMs, while little attention has been paid to damage detection for these materials. The performance of RAMs is reflected by their dielectric constant and vertical reflectivity in most existing studies. Weir et al. [2] proposed the transmission reflection method to obtain the dielectric constant based on the reflection and transmission coefficients. Wu et al. [3] used the transmission line method to achieve onsite target reflectivity detection. Chen et al. [4] used the coaxial reflection method to measure the reflectivity of a standard sample in the laboratory. However, these methods are not suitable for real-time detection for weaponry in the outfield; the results only show reflectivity or dielectric constants of standard samples, and thus, it is difficult to directly show the location, shape and size of RAM damage. Wang et al. [5] applied infrared thermography in the defect detection of absorbing coatings, and Duan [6] applied laser shear speckle technology in RAM defect detection. However, these methods have some practical disadvantages, such as low detection accuracy, a high dependence on professional assessment, and difficulty in visualizing the impact of RAM damage on the scattering and stealth performance of the materials. In addition, it is difficult for first-line detection personnel to quickly obtain the required expertise, leading to additional challenges in the detection and maintenance of stealth equipment in the outfield.

In recent years, deep learning has developed rapidly and has been widely used in damage detection. Han et al. [7] applied Faster-RCNN [8] to detect defects on the surface of wheel hubs, solved the image background unification problem from traditional detection methods, and realized the detection of scratches and points on wheel hubs in images with complex backgrounds, achieving a mean average precision (mAP) of 86.3%. Dung et al. [9] used a deep fully convolutional neural network (FCN) to detect concrete cracks and achieved an average accuracy of more than 90%. Feng et al. [10] designed a new one-stage object detector to detect defects on rail surfaces, overcoming the inaccurate detection results of traditional machine vision algorithms under fixed and variable lighting environments. Tabernik et al. [11] applied segmentation-based deep learning in surface-defect detection and proposed a method that can learn from a small number of training samples, which allows the deep learning method to be used in industries with a limited number of defect samples. These studies were all based on visual images and did not focus on the real-time detection problem; the outfield detection and maintenance of stealth equipment requires high real-time performance in a variable environment; sometimes, it needs to be carried out in a poor visibility environment or even at night. Obviously, a deep learning model created to detect RAM damage based only on visual images will have a low detection accuracy and a high misclassification rate.

Recently, array-based near-field microwave imaging technology has received widespread attention in many applications [12], especially sparse multiple-input multiple-output (MIMO) array topology, which has promoted the development of microwave imaging technology [13]. A MIMO array can achieve better spatial diversity and improved imaging resolution than traditional single-input single-output and single-input multiple-output arrays. MIMO arrays also have fewer antenna elements in the same aperture dimension than these traditional arrays [14]. Most of the existing dictionary matrices used in compressed sensing microwave imaging have orthogonal bases; while this kind of dictionary matrix can often achieve good reconstruction results, it may require a large amount of imaging calculation and computational memory. To speed up the imaging calculations, Sun et al. [15] proposed a compressed sensing fast imaging method based on a nonuniform fast Fourier transform (NUFFT). Compared with the fast Fourier transform (FFT) dictionary matrix, the NUFFT dictionary matrix had higher imaging efficiency. Austin et al. [16] proposed a fast imaging method based on the adjacent Stolt interpolation ω-k imaging operator by combining compressed sensing with a matched filter imaging method. However, this method uses only the forward process of the ω-k transformation to transform a nonuniform acquisition signal into a uniform acquisition space and then reconstructs it iteratively through compressed sensing. Yang et al. [17] used the forward and inverse processes of range migration algorithm (RMA) transformation to construct a fast imaging operator and realized image reconstruction through iterative discrimination. However, this method has poor imaging quality because it is also based on Stolt interpolation. Starting from the original observation data domain, we combine approximate observations with sparse signals and propose a compressed sensing planar-scanning microwave imaging method based on the RMA imaging operator and FGG-NUFFT. According to the forward and inverse processes of frequency-domain RMA imaging, a fast imaging operator is constructed that ensures high imaging quality and efficiency.

Microwave imaging technology can be used to show, to a certain extent, the location and degree of damage to RAMs and the corresponding stealth performance changes. However, for the same degree and kind of damage at different locations on curved RAMs, the relative distances and scattering angles from the MIMO array will be different, which will result in the same degree and kind of damage showing different scattering characteristics on the microwave image. This makes the direct detection of RAM damage with microwave imaging difficult and highly dependent on experienced operators. In this study, we implemented the deep learning method to detect damage on curved RAMs. A dual-modality convolutional neural network (CNN) is designed that can simultaneously extract and fuse the features of visual and microwave images of RAM damage and then detect RAM damage according to the fused features.

In this paper, an intelligent damage detection method for curved RAMs based on visual images and microwave images is proposed that promotes the development of outfield detection and maintenance of stealth weaponry. Our main contributions are listed as follows:

  • (1) To improve the quality and efficiency of microwave imaging, a compressed sensing planar-scanning microwave imaging method based on the RMA imaging operator and FGG-NUFFT is proposed. NUFFT is introduced to replace the interpolation and Fourier transform in RMA imaging to increase accuracy and speed up the calculations. FGG-NUFFT uses a Gaussian spread function to accelerate the speed of the nonuniform Fourier transform.
  • (2) Curved specimens of RAMs are constructed, visual images and microwave images of RAMs are collected, and a dual-modality curved RAM dataset (DCR dataset) is constructed. The number of images in the DCR dataset is expanded through geometric distortions, such as random scaling, rotation, and flipping, as well as the adoption of a new data augmentation method, namely, mosaic data augmentation. The DCR dataset contains images showing two types of damage, round shedding and striped cracks, and is characterized by large target size changes, large aspect ratio changes, low-resolution microwave images, and a high degree of clutter.
  • (3) To realize real-time RAM damage detection, compensate for the low accuracy in damage detection of deep learning models constructed only from visual images, and remove the high dependence on professionals detecting RAM damage directly by interpreting microwave images, a new dual-modality target detection network, the visual-microwave fusion network (VMFNet), is designed in this paper. It can extract and fuse the feature information from visual and microwave modalities of RAMs simultaneously and use this fused feature information to detect RAM damage. Compared with that of damage detection based on single modality information, the detection accuracy of VMFNet is higher, and its mAP reaches 81.87%.

2. Microwave imaging algorithm

In near-field imaging, because the wavefront is a spherical wave, the three-dimensional spatial spectrum has a nonuniform distribution in a rectangular coordinate system, and the Fourier transform cannot be directly used for range direction. Typically, the spherical spectrum is transformed into a uniform spectrum that can satisfy the FFT by using three-dimensional interpolation and then use the three-dimensional inverse Fourier transform to calculate the target scattering function value. This process is not only time-consuming but also leads to imaging errors due to inaccuracies in the interpolation. To solve this problem, NUFFT is introduced to replace the interpolation and Fourier transform in RMA imaging, improving the accuracy of the transform and increasing the calculation speed. The FGG-based NUFFT can further increase the speed of the nonuniform Fourier transform due to the use of the Gaussian spread function.

2.1. Fast imaging operator based on the RMA forward and inverse transforms

The RMA-based planar-scanning microwave imaging process is expressed in matrix form in Eq. (1).

$${\mathbf {g = F}}_{3D}^{ - 1}\{{{\mathbf H}\{{{{\mathbf F}_{2D}}({\mathbf S} )\cdot {\mathbf E}} \}} \}{\mathbf = }{{\mathbf A}^{ - 1}}{\mathbf S},$$
where ${\mathbf S}$ represents the original echo signal, ${\mathbf E}$ represents the matched filter factor $\mathrm{exp} ({ - j{k_z}{z_0}} )$, ${\mathbf F}_{3D}^{ - 1}$ represents the three-dimensional inverse Fourier transform, ${{\mathbf F}_{2D}}$ represents the two-dimensional Fourier transform, ${\mathbf H}$ represents the three-dimensional interpolation, and ${{\mathbf A}^{{\mathbf - 1}}}$ represents the inverse matrix of dictionary ${\mathbf A}$, ${\mathbf {A = F}}_{3D}^{ - 1}\{{{\mathbf H}\{{{{\mathbf F}_{2D}}({\mathbf S} )\cdot {\mathbf E}} \}} \}$.

To improve the calculation efficiency and reduce the interpolation error, FGG-NUFFT is used to replace the interpolation and the inverse Fourier transform of the distance in Eq. (1) as:

$$\mathbf {g} = \mathbf {F}_{2D,{k_x},{k_y}}^{ - 1}\{{\{{{\mathbf F}_{NU,{k_z}}^{ - 1}\{{{{\mathbf F}_{2D,x^{\prime},y^{\prime}}}({\mathbf S} )} \}} \}\cdot {\mathbf E}} \}{\mathbf = }{{\underline{\mathbf {A}} }^{{\mathbf - 1}}}{\mathbf S}.$$

Equation (2) represents the forward transform based on FGG-NUFFT imaging; the inverse transform is expressed as:

$$\mathbf {S} = \mathbf {F}_{2D,x^{\prime},y^{\prime}}^{ - 1}\{{\{{{{\mathbf F}_{NU,z}}\{{{{\mathbf F}_{2D,{k_x},{k_y}}}({\mathbf g} )} \}} \}\cdot {{\mathbf E}^\ast }} \}{ = \underline{\mathbf {A}} \mathbf {g}},$$
where ${{\mathbf E}^\ast }$ represents the conjugate of ${\mathbf E}$. Equation (3) can also be considered the compressed sensing imaging model based on RMA.

The dictionary matrix can be expressed as:

$${\underline{\mathbf {A}} = \mathbf {F}}_{2D,x^{\prime},y^{\prime}}^{ - 1}\{{\{{{{\mathbf F}_{NU,z}}\{{{{\mathbf F}_{2D,{k_x},{k_y}}}({\cdot} )} \}} \}\cdot {{\mathbf E}^\ast }} \} = {\mathbf F}_{2D,x^{\prime},y^{\prime}}^{ - 1} \times ({{{\mathbf F}_{NU,z}} \times ({{{\mathbf F}_{2D,{k_x},{k_y}}} \circ {{\mathbf E}^\ast }} )} ),$$
where ${\times}$ represents the matrix product and ${\circ}$ represents the matrix Hadamard product.

The specific representation of each matrix in Eq. (4) is given below.

$${{\mathbf F}_{2D}} = {\mathbf F}_{1D}^X \otimes {\mathbf F}_{1D}^Y,$$
where ${\otimes}$ represents the Kronecker product, and ${\mathbf F}_{1D}^X$ and ${\mathbf F}_{1D}^Y$ represent the one-dimensional Fourier transform along the X-axis and Y-axis, respectively, as shown in Eq. (6) for the X-axis.
$${\mathbf F}_{1D}^X = \frac{1}{{\sqrt M }}\left[ {\begin{array}{lcccc} 1&1&1& \cdots &1\\ 1&f&{{f^2}}& \cdots &{{f^{(M - 1)}}}\\ 1&{{f^2}}&{{f^4}}& \cdots &{{f^{2(M - 1)}}}\\ \vdots & \vdots & \vdots &{}& \vdots \\ 1&{{f^{(M - 1)}}}&{{f^{2(M - 1)}}}& \cdots &{{f^{(M - 1)(M - 1)}}} \end{array}} \right],$$
where $f = {e^{ - \frac{{2\pi j}}{M}}}$. The one-dimensional Fourier transform expression along the Y-axis can be obtained similarly.

Matrix ${\mathbf E}$ represents the matched filter index term obtained from the echo signal as defined as Eq. (7).

$$\left\{ \begin{array}{lccccc} {\mathbf E} = \bar{{\mathbf e}} \otimes {\left[ {\begin{array}{cccc} 1&1& \cdots &1 \end{array}} \right]_{1 \times ({NML} )}}\\ \bar{{\mathbf e}} = \left[ {\begin{array}{cccccc} {e_{({1,1} )}^{\mathbf H}}&{e_{({1,2} )}^{\mathbf H}}& \cdots &{e_{({1,n} )}^{\mathbf H}}& \cdots &{e_{({1,N} )}^{\mathbf H}}\\ \vdots &{}& \ddots &{}&{}& \vdots \\ {e_{({M,1} )}^{\mathbf H}}&{e_{({M,2} )}^{\mathbf H}}& \cdots &{e_{({M,n} )}^{\mathbf H}}& \cdots &{e_{({M,N} )}^{\mathbf H}} \end{array}} \right] \end{array} \right.,$$
where M, N and L respectively represent the number of sampling points along the X-axis, Y-axis and Z-axis (distance direction) and ${e_{m,n}}$ represents the column vector of sampling points in the distance direction in the matrix ${\mathbf e}$, which can be expressed as:
$${\mathbf e} = {[{\mathrm{exp} ({ - j{k_z}{z_0}} )} ]_{MNL}},$$
${{\mathbf F}_{NU}}$ represents the one-dimensional NUFFT and can be expressed as:
$${{\mathbf F}_{NU}} = \frac{1}{{\sqrt L }}\left[ {\begin{array}{ccccc} 1&1&1& \cdots &1\\ 1&{{f_{nu}}}&{f_{nu}^2}& \cdots &{f_{nu}^{L - 1}}\\ 1&{f_{nu}^2}&{f_{nu}^4}& \cdots &{f_{nu}^{2({L - 1} )}}\\ \vdots & \vdots & \vdots &{}& \vdots \\ 1&{f_{nu}^{L - 1}}&{f_{nu}^{2({L - 1} )}}& \cdots &{f_{nu}^{({L - 1} )({L - 1} )}} \end{array}} \right],$$
where ${f_{nu}} = {e^{\frac{{ - 2\pi j}}{L}}}$ and whose derivation process is as follows. The one-dimensional NUFFT is defined as:
$$F(k )= \frac{1}{N}\sum\limits_{i = 0}^{N - 1} {{f_i}{e^{ - jk{x_i}}}} ,k ={-} \frac{M}{2}, \cdots ,\frac{M}{2} - 1,$$
where ${x_i} \in [{0,2\pi } ]$ and is nonuniformly distributed; ${f_i}({i = 0,1, \cdots ,N - 1} )$ represents the nonuniform spectral data in the wavenumber domain; and $F(k )$ is the uniformly distributed signal in the spatial spectral domain. Assume that $f(x )$ is a periodic function in the interval $[{0,2\pi } ]$, defined as:
$$f(x )= \sum\limits_{i = 0}^{N - 1} {{f_i}\delta ({x - {x_i}} )}.$$

Assume also that ${g_\eta }(x )$ is a one-dimensional periodic thermal kernel function in the interval $[{0,2\pi } ]$, expressed as:

$${g_\eta }(x )= \sum\limits_{l ={-} \infty }^\infty {{e^{{{ - {{({x - 2l\pi } )}^2}} / {4\eta }}}}}.$$

Define the function ${f_\eta }(x )$, which is obtained by convolving Eqs. (11) and e1(12) as follows:

$${f_\eta }(x )= f(x )\ast {g_\eta }(x )= \int_0^{2\pi } {f(s )} {g_n}({x - s} )ds.$$

It can be seen from the above formula that ${f_\eta }(x )$ is a periodic function with a period of $2\pi$ on ${C^{ - \infty }}$, which can be solved with a uniform grid on x, and the grid interval is determined by $\eta$. According to the number of oversamplings ${M_r} = R \times N$ required to determine the appropriate grid, where R is the oversampling coefficient, Eq. (13) can then be solved by Eq. (14).

$${F_\eta }(k )\approx \sum\limits_{m = 0}^{{M_r} - 1} {{f_\eta }({{{2\pi m} / {{M_r}}}} )} {e^{{{ - jk2\pi m} / {{M_r}}}}},$$
where
$${f_\eta }({{{2\pi m} / {{M_r}}}} )= \sum\limits_{i = 0}^{N - 1} {{f_i}{g_\eta }} ({{{2\pi m} / {{M_r} - {x_i}}}} )= \sum\limits_{i = 0}^{N - 1} {{f_i}} \sum\limits_{l ={-} \infty }^\infty {{e^{{{ - {{({{x_i} - {{2\pi m} / {{M_r}}} - 2l\pi } )}^2}} / {4\eta }}}}}.$$

When the value of ${F_\eta }(k )$ is known, $F(k )= \sqrt {\frac{\pi }{\eta }} {e^{{k^2}\eta }}{F_\eta }(k )$ can be obtained. The main task of NUFFT is to calculate the value of ${f_\eta }({{{2\pi m} / {{M_r}}}} )$ in Eq. (14) based on grid processing. Since the Gaussian hot core is a spike, we can map the receiver point ${{2\pi m} / {{M_r}}}$ to the source point ${x_i}$ through a Gaussian source, and then we can obtain Eq. (16).

$${f_n}[{m + m^{\prime}} ]\leftarrow {f_n}[{m + m^{\prime}} ]+ {f_i}{e^{{{ - ({{x_i} - {{2\pi m} / {{M_r}}} - {{2\pi m^{\prime}} / {{M_r}}}} )} / {4\eta }}}},$$
where ${{2\pi m} / {{M_r}}}$ is the square grid point closest to ${x_i}$, $i = {{ - N} / 2}, \cdots {N / 2} - 1$, and $m^{\prime} ={-} {M_{sp}} + 1, \cdots ,{M_{sp}}$, where ${M_{sp}}$ is the expansion number. The above process can accelerate the convolution. Figure 1 shows the corresponding relationship between the dictionary matrix and the RMA forward and inverse transformations.

 figure: Fig. 1.

Fig. 1. Correspondence between the dictionary matrix and the RMA forward/inverse transformations.

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To reconstruct the target image well, the constructed dictionary matrix must be orthogonal. ${{\mathbf F}_{2D}}$, ${\mathbf F}_{2D}^{ - 1}$ and ${{\mathbf F}_{NU}}$ represent the two-dimensional Fourier transform, inverse transform and one-dimensional nonuniform Fourier transform, respectively, and so to meet the orthogonality requirements:

$$\left\{ {\begin{array}{c} {{{\mathbf F}_{2D}} \cdot {\mathbf F}_{2D}^H = {\mathbf I}}\\ {{\mathbf F}_{2D}^{ - 1} \cdot {{({{\mathbf F}_{2D}^{ - 1}} )}^H} = {\mathbf I}}\\ {{{\mathbf F}_{NU}} \cdot {\mathbf F}_{NU}^H = {\mathbf I}} \end{array}} \right.$$
In Eq. (7), E is a complex diagonal matrix; therefore:
$${\mathbf E} \cdot {{\mathbf E}^H} = {\rm diag}({{e_1},{e_2}, \cdots ,{e_{MNL \times PQT}}} )$$
$$\begin{aligned} {\underline{\mathbf {A}} } \cdot {{{\underline{\mathbf {A}} }}^H} & = {\mathbf F}_{2D}^{ - 1} \cdot {{\mathbf F}_{NU}} \cdot {\mathbf E} \cdot {{\mathbf F}_{2D}} \cdot {({{\mathbf F}_{2D}^{ - 1} \cdot {{\mathbf F}_{NU}} \cdot {\mathbf E} \cdot {{\mathbf F}_{2D}}} )^H}\\ & = {\mathbf F}_{2D}^{ - 1} \cdot ({{{\mathbf F}_{NU}} \cdot ({{\mathbf E} \cdot ({{{\mathbf F}_{2D}}{\mathbf F}_{2D}^H} )\cdot {{\mathbf E}^H}} )\cdot {\mathbf F}_{NU}^H} )\cdot {({{\mathbf F}_{2D}^{ - 1}} )^H}\\ & = {\rm diag}({{e_1},{e_2}, \cdots ,{e_{MNL \times PQT}}} )\end{aligned}$$
As shown in Eq. (19), $\Phi {\underline{\mathbf {A}} }$ satisfies the requirements of the compressed sensing restricted isometry property because dictionary ${\underline{\mathbf {A}} }$ is orthogonal.

2.2. Fast reconstruction method based on separable surrogate functionals

In this model, the imaging model shown in Eq. (3) is solved with the regularization-based iterative shrinkage optimization reconstruction method. This method transforms the multiplication of a high-dimensional matrix into the multiplication of a matrix and vector. In addition, this paper uses a linear search to speed up the convergence. Equation (3) is written as follows:

$$f({\mathbf g} )= \frac{1}{2}\left\|{{\mathbf S} - {\underline{\mathbf {A}} g}} \right\|_2^2 + \lambda {\left\|{\mathbf g} \right\|_1}.$$

Let ${{\mathbf g}_0} = {{\underline{\mathbf {A}} }^{ - 1}}{\mathbf S}$, then:

$$f({\mathbf g} )= \frac{1}{2}\left\|{{\mathbf S} - {\underline{\mathbf {A}} g}} \right\|_2^2 + \lambda {\left\|{\mathbf g} \right\|_1} = \sum\limits_{k = 1}^m {\left[ {\frac{1}{2}{{({{{\mathbf g}_0}(k )- {\mathbf g}(k )} )}^2} + \lambda \left|{{\mathbf g}(k )} \right|} \right]}.$$

The planar-scanning microwave imaging process based on the RMA imaging operator and FGG-NUFFT is shown in Fig. 2. The imaging method proposed in this paper has the following advantages:

  • (1) The RMA imaging process is represented as a compression-sensing imaging dictionary. The echo is processed by an imaging operator, for example, RMA imaging, which avoids the need to construct a large-scale dictionary and the multiplication of a large dictionary and accelerates the imaging speed;
  • (2) The forward and inverse RMA processes are used, increasing the accuracy of the estimation of the scattering coefficient;
  • (3) FGG-NUFFT replaced the interpolation and one-dimensional Fourier transforms used in traditional RMA imaging, which reduces interpolation error and improves imaging efficiency;
  • (4) The reconstruction model based on regularization gives the algorithm strong noise suppression.

 figure: Fig. 2.

Fig. 2. Flow chart for microwave imaging based on the RMA imaging operator and FGG-NUFFT.

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The compressed sensing microwave imaging method based on explicit dictionary and the imaging method proposed in this paper are respectively used to obtain the microwave image of RAM damage, as shown in Fig. 3. The imaging quality of the proposed microwave imaging method based on RMA imaging operator and FGG-NUFFT is almost the same as that of the compressed sensing method based on explicit dictionary, both of which have higher imaging quality. The time required for processing data by computer is used to compare the efficiency of the compressed sending method based on explicit dictionary and the method proposed in this paper. The hardware configuration of the computer is: CPU of Intel Core i7-4770HQ CPU @ 2.2 GHz 2.19 GHz, memory 8GB. The comparison of imaging time in Table 1 shows that the calculation time of microwave imaging method based on RMA imaging operator and FGG-NUFFT is about 1 / 100 of that of compressed sensing microwave imaging method based on explicit dictionary, which greatly improves the imaging efficiency. The experimental results show that the microwave imaging method proposed in this paper can greatly improve the imaging efficiency while ensuring the imaging quality.

 figure: Fig. 3.

Fig. 3. Microwave images of damage on curved RAMs. (a) Compressed sensing microwave imaging method based on explicit dictionary matrix. (b) Microwave imaging method based on RMA imaging operator and FGG-NUFFT.

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Table 1. Comparison of Imaging Performance of Different Methods

The target clutter ratio (TCR) of the microwave image can be calculated by Eq. (22).

$$\textrm{TCR} = \frac{{(1/{N_t})\sum\nolimits_{(x,y,z) \in {\textrm{D}_t}} {{{|{I(x,y,z)} |}^2}} }}{{(1/{N_c})\sum\nolimits_{(x,y,z) \in {\textrm{D}_c}} {{{|{I(x,y,z)} |}^2}} }},$$
where ${N_t}$ and ${N_c}$ respectively represent the number of imaging pixels in the target area and the clutter area; ${\textrm{D}_t}$ and ${\textrm{D}_c}$ respectively represent the target area and the background area remaining after removing the target; $I(x,y,z)$ represents the image pixel value.

The above algorithm is used to obtain microwave images of RAM damage, as shown in Fig. 3(b). The microwave image quality is high, and the relative positions of damage are well displayed. However, when the locations of the damage on the curved RAMs are different, the distances and scattering angles of the damage relative to the MIMO array are different, causing the same degree and kind of damage demonstrate different scattering characteristics in the microwave image. In particular, the damage at the detection edge presents weak scattering characteristics in the microwave image, and even presents the same scattering intensity as the clutter, which brings challenges to the detection. This makes it difficult to accurately detect the damage on cured RAMs only by microwave imaging, requiring the inclusion of the locations, distances, angles and other features extracted from visual images.

3. DCR dataset

3.1. Construction of the DCR dataset

During the actual use of stealth equipment, whose surface typically has a certain, non-zero curvature, RAM damage mainly manifests as strip cracks and round shedding at rivets. Therefore, curved RAM specimens with strip-shaped and round damage are constructed in this paper.

The Microwave imaging algorithm proposed in Section 2 is used to obtain microwave images of the curved RAM damage. An industrial camera is used to collect visual images at a fixed angle and position, onto which the damage is marked. Through observation, we can see that there is some clutter caused by coupling scattering in the microwave image, increasing the difficulty in artificially analyzing and interpreting it. However, we hypothesize that the clutter also contains much scattering information that could be useful to the deep learning model for extracting damage features, integrating characteristic information and detecting damage. The DCR dataset, as shown in Fig. 4, is composed of 416 × 416 visual images and their corresponding microwave images. To the best of our knowledge, our DCR dataset is the first RAM target detection dataset containing both microwave and visual images. There are 3154 images (1577 visible images and 1577 microwave images) in the dataset, including 3065 images with round shedding damage and 3172 with strip crack damage. In this study, the DCR dataset is divided into train set and test set according to the ratio of 9:1. The train set is used to train the model, and the test set is used to test the performance of the model. Other scholars in this field can use the dataset to further perform damage detection research.

3.2. Augmentation of DCR dataset

For neural networks applied in computer vision, the use of larger training data sets can effectively enhance the generalizability of the model, but it is often difficult or even impossible to collect enough data in practice. For the sake of practicality, only a limited number of curved RAM damage specimens were constructed in this study; the dataset was then expanded by data augmentation to reduce the difficulty of the model training, reduce the model error and enhance its generalizability. The purpose of data augmentation is to increase the variability of the input images so that the designed object detection model has greater robustness to images obtained from different environments. For example, photometric distortions and geometric distortions are two commonly used data augmentation methods and have been used extensively in the object detection task [18]. However, in this study, the color, contrast and other photometric information from microwave images have special meaning: they represent the scattering intensity and indicate the stealth performance variations in different RAMs. Therefore, in this paper, photometric distortions are not used to perform data augmentation; instead, geometric distortions are used, including random scaling, rotation, and flipping.

This paper also uses a new data augmentation method, namely, mosaic data augmentation [18], in which 4 training images, and thus 4 different contexts, are combined and mixed. This approach allows the detection of objects outside their normal context. In addition, batch normalization is used to calculate the activation statistics from 4 different images in each layer. This method significantly reduces the need for a large mini-batch size. The original mosaic is composed of scaled, stretched, rotated, flipped and cropped images. Because of the particularity of the dataset constructed in this paper, the relative positions of the damage between the microwave and visual images can be variable. When the image is cropped, the damage may still be present in the microwave image but removed from the visual image and vice versa. Therefore, the cropping operation is not performed in this paper. The mosaic data augmentation method is illustrated in Fig. 5.

 figure: Fig. 5.

Fig. 5. Mosaic data augmentation.

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4. Deep learning method

Generic object detection based on a CNN [19] plays a key role in object detection research. The mainstream object detectors can be divided into two categories: one-stage object detectors [2022] and two-stage object detectors [8, 23, 24]. One-stage object detectors have fast detection speeds, but their detection accuracies are usually low. In contrast, two-stage object detectors have high detection accuracies, but the detection speeds are low. Considering the real-time requirement for damage detection, the VMFNet designed in this paper is a one-stage object detector.

4.1. VMFNet

The architecture of VMFNet is illustrated in Fig. 6. VMFNet is composed of a backbone, a neck and a head. The backbone is composed of a visual network (VisNet) and a microwave network (MicNet). VisNet is used to extract the features of visual RAM images, and MicNet is used to extract the features of the microwave RAM images. The neck is composed of a PANet unit, in which the visual and microwave image features of the RAM damage extracted by the backbone are fused and strengthened. The head consists of three 3 × 3 Conv-BN-Mish layers and three 1 × 1 Conv-BN-Mish layers. The 3 × 3 Conv-BN-Mish layers further integrate the extracted features, and the 1 × 1 Conv-BN-Mish layers transform the features into the prediction results for VMFNet. The Conv-BN-Mish layers each contain a convolution layer (Conv), a batch normalization layer (BN) and a Mish [25] activation function layer (Mish). BN can integrate the data distribution after convolution processing, reduce the training difficulty of the model, prevent the gradient disappearing problem in the training process, make the new data distribution more consistent with the real data distribution, and ensure the nonlinear expression ability of the model. The algorithm flow of BN is shown in Table 2. The non-monotonicity of the Mish activation function helps the data flow to maintain a small negative value, thereby stabilizing the network gradient flow. Moreover, the Mish activation function is a smooth function with good generalization ability and effective optimization ability, as shown in Eq. (23).

$${\rm Mish} = x \cdot \tanh ({\ln ({1 + {e^x}} )} ).$$

 figure: Fig. 6.

Fig. 6. Illustration of the proposed VMFNet architecture.

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Table 2. Algorithm Flow of BN

4.2. Backbone

The damage in the visual images of RAMs is characterized by large size and aspect ratio changes, while the visual images themselves have complex backgrounds and rich colors and contain much interference information, which makes it challenging for the CNN to extract the damage features. To better extract the features in the visual images, the VisNet designed in this paper has a large number of layers, as detailed in Table 3. The VisNet contains 5 modules; the first two modules contain a 3 × 3 Conv with a stride of 2 (s = 2), a BN, and a Mish. The last 3 modules contain 2, 2, and 3 CSPNet blocks (CSP blocks). The stride of the first CSP block of each module is 2, and the number of output channels is twice the number of input channels. The stride of other CSP blocks is 1, and the number of output channels is equal to the number of input channels. Finally, each CSP block contains r residual blocks (ResBlocks).

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Table 3. VisNet Architecture

In this paper, a CSP block is designed based on the idea of CSPNet [26], and its structure is shown in Fig. 7. The feature map input into the CSP block is first downsampled through a Conv-BN-Mish layer with a stride of 2 (downsampling is performed only in the first CSP block of each module) and then divided into two parts, P0 and P1, by two 1 × 1 Conv-BN-Mish layers whose number of output channels is half of the number of input channels. P1 is stacked with P0 after r ResBlocks, and then the extracted features are further integrated by a 3 × 3 Conv-BN-Mish layer.

 figure: Fig. 7.

Fig. 7. Illustration of the CSPNet block architecture.

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VisNet contains 7 CSP blocks that extract the features of the visual RAM images and contain 1, 2, 2, 4, 2, 4, and 3 Resblocks. To increase the inference speed of the network, the number of output channels of each CSP block is set to be relatively small, and the number of channels of the feature map is reduced by half through the Conv-BN-Mish layers. The CSP block separates the gradient flow and spreads it onto different network paths, allowing the network to obtain richer gradient fusion information while reducing the number of calculations and improving the inference speed and detection accuracy.

The microwave RAM images are pseudocolor images that represent the scattering intensity of the RAMs. The information they contained is more concise than that in the visual images, and there are few interfering factors, such as complex backgrounds. Therefore, to prevent overfitting and improve the inference speed of the network, the MicNet designed in this paper for extracting the features of the microwave RAM images has a simpler structure and fewer layers than the VisNet and is detailed in Table 4. Like VisNet, MicNet is also composed of 5 modules. The first two modules contain Conv-BN-Mish layers with a stride of 1 and maximum (Max) pooling layers. The remaining three modules are composed of multiple Conv-BN-Mish layers with a stride of 1 and a Conv-BN-Mish layer with a stride of 2. The Max pooling method is used to downsample the feature map to reduce the number of spatial features, as shown in Fig. 8. Max pooling can effectively preserve the texture features of the feature map and weaken the position weights, enhancing the robustness of the network. However, the position features are also important for damage detection, so they cannot be overly weakened. Module 1 and Module 2 are in the shallow position of the MicNet, where the receptive field for the microwave images is small and the position weights will not be excessively weakened; therefore, Max pooling is used to downsample the feature map in these modules. The remaining modules are in the deep position of the MicNet and have a large receptive field for the microwave images. Therefore, a Conv-BN-Mish layer with a stride of 2 is used instead of Max pooling to downsample the feature map.

 figure: Fig. 8.

Fig. 8. Illustration of the Max pooling operation.

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Tables Icon

Table 4. MicNet Architecture

4.3. Neck and head

Inspired by the path aggregation network (PANet) for instance segmentation [27], we designed a PANet unit as the neck of VMFNet. Our PANet unit integrates the feature maps of the visual and microwave images with different scales (Vis-Mic feature maps) and then integrates the Vis-Mic feature maps of different levels through a top-down and a bottom-up path. Shallow-level features would lose much information in the process of being extracted into deep features by the CSP block in VisNet. The shallow features are directly obtained by the PANet unit, which fuses them with deep-level features after a few layers, retaining more shallow-level feature information and thus producing feature maps with more semantic information.

The structure of the PANet unit, shown in Fig. 6, consists of a Conv-BN-Mish layer, a concatenation (Concat) layer, an upsampling layer and a downsampling layer. The structure of the Concat layer is shown in Fig. 9. The visual feature map and the microwave feature map are concatenated in the channel dimension, which increases the depth of the feature map, so that the information of the visual feature map and the microwave feature map is completely preserved, and then integrated by a 3 × 3 Conv to generate a new Vis-Mic feature map. This new Vis-Mic feature map and the Vis-Mic feature map from the last layer are added elementwise to obtain the final Vis-Mic feature map. The nearest method is applied to the upsampling layer, and a 3 × 3 Conv with a stride of 2 is applied to the downsampling layer.

 figure: Fig. 9.

Fig. 9. Illustration of the Concat architecture.

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The head of the network designed in this paper, as shown in Fig. 6, consists of three scales: 13 × 13, 26 × 26 and 52 × 52. The sizes of the corresponding receptive fields of the visual and microwave RAM images are 32 × 32, 16 × 16 and 8 × 8, respectively. Therefore, the head portion can effectively detect RAM damage of different sizes even when large changes in damage size are present.

5. Experiments and results

We carry out experiments to verify the performance of the deep learning model designed in this paper for detecting RAM damage. The experiments were carried out on an NVIDIA Quadro RTX 6000, and the model is written based on PyTorch. mAP is selected as the index for evaluating the model. The effects of different activation functions, learning rate adjustment methods and model optimization methods on the damage detection accuracy of VMFNet are studied, and the real-time performance of VMFNet is assessed through comparative experiments.

The effects of three activation functions, ReLU, ReLU6 and Mish, on VMFNet are studied, and the experimental results are shown in Table 5. When using Mish, VMFNet has the largest mAP. This is because, unlike ReLU and ReLU6, Mish does not completely truncate the input value when it is negative; rather, because it is nonmonotonic, it allows a relatively small negative gradient to flow in, the flow of information is ensured, and the network gradient flow is stabilized. Additionally, Mish is a smooth function, with good generalizability and effective optimization ability.

Tables Icon

Table 5. VMFNet Damage Detection Accuracy Under Different Activation Functions

The effect of three learning rate adjustment methods, step-by-step adjustment, adaptive adjustment and cosine annealing, on VMFNet is studied, and the experimental results are shown in Table 6. When cosine annealing is used, VMFNet has the highest damage detection accuracy. This is because cosine annealing causes the learning rate to abruptly increase when it decays to a certain value, a process known as warm restart. During the training process, if the model converges to a local optimal solution, the warm restart process activates, increasing the learning rate abruptly and causing the model to jump out of the local optimal solution with a certain probability and continue updating.

Tables Icon

Table 6. VMFNet Damage Detection Accuracy Under Different Learning Rate Adjustment Methods

The influence of three model optimization methods, momentum, RMSprop and Adam, on VMFNet is studied, and the experimental results are shown in Table 7. When Adam is used, VMFNet has the highest damage detection accuracy. This is because Adam combines the advantages of momentum and RMSprop; it can accelerate the learning of parameters with the same gradient direction, reduce the updating of parameters with different gradient directions, suppress oscillations, and accelerate convergence. Additionally, Adam is an adaptive learning rate optimization algorithm; in the early stage of training, the learning speed is high, and the model convergence is accelerated. In the late stage of training, the learning speed is gradually reduced to find the optimal solution. In addition, Tables 5 to 7 show that the accuracy of RAM damage detection is improved by using the data augmentation method to expand the dataset. This is because data augmentation reduces the training difficulty of the model and improves the generalization ability of the model.

Tables Icon

Table 7. VMFNet Damage Detection Accuracy Under Different model Optimization Methods

By comparing the proposed model with existing target detection models, the real-time performance and accuracy can be tested. Compared with using only visual or microwave images to detect damage, we verify that the use of dual modalities can improve the accuracy in RAM damage detection. The experimental results are shown in Table 8.

Tables Icon

Table 8. Results of Comparative Experiments

Table 8 shows that the inference speed of the proposed VMFNet reaches 35.91 fps, second only to YOLOv3, YOLOv4 and CenterNet, and the real-time performance of the proposed model in damage detection is guaranteed. VMFNet achieves the best accuracy in detecting curved RAM damage, with the mAP on the DCR dataset reaching 81.87%, much higher than that of the other target detection models, such as YOLOv3, YOLOv4 and CenterNet. The mAP of VMFNet using both visual and microwave images is 3.14 percentage points higher than that of VMFNet using only visual images and 4.36 percentage points higher than that of VMFNet using only microwave images. This is because VMFNet fuses the features of visual and microwave images; the characteristics of the two kinds of images complement each other. In this way, the effects of low light and visibility on damage in the visual images and of the differences in scattering features from the same degree and type of damage at different locations in the microwave images are minimized. Figure 10 shows the visual result of RAM damage detection from VMFNet. Crack and shedding damage is marked with red and purple boxes, respectively, and the green and blue boxes are the ground truth.

 figure: Fig. 10.

Fig. 10. Some prediction examples from VMFNet on the DCR dataset. (a) Visual images. (b) Microwave images. (c) Ground truth. (d) VMFNet using only visual images. (e) VMFNet using only microwave images. (f) VMFNet using both visual and microwave images.

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6. Conclusions

In this paper, based on the deep learning method, visual and microwave dual-modality real-time damage detection of curved RAMs is investigated. We propose a compressed sensing planar-scanning microwave imaging method based on the RMA imaging operator and FGG-NUFFT. A fast imaging operator is constructed based on the forward and inverse processes of frequency-domain RMA imaging, which can ensure high imaging quality and efficiency. We propose a new dual-modality CNN framework, namely, VMFNet, to detect curved RAM damage through visual and microwave images with a mAP of 81.87%, which is much higher than that of other target detection frameworks. Additionally, the inference speed reaches 35.91 fps, which meets the real-time requirement for damage detection. Furthermore, compared with other methods, the performance of VMFNet is significantly improved by using the Mish activation function, cosine annealing and the Adam optimization method. We also built a DCR dataset, which can serve as a convenient tool for other scholars to perform further research.

In this study, a visual and microwave dual-modality intelligent damage detection method for curved RAMs is proposed for the first time; it improves the detection accuracy over existing methods and realizes real-time detection and can be used to further improve the detection of damage and maintenance efficiency for stealth equipment and reduce the need for human resources.

Funding

National Natural Science Foundation of China (11805277, 12075319, 51975583); China Postdoctoral Science Foundation (BX2019); Basic Research Project of Natural Science in Shaanxi Province (2019JQ-266).

Acknowledgments

We thank the National Natural Science Foundation, the China Postdoctoral Science Foundation and the Basic Research Project of Natural Science in Shaanxi Province for the financial support.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. S. Lu, J. Huang, L Song, and M. Yi, “A study on zoning coating method of absorbing materials for stealth aircraft,” Optik 208, 163912 (2020). [CrossRef]  

2. W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62, 33–36 (1974). [CrossRef]  

3. L. Wu, H. Yu, and L. Song, “An on-site measurement technique of radar absorbing coatings,” Development and Application of Materials. 26, 56–62 (2011).

4. Z. Chen and A. Adhyapak, “A study of the low-frequency coaxial reflectometer measurement procedure for evaluation of RF absorbers’ reflectivity,” inIEEE 2016 Antenna Measurement Techniques Association Symposium (2016), pp. 1–5.

5. Z. Wang, Y. Liu, X. Wang, T. Zhang, Y. Li, and Y. Huo, “Application of infrared thermography in research of radar absorbing coating defects,” J. Aero. Mat. 32, 91–95 (2012). [CrossRef]  

6. B. Duan, “Research on defect detection technology of radar absorbing coating based on sherography,” (University of Electronic Science and Technology of China, 2018).

7. K. Han, M. Sun, X. Zhou, G. Zhang, H. Dang, and Z. Liu, “A new method in wheel hub surface defect detection: object detection algorithm based on deep learning,” inIEEE 2017 International Conference on Advanced Mechatronic Systems (2017) pp. 335–338.

8. S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: towards real-time object detection with region proposal networks,” IEEE Trans. Pattern Anal. Mach. Intell. 391137–1149 (2017). [CrossRef]  

9. C. V. Dung and L. D. Anh, “Autonomous concrete crack detection using deep fully convolutional neural network,” Autom. Constr. 99, 52–58 (2019). [CrossRef]  

10. J. H. Feng, H. Yuan, Y. Q. Hu, J. Lin, S. W. Liu, and X. Luo, “Research on deep learning method for rail surface defect detection,” IET Electr. Syst. Transp. 10, 436–442 (2020). [CrossRef]  

11. D. Tabernik, S. Ela, J. Skvar, and D. Skoaj, “Segmentation-based deep-learning approach for surface-defect detection,” J. Intell. Manuf. 31, 759–776 (2020). [CrossRef]  

12. X. Zhuge and G. A. Yarovoy, “A sparse aperture MIMO-SAR-based UWB imaging system for concealed weapon detection,” IEEE Trans. Geosci. Remote Sensing 49, 509–518 (2011). [CrossRef]  

13. X. Yang, Y. R. Zheng, M. T. Ghasr, and K. M. Donnell, “Microwave imaging from sparse measurements for near-field synthetic aperture radar,” IEEE Trans. Instrum. Meas. 66, 2680–2692 (2017). [CrossRef]  

14. H. Wang, S. Wu, and G. Fang, “Fast near-field two-dimensional imaging algorithm based on sparse MIMO array,” Antennas Wirel. Propag. Lett. 43, 40–45 (2020). [CrossRef]  

15. S. L. Sun, G. F. Zhu, and T. Jin, “Novel methods to accelerate CS radar imaging by NUFFT,” IEEE Trans. Geosci. Remote Sensing 53, 557–566 (2015). [CrossRef]  

16. C. D. Austin, E. Ertin, and R. L. Moses, “Sparse signal methods for 3-D radar imaging,” IEEE J. Sel. Top. Signal Process. 5, 408–423 (2011). [CrossRef]  

17. Z. Yang and Y. R. Zheng, “A comparative study of compressed sensing approaches for 3-D synthetic aperture radar image reconstruction,” Digit. Signal Process. 32, 24–33 (2014). [CrossRef]  

18. A. Bochkovskiy, C. Y. Wang, and H. Y. M. Liao, “YOLOv4: optimal speed and accuracy of object detection,” arXiv:2004.10934 (2020).

19. D. S. Touretzky, M. Mozer, and M. E. Hasselmo, eds. Advances in Neural Information Processing Systems 8 (NIPS 1995), (MIT Press, 2000).

20. W. Liu, D. Anguelov, D. Erhan, C. Szegedy, and A. C. Berg, “SSD: single shot multibox detector,” in European Conference on Computer Vision (2016), pp. 31–37.

21. J. Redmon and A. Farhadi, “YOLO9000: better, faster, stronger,” in IEEE Conference on Computer Vision and Pattern Recognition (2017) pp. 6517–6525.

22. J. Redmon and A. Farhadi, “YOLOv3: an incremental improvement,” arXiv:1804.02767 (2018).

23. K. He, G. Gkioxari, D. Piotr, and R. Girshick, “Mask R-CNN,” in IEEE Transactions on Pattern Analysis & Machine Intelligence (2017), pp. 2961–2969.

24. P. Purkait, C. Zhao, and C. Zach, “SPP-net: deep absolute pose regression with synthetic views,” arXiv:1712.03452 (2017).

25. D. Misra, “Mish: a self regularized non-monotonic activation function,” arXiv:1908.08681 (2019).

26. C. Y. Wang, H. Y. M. Liao, Y. H. Wu, P. Y. Chen, and I. H. Yeh, “CSPNet: a new backbone that can enhance learning capability of CNN,” in 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) (2020), pp. 1571–1580.

27. S. Liu, L. Qi, H. Qin, J. Shi, and J. Jia, “Path aggregation network for instance segmentation,” in IEEE 2018 Conference on Computer Vision and Pattern Recognition (2018), pp. 8759–8768.

References

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  • |

  1. S. Lu, J. Huang, L Song, and M. Yi, “A study on zoning coating method of absorbing materials for stealth aircraft,” Optik 208, 163912 (2020).
    [Crossref]
  2. W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62, 33–36 (1974).
    [Crossref]
  3. L. Wu, H. Yu, and L. Song, “An on-site measurement technique of radar absorbing coatings,” Development and Application of Materials. 26, 56–62 (2011).
  4. Z. Chen and A. Adhyapak, “A study of the low-frequency coaxial reflectometer measurement procedure for evaluation of RF absorbers’ reflectivity,” inIEEE 2016 Antenna Measurement Techniques Association Symposium (2016), pp. 1–5.
  5. Z. Wang, Y. Liu, X. Wang, T. Zhang, Y. Li, and Y. Huo, “Application of infrared thermography in research of radar absorbing coating defects,” J. Aero. Mat. 32, 91–95 (2012).
    [Crossref]
  6. B. Duan, “Research on defect detection technology of radar absorbing coating based on sherography,” (University of Electronic Science and Technology of China, 2018).
  7. K. Han, M. Sun, X. Zhou, G. Zhang, H. Dang, and Z. Liu, “A new method in wheel hub surface defect detection: object detection algorithm based on deep learning,” inIEEE 2017 International Conference on Advanced Mechatronic Systems (2017) pp. 335–338.
  8. S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: towards real-time object detection with region proposal networks,” IEEE Trans. Pattern Anal. Mach. Intell. 391137–1149 (2017).
    [Crossref]
  9. C. V. Dung and L. D. Anh, “Autonomous concrete crack detection using deep fully convolutional neural network,” Autom. Constr. 99, 52–58 (2019).
    [Crossref]
  10. J. H. Feng, H. Yuan, Y. Q. Hu, J. Lin, S. W. Liu, and X. Luo, “Research on deep learning method for rail surface defect detection,” IET Electr. Syst. Transp. 10, 436–442 (2020).
    [Crossref]
  11. D. Tabernik, S. Ela, J. Skvar, and D. Skoaj, “Segmentation-based deep-learning approach for surface-defect detection,” J. Intell. Manuf. 31, 759–776 (2020).
    [Crossref]
  12. X. Zhuge and G. A. Yarovoy, “A sparse aperture MIMO-SAR-based UWB imaging system for concealed weapon detection,” IEEE Trans. Geosci. Remote Sensing 49, 509–518 (2011).
    [Crossref]
  13. X. Yang, Y. R. Zheng, M. T. Ghasr, and K. M. Donnell, “Microwave imaging from sparse measurements for near-field synthetic aperture radar,” IEEE Trans. Instrum. Meas. 66, 2680–2692 (2017).
    [Crossref]
  14. H. Wang, S. Wu, and G. Fang, “Fast near-field two-dimensional imaging algorithm based on sparse MIMO array,” Antennas Wirel. Propag. Lett. 43, 40–45 (2020).
    [Crossref]
  15. S. L. Sun, G. F. Zhu, and T. Jin, “Novel methods to accelerate CS radar imaging by NUFFT,” IEEE Trans. Geosci. Remote Sensing 53, 557–566 (2015).
    [Crossref]
  16. C. D. Austin, E. Ertin, and R. L. Moses, “Sparse signal methods for 3-D radar imaging,” IEEE J. Sel. Top. Signal Process. 5, 408–423 (2011).
    [Crossref]
  17. Z. Yang and Y. R. Zheng, “A comparative study of compressed sensing approaches for 3-D synthetic aperture radar image reconstruction,” Digit. Signal Process. 32, 24–33 (2014).
    [Crossref]
  18. A. Bochkovskiy, C. Y. Wang, and H. Y. M. Liao, “YOLOv4: optimal speed and accuracy of object detection,” arXiv:2004.10934 (2020).
  19. D. S. Touretzky, M. Mozer, and M. E. Hasselmo, eds. Advances in Neural Information Processing Systems 8 (NIPS 1995), (MIT Press, 2000).
  20. W. Liu, D. Anguelov, D. Erhan, C. Szegedy, and A. C. Berg, “SSD: single shot multibox detector,” in European Conference on Computer Vision (2016), pp. 31–37.
  21. J. Redmon and A. Farhadi, “YOLO9000: better, faster, stronger,” in IEEE Conference on Computer Vision and Pattern Recognition (2017) pp. 6517–6525.
  22. J. Redmon and A. Farhadi, “YOLOv3: an incremental improvement,” arXiv:1804.02767 (2018).
  23. K. He, G. Gkioxari, D. Piotr, and R. Girshick, “Mask R-CNN,” in IEEE Transactions on Pattern Analysis & Machine Intelligence (2017), pp. 2961–2969.
  24. P. Purkait, C. Zhao, and C. Zach, “SPP-net: deep absolute pose regression with synthetic views,” arXiv:1712.03452 (2017).
  25. D. Misra, “Mish: a self regularized non-monotonic activation function,” arXiv:1908.08681 (2019).
  26. C. Y. Wang, H. Y. M. Liao, Y. H. Wu, P. Y. Chen, and I. H. Yeh, “CSPNet: a new backbone that can enhance learning capability of CNN,” in 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) (2020), pp. 1571–1580.
  27. S. Liu, L. Qi, H. Qin, J. Shi, and J. Jia, “Path aggregation network for instance segmentation,” in IEEE 2018 Conference on Computer Vision and Pattern Recognition (2018), pp. 8759–8768.

2020 (4)

S. Lu, J. Huang, L Song, and M. Yi, “A study on zoning coating method of absorbing materials for stealth aircraft,” Optik 208, 163912 (2020).
[Crossref]

J. H. Feng, H. Yuan, Y. Q. Hu, J. Lin, S. W. Liu, and X. Luo, “Research on deep learning method for rail surface defect detection,” IET Electr. Syst. Transp. 10, 436–442 (2020).
[Crossref]

D. Tabernik, S. Ela, J. Skvar, and D. Skoaj, “Segmentation-based deep-learning approach for surface-defect detection,” J. Intell. Manuf. 31, 759–776 (2020).
[Crossref]

H. Wang, S. Wu, and G. Fang, “Fast near-field two-dimensional imaging algorithm based on sparse MIMO array,” Antennas Wirel. Propag. Lett. 43, 40–45 (2020).
[Crossref]

2019 (1)

C. V. Dung and L. D. Anh, “Autonomous concrete crack detection using deep fully convolutional neural network,” Autom. Constr. 99, 52–58 (2019).
[Crossref]

2017 (2)

S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: towards real-time object detection with region proposal networks,” IEEE Trans. Pattern Anal. Mach. Intell. 391137–1149 (2017).
[Crossref]

X. Yang, Y. R. Zheng, M. T. Ghasr, and K. M. Donnell, “Microwave imaging from sparse measurements for near-field synthetic aperture radar,” IEEE Trans. Instrum. Meas. 66, 2680–2692 (2017).
[Crossref]

2015 (1)

S. L. Sun, G. F. Zhu, and T. Jin, “Novel methods to accelerate CS radar imaging by NUFFT,” IEEE Trans. Geosci. Remote Sensing 53, 557–566 (2015).
[Crossref]

2014 (1)

Z. Yang and Y. R. Zheng, “A comparative study of compressed sensing approaches for 3-D synthetic aperture radar image reconstruction,” Digit. Signal Process. 32, 24–33 (2014).
[Crossref]

2012 (1)

Z. Wang, Y. Liu, X. Wang, T. Zhang, Y. Li, and Y. Huo, “Application of infrared thermography in research of radar absorbing coating defects,” J. Aero. Mat. 32, 91–95 (2012).
[Crossref]

2011 (3)

L. Wu, H. Yu, and L. Song, “An on-site measurement technique of radar absorbing coatings,” Development and Application of Materials. 26, 56–62 (2011).

X. Zhuge and G. A. Yarovoy, “A sparse aperture MIMO-SAR-based UWB imaging system for concealed weapon detection,” IEEE Trans. Geosci. Remote Sensing 49, 509–518 (2011).
[Crossref]

C. D. Austin, E. Ertin, and R. L. Moses, “Sparse signal methods for 3-D radar imaging,” IEEE J. Sel. Top. Signal Process. 5, 408–423 (2011).
[Crossref]

1974 (1)

W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62, 33–36 (1974).
[Crossref]

Adhyapak, A.

Z. Chen and A. Adhyapak, “A study of the low-frequency coaxial reflectometer measurement procedure for evaluation of RF absorbers’ reflectivity,” inIEEE 2016 Antenna Measurement Techniques Association Symposium (2016), pp. 1–5.

Anguelov, D.

W. Liu, D. Anguelov, D. Erhan, C. Szegedy, and A. C. Berg, “SSD: single shot multibox detector,” in European Conference on Computer Vision (2016), pp. 31–37.

Anh, L. D.

C. V. Dung and L. D. Anh, “Autonomous concrete crack detection using deep fully convolutional neural network,” Autom. Constr. 99, 52–58 (2019).
[Crossref]

Austin, C. D.

C. D. Austin, E. Ertin, and R. L. Moses, “Sparse signal methods for 3-D radar imaging,” IEEE J. Sel. Top. Signal Process. 5, 408–423 (2011).
[Crossref]

Berg, A. C.

W. Liu, D. Anguelov, D. Erhan, C. Szegedy, and A. C. Berg, “SSD: single shot multibox detector,” in European Conference on Computer Vision (2016), pp. 31–37.

Bochkovskiy, A.

A. Bochkovskiy, C. Y. Wang, and H. Y. M. Liao, “YOLOv4: optimal speed and accuracy of object detection,” arXiv:2004.10934 (2020).

Chen, P. Y.

C. Y. Wang, H. Y. M. Liao, Y. H. Wu, P. Y. Chen, and I. H. Yeh, “CSPNet: a new backbone that can enhance learning capability of CNN,” in 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) (2020), pp. 1571–1580.

Chen, Z.

Z. Chen and A. Adhyapak, “A study of the low-frequency coaxial reflectometer measurement procedure for evaluation of RF absorbers’ reflectivity,” inIEEE 2016 Antenna Measurement Techniques Association Symposium (2016), pp. 1–5.

Dang, H.

K. Han, M. Sun, X. Zhou, G. Zhang, H. Dang, and Z. Liu, “A new method in wheel hub surface defect detection: object detection algorithm based on deep learning,” inIEEE 2017 International Conference on Advanced Mechatronic Systems (2017) pp. 335–338.

Donnell, K. M.

X. Yang, Y. R. Zheng, M. T. Ghasr, and K. M. Donnell, “Microwave imaging from sparse measurements for near-field synthetic aperture radar,” IEEE Trans. Instrum. Meas. 66, 2680–2692 (2017).
[Crossref]

Duan, B.

B. Duan, “Research on defect detection technology of radar absorbing coating based on sherography,” (University of Electronic Science and Technology of China, 2018).

Dung, C. V.

C. V. Dung and L. D. Anh, “Autonomous concrete crack detection using deep fully convolutional neural network,” Autom. Constr. 99, 52–58 (2019).
[Crossref]

Ela, S.

D. Tabernik, S. Ela, J. Skvar, and D. Skoaj, “Segmentation-based deep-learning approach for surface-defect detection,” J. Intell. Manuf. 31, 759–776 (2020).
[Crossref]

Erhan, D.

W. Liu, D. Anguelov, D. Erhan, C. Szegedy, and A. C. Berg, “SSD: single shot multibox detector,” in European Conference on Computer Vision (2016), pp. 31–37.

Ertin, E.

C. D. Austin, E. Ertin, and R. L. Moses, “Sparse signal methods for 3-D radar imaging,” IEEE J. Sel. Top. Signal Process. 5, 408–423 (2011).
[Crossref]

Fang, G.

H. Wang, S. Wu, and G. Fang, “Fast near-field two-dimensional imaging algorithm based on sparse MIMO array,” Antennas Wirel. Propag. Lett. 43, 40–45 (2020).
[Crossref]

Farhadi, A.

J. Redmon and A. Farhadi, “YOLO9000: better, faster, stronger,” in IEEE Conference on Computer Vision and Pattern Recognition (2017) pp. 6517–6525.

J. Redmon and A. Farhadi, “YOLOv3: an incremental improvement,” arXiv:1804.02767 (2018).

Feng, J. H.

J. H. Feng, H. Yuan, Y. Q. Hu, J. Lin, S. W. Liu, and X. Luo, “Research on deep learning method for rail surface defect detection,” IET Electr. Syst. Transp. 10, 436–442 (2020).
[Crossref]

Ghasr, M. T.

X. Yang, Y. R. Zheng, M. T. Ghasr, and K. M. Donnell, “Microwave imaging from sparse measurements for near-field synthetic aperture radar,” IEEE Trans. Instrum. Meas. 66, 2680–2692 (2017).
[Crossref]

Girshick, R.

S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: towards real-time object detection with region proposal networks,” IEEE Trans. Pattern Anal. Mach. Intell. 391137–1149 (2017).
[Crossref]

K. He, G. Gkioxari, D. Piotr, and R. Girshick, “Mask R-CNN,” in IEEE Transactions on Pattern Analysis & Machine Intelligence (2017), pp. 2961–2969.

Gkioxari, G.

K. He, G. Gkioxari, D. Piotr, and R. Girshick, “Mask R-CNN,” in IEEE Transactions on Pattern Analysis & Machine Intelligence (2017), pp. 2961–2969.

Han, K.

K. Han, M. Sun, X. Zhou, G. Zhang, H. Dang, and Z. Liu, “A new method in wheel hub surface defect detection: object detection algorithm based on deep learning,” inIEEE 2017 International Conference on Advanced Mechatronic Systems (2017) pp. 335–338.

He, K.

S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: towards real-time object detection with region proposal networks,” IEEE Trans. Pattern Anal. Mach. Intell. 391137–1149 (2017).
[Crossref]

K. He, G. Gkioxari, D. Piotr, and R. Girshick, “Mask R-CNN,” in IEEE Transactions on Pattern Analysis & Machine Intelligence (2017), pp. 2961–2969.

Hu, Y. Q.

J. H. Feng, H. Yuan, Y. Q. Hu, J. Lin, S. W. Liu, and X. Luo, “Research on deep learning method for rail surface defect detection,” IET Electr. Syst. Transp. 10, 436–442 (2020).
[Crossref]

Huang, J.

S. Lu, J. Huang, L Song, and M. Yi, “A study on zoning coating method of absorbing materials for stealth aircraft,” Optik 208, 163912 (2020).
[Crossref]

Huo, Y.

Z. Wang, Y. Liu, X. Wang, T. Zhang, Y. Li, and Y. Huo, “Application of infrared thermography in research of radar absorbing coating defects,” J. Aero. Mat. 32, 91–95 (2012).
[Crossref]

Jia, J.

S. Liu, L. Qi, H. Qin, J. Shi, and J. Jia, “Path aggregation network for instance segmentation,” in IEEE 2018 Conference on Computer Vision and Pattern Recognition (2018), pp. 8759–8768.

Jin, T.

S. L. Sun, G. F. Zhu, and T. Jin, “Novel methods to accelerate CS radar imaging by NUFFT,” IEEE Trans. Geosci. Remote Sensing 53, 557–566 (2015).
[Crossref]

Li, Y.

Z. Wang, Y. Liu, X. Wang, T. Zhang, Y. Li, and Y. Huo, “Application of infrared thermography in research of radar absorbing coating defects,” J. Aero. Mat. 32, 91–95 (2012).
[Crossref]

Liao, H. Y. M.

A. Bochkovskiy, C. Y. Wang, and H. Y. M. Liao, “YOLOv4: optimal speed and accuracy of object detection,” arXiv:2004.10934 (2020).

C. Y. Wang, H. Y. M. Liao, Y. H. Wu, P. Y. Chen, and I. H. Yeh, “CSPNet: a new backbone that can enhance learning capability of CNN,” in 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) (2020), pp. 1571–1580.

Lin, J.

J. H. Feng, H. Yuan, Y. Q. Hu, J. Lin, S. W. Liu, and X. Luo, “Research on deep learning method for rail surface defect detection,” IET Electr. Syst. Transp. 10, 436–442 (2020).
[Crossref]

Liu, S.

S. Liu, L. Qi, H. Qin, J. Shi, and J. Jia, “Path aggregation network for instance segmentation,” in IEEE 2018 Conference on Computer Vision and Pattern Recognition (2018), pp. 8759–8768.

Liu, S. W.

J. H. Feng, H. Yuan, Y. Q. Hu, J. Lin, S. W. Liu, and X. Luo, “Research on deep learning method for rail surface defect detection,” IET Electr. Syst. Transp. 10, 436–442 (2020).
[Crossref]

Liu, W.

W. Liu, D. Anguelov, D. Erhan, C. Szegedy, and A. C. Berg, “SSD: single shot multibox detector,” in European Conference on Computer Vision (2016), pp. 31–37.

Liu, Y.

Z. Wang, Y. Liu, X. Wang, T. Zhang, Y. Li, and Y. Huo, “Application of infrared thermography in research of radar absorbing coating defects,” J. Aero. Mat. 32, 91–95 (2012).
[Crossref]

Liu, Z.

K. Han, M. Sun, X. Zhou, G. Zhang, H. Dang, and Z. Liu, “A new method in wheel hub surface defect detection: object detection algorithm based on deep learning,” inIEEE 2017 International Conference on Advanced Mechatronic Systems (2017) pp. 335–338.

Lu, S.

S. Lu, J. Huang, L Song, and M. Yi, “A study on zoning coating method of absorbing materials for stealth aircraft,” Optik 208, 163912 (2020).
[Crossref]

Luo, X.

J. H. Feng, H. Yuan, Y. Q. Hu, J. Lin, S. W. Liu, and X. Luo, “Research on deep learning method for rail surface defect detection,” IET Electr. Syst. Transp. 10, 436–442 (2020).
[Crossref]

Misra, D.

D. Misra, “Mish: a self regularized non-monotonic activation function,” arXiv:1908.08681 (2019).

Moses, R. L.

C. D. Austin, E. Ertin, and R. L. Moses, “Sparse signal methods for 3-D radar imaging,” IEEE J. Sel. Top. Signal Process. 5, 408–423 (2011).
[Crossref]

Piotr, D.

K. He, G. Gkioxari, D. Piotr, and R. Girshick, “Mask R-CNN,” in IEEE Transactions on Pattern Analysis & Machine Intelligence (2017), pp. 2961–2969.

Purkait, P.

P. Purkait, C. Zhao, and C. Zach, “SPP-net: deep absolute pose regression with synthetic views,” arXiv:1712.03452 (2017).

Qi, L.

S. Liu, L. Qi, H. Qin, J. Shi, and J. Jia, “Path aggregation network for instance segmentation,” in IEEE 2018 Conference on Computer Vision and Pattern Recognition (2018), pp. 8759–8768.

Qin, H.

S. Liu, L. Qi, H. Qin, J. Shi, and J. Jia, “Path aggregation network for instance segmentation,” in IEEE 2018 Conference on Computer Vision and Pattern Recognition (2018), pp. 8759–8768.

Redmon, J.

J. Redmon and A. Farhadi, “YOLOv3: an incremental improvement,” arXiv:1804.02767 (2018).

J. Redmon and A. Farhadi, “YOLO9000: better, faster, stronger,” in IEEE Conference on Computer Vision and Pattern Recognition (2017) pp. 6517–6525.

Ren, S.

S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: towards real-time object detection with region proposal networks,” IEEE Trans. Pattern Anal. Mach. Intell. 391137–1149 (2017).
[Crossref]

Shi, J.

S. Liu, L. Qi, H. Qin, J. Shi, and J. Jia, “Path aggregation network for instance segmentation,” in IEEE 2018 Conference on Computer Vision and Pattern Recognition (2018), pp. 8759–8768.

Skoaj, D.

D. Tabernik, S. Ela, J. Skvar, and D. Skoaj, “Segmentation-based deep-learning approach for surface-defect detection,” J. Intell. Manuf. 31, 759–776 (2020).
[Crossref]

Skvar, J.

D. Tabernik, S. Ela, J. Skvar, and D. Skoaj, “Segmentation-based deep-learning approach for surface-defect detection,” J. Intell. Manuf. 31, 759–776 (2020).
[Crossref]

Song, L

S. Lu, J. Huang, L Song, and M. Yi, “A study on zoning coating method of absorbing materials for stealth aircraft,” Optik 208, 163912 (2020).
[Crossref]

Song, L.

L. Wu, H. Yu, and L. Song, “An on-site measurement technique of radar absorbing coatings,” Development and Application of Materials. 26, 56–62 (2011).

Sun, J.

S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: towards real-time object detection with region proposal networks,” IEEE Trans. Pattern Anal. Mach. Intell. 391137–1149 (2017).
[Crossref]

Sun, M.

K. Han, M. Sun, X. Zhou, G. Zhang, H. Dang, and Z. Liu, “A new method in wheel hub surface defect detection: object detection algorithm based on deep learning,” inIEEE 2017 International Conference on Advanced Mechatronic Systems (2017) pp. 335–338.

Sun, S. L.

S. L. Sun, G. F. Zhu, and T. Jin, “Novel methods to accelerate CS radar imaging by NUFFT,” IEEE Trans. Geosci. Remote Sensing 53, 557–566 (2015).
[Crossref]

Szegedy, C.

W. Liu, D. Anguelov, D. Erhan, C. Szegedy, and A. C. Berg, “SSD: single shot multibox detector,” in European Conference on Computer Vision (2016), pp. 31–37.

Tabernik, D.

D. Tabernik, S. Ela, J. Skvar, and D. Skoaj, “Segmentation-based deep-learning approach for surface-defect detection,” J. Intell. Manuf. 31, 759–776 (2020).
[Crossref]

Wang, C. Y.

A. Bochkovskiy, C. Y. Wang, and H. Y. M. Liao, “YOLOv4: optimal speed and accuracy of object detection,” arXiv:2004.10934 (2020).

C. Y. Wang, H. Y. M. Liao, Y. H. Wu, P. Y. Chen, and I. H. Yeh, “CSPNet: a new backbone that can enhance learning capability of CNN,” in 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) (2020), pp. 1571–1580.

Wang, H.

H. Wang, S. Wu, and G. Fang, “Fast near-field two-dimensional imaging algorithm based on sparse MIMO array,” Antennas Wirel. Propag. Lett. 43, 40–45 (2020).
[Crossref]

Wang, X.

Z. Wang, Y. Liu, X. Wang, T. Zhang, Y. Li, and Y. Huo, “Application of infrared thermography in research of radar absorbing coating defects,” J. Aero. Mat. 32, 91–95 (2012).
[Crossref]

Wang, Z.

Z. Wang, Y. Liu, X. Wang, T. Zhang, Y. Li, and Y. Huo, “Application of infrared thermography in research of radar absorbing coating defects,” J. Aero. Mat. 32, 91–95 (2012).
[Crossref]

Weir, W. B.

W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62, 33–36 (1974).
[Crossref]

Wu, L.

L. Wu, H. Yu, and L. Song, “An on-site measurement technique of radar absorbing coatings,” Development and Application of Materials. 26, 56–62 (2011).

Wu, S.

H. Wang, S. Wu, and G. Fang, “Fast near-field two-dimensional imaging algorithm based on sparse MIMO array,” Antennas Wirel. Propag. Lett. 43, 40–45 (2020).
[Crossref]

Wu, Y. H.

C. Y. Wang, H. Y. M. Liao, Y. H. Wu, P. Y. Chen, and I. H. Yeh, “CSPNet: a new backbone that can enhance learning capability of CNN,” in 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) (2020), pp. 1571–1580.

Yang, X.

X. Yang, Y. R. Zheng, M. T. Ghasr, and K. M. Donnell, “Microwave imaging from sparse measurements for near-field synthetic aperture radar,” IEEE Trans. Instrum. Meas. 66, 2680–2692 (2017).
[Crossref]

Yang, Z.

Z. Yang and Y. R. Zheng, “A comparative study of compressed sensing approaches for 3-D synthetic aperture radar image reconstruction,” Digit. Signal Process. 32, 24–33 (2014).
[Crossref]

Yarovoy, G. A.

X. Zhuge and G. A. Yarovoy, “A sparse aperture MIMO-SAR-based UWB imaging system for concealed weapon detection,” IEEE Trans. Geosci. Remote Sensing 49, 509–518 (2011).
[Crossref]

Yeh, I. H.

C. Y. Wang, H. Y. M. Liao, Y. H. Wu, P. Y. Chen, and I. H. Yeh, “CSPNet: a new backbone that can enhance learning capability of CNN,” in 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) (2020), pp. 1571–1580.

Yi, M.

S. Lu, J. Huang, L Song, and M. Yi, “A study on zoning coating method of absorbing materials for stealth aircraft,” Optik 208, 163912 (2020).
[Crossref]

Yu, H.

L. Wu, H. Yu, and L. Song, “An on-site measurement technique of radar absorbing coatings,” Development and Application of Materials. 26, 56–62 (2011).

Yuan, H.

J. H. Feng, H. Yuan, Y. Q. Hu, J. Lin, S. W. Liu, and X. Luo, “Research on deep learning method for rail surface defect detection,” IET Electr. Syst. Transp. 10, 436–442 (2020).
[Crossref]

Zach, C.

P. Purkait, C. Zhao, and C. Zach, “SPP-net: deep absolute pose regression with synthetic views,” arXiv:1712.03452 (2017).

Zhang, G.

K. Han, M. Sun, X. Zhou, G. Zhang, H. Dang, and Z. Liu, “A new method in wheel hub surface defect detection: object detection algorithm based on deep learning,” inIEEE 2017 International Conference on Advanced Mechatronic Systems (2017) pp. 335–338.

Zhang, T.

Z. Wang, Y. Liu, X. Wang, T. Zhang, Y. Li, and Y. Huo, “Application of infrared thermography in research of radar absorbing coating defects,” J. Aero. Mat. 32, 91–95 (2012).
[Crossref]

Zhao, C.

P. Purkait, C. Zhao, and C. Zach, “SPP-net: deep absolute pose regression with synthetic views,” arXiv:1712.03452 (2017).

Zheng, Y. R.

X. Yang, Y. R. Zheng, M. T. Ghasr, and K. M. Donnell, “Microwave imaging from sparse measurements for near-field synthetic aperture radar,” IEEE Trans. Instrum. Meas. 66, 2680–2692 (2017).
[Crossref]

Z. Yang and Y. R. Zheng, “A comparative study of compressed sensing approaches for 3-D synthetic aperture radar image reconstruction,” Digit. Signal Process. 32, 24–33 (2014).
[Crossref]

Zhou, X.

K. Han, M. Sun, X. Zhou, G. Zhang, H. Dang, and Z. Liu, “A new method in wheel hub surface defect detection: object detection algorithm based on deep learning,” inIEEE 2017 International Conference on Advanced Mechatronic Systems (2017) pp. 335–338.

Zhu, G. F.

S. L. Sun, G. F. Zhu, and T. Jin, “Novel methods to accelerate CS radar imaging by NUFFT,” IEEE Trans. Geosci. Remote Sensing 53, 557–566 (2015).
[Crossref]

Zhuge, X.

X. Zhuge and G. A. Yarovoy, “A sparse aperture MIMO-SAR-based UWB imaging system for concealed weapon detection,” IEEE Trans. Geosci. Remote Sensing 49, 509–518 (2011).
[Crossref]

Antennas Wirel. Propag. Lett. (1)

H. Wang, S. Wu, and G. Fang, “Fast near-field two-dimensional imaging algorithm based on sparse MIMO array,” Antennas Wirel. Propag. Lett. 43, 40–45 (2020).
[Crossref]

Autom. Constr. (1)

C. V. Dung and L. D. Anh, “Autonomous concrete crack detection using deep fully convolutional neural network,” Autom. Constr. 99, 52–58 (2019).
[Crossref]

Development and Application of Materials. (1)

L. Wu, H. Yu, and L. Song, “An on-site measurement technique of radar absorbing coatings,” Development and Application of Materials. 26, 56–62 (2011).

Digit. Signal Process. (1)

Z. Yang and Y. R. Zheng, “A comparative study of compressed sensing approaches for 3-D synthetic aperture radar image reconstruction,” Digit. Signal Process. 32, 24–33 (2014).
[Crossref]

IEEE J. Sel. Top. Signal Process. (1)

C. D. Austin, E. Ertin, and R. L. Moses, “Sparse signal methods for 3-D radar imaging,” IEEE J. Sel. Top. Signal Process. 5, 408–423 (2011).
[Crossref]

IEEE Trans. Geosci. Remote Sensing (2)

S. L. Sun, G. F. Zhu, and T. Jin, “Novel methods to accelerate CS radar imaging by NUFFT,” IEEE Trans. Geosci. Remote Sensing 53, 557–566 (2015).
[Crossref]

X. Zhuge and G. A. Yarovoy, “A sparse aperture MIMO-SAR-based UWB imaging system for concealed weapon detection,” IEEE Trans. Geosci. Remote Sensing 49, 509–518 (2011).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

X. Yang, Y. R. Zheng, M. T. Ghasr, and K. M. Donnell, “Microwave imaging from sparse measurements for near-field synthetic aperture radar,” IEEE Trans. Instrum. Meas. 66, 2680–2692 (2017).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. Ren, K. He, R. Girshick, and J. Sun, “Faster R-CNN: towards real-time object detection with region proposal networks,” IEEE Trans. Pattern Anal. Mach. Intell. 391137–1149 (2017).
[Crossref]

IET Electr. Syst. Transp. (1)

J. H. Feng, H. Yuan, Y. Q. Hu, J. Lin, S. W. Liu, and X. Luo, “Research on deep learning method for rail surface defect detection,” IET Electr. Syst. Transp. 10, 436–442 (2020).
[Crossref]

J. Aero. Mat. (1)

Z. Wang, Y. Liu, X. Wang, T. Zhang, Y. Li, and Y. Huo, “Application of infrared thermography in research of radar absorbing coating defects,” J. Aero. Mat. 32, 91–95 (2012).
[Crossref]

J. Intell. Manuf. (1)

D. Tabernik, S. Ela, J. Skvar, and D. Skoaj, “Segmentation-based deep-learning approach for surface-defect detection,” J. Intell. Manuf. 31, 759–776 (2020).
[Crossref]

Optik (1)

S. Lu, J. Huang, L Song, and M. Yi, “A study on zoning coating method of absorbing materials for stealth aircraft,” Optik 208, 163912 (2020).
[Crossref]

Proc. IEEE (1)

W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62, 33–36 (1974).
[Crossref]

Other (13)

Z. Chen and A. Adhyapak, “A study of the low-frequency coaxial reflectometer measurement procedure for evaluation of RF absorbers’ reflectivity,” inIEEE 2016 Antenna Measurement Techniques Association Symposium (2016), pp. 1–5.

B. Duan, “Research on defect detection technology of radar absorbing coating based on sherography,” (University of Electronic Science and Technology of China, 2018).

K. Han, M. Sun, X. Zhou, G. Zhang, H. Dang, and Z. Liu, “A new method in wheel hub surface defect detection: object detection algorithm based on deep learning,” inIEEE 2017 International Conference on Advanced Mechatronic Systems (2017) pp. 335–338.

A. Bochkovskiy, C. Y. Wang, and H. Y. M. Liao, “YOLOv4: optimal speed and accuracy of object detection,” arXiv:2004.10934 (2020).

D. S. Touretzky, M. Mozer, and M. E. Hasselmo, eds. Advances in Neural Information Processing Systems 8 (NIPS 1995), (MIT Press, 2000).

W. Liu, D. Anguelov, D. Erhan, C. Szegedy, and A. C. Berg, “SSD: single shot multibox detector,” in European Conference on Computer Vision (2016), pp. 31–37.

J. Redmon and A. Farhadi, “YOLO9000: better, faster, stronger,” in IEEE Conference on Computer Vision and Pattern Recognition (2017) pp. 6517–6525.

J. Redmon and A. Farhadi, “YOLOv3: an incremental improvement,” arXiv:1804.02767 (2018).

K. He, G. Gkioxari, D. Piotr, and R. Girshick, “Mask R-CNN,” in IEEE Transactions on Pattern Analysis & Machine Intelligence (2017), pp. 2961–2969.

P. Purkait, C. Zhao, and C. Zach, “SPP-net: deep absolute pose regression with synthetic views,” arXiv:1712.03452 (2017).

D. Misra, “Mish: a self regularized non-monotonic activation function,” arXiv:1908.08681 (2019).

C. Y. Wang, H. Y. M. Liao, Y. H. Wu, P. Y. Chen, and I. H. Yeh, “CSPNet: a new backbone that can enhance learning capability of CNN,” in 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) (2020), pp. 1571–1580.

S. Liu, L. Qi, H. Qin, J. Shi, and J. Jia, “Path aggregation network for instance segmentation,” in IEEE 2018 Conference on Computer Vision and Pattern Recognition (2018), pp. 8759–8768.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (10)

Fig. 1.
Fig. 1. Correspondence between the dictionary matrix and the RMA forward/inverse transformations.
Fig. 2.
Fig. 2. Flow chart for microwave imaging based on the RMA imaging operator and FGG-NUFFT.
Fig. 3.
Fig. 3. Microwave images of damage on curved RAMs. (a) Compressed sensing microwave imaging method based on explicit dictionary matrix. (b) Microwave imaging method based on RMA imaging operator and FGG-NUFFT.
Fig. 4.
Fig. 4. DCR dataset.
Fig. 5.
Fig. 5. Mosaic data augmentation.
Fig. 6.
Fig. 6. Illustration of the proposed VMFNet architecture.
Fig. 7.
Fig. 7. Illustration of the CSPNet block architecture.
Fig. 8.
Fig. 8. Illustration of the Max pooling operation.
Fig. 9.
Fig. 9. Illustration of the Concat architecture.
Fig. 10.
Fig. 10. Some prediction examples from VMFNet on the DCR dataset. (a) Visual images. (b) Microwave images. (c) Ground truth. (d) VMFNet using only visual images. (e) VMFNet using only microwave images. (f) VMFNet using both visual and microwave images.

Tables (8)

Tables Icon

Table 1. Comparison of Imaging Performance of Different Methods

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Table 2. Algorithm Flow of BN

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Table 3. VisNet Architecture

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Table 4. MicNet Architecture

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Table 5. VMFNet Damage Detection Accuracy Under Different Activation Functions

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Table 6. VMFNet Damage Detection Accuracy Under Different Learning Rate Adjustment Methods

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Table 7. VMFNet Damage Detection Accuracy Under Different model Optimization Methods

Tables Icon

Table 8. Results of Comparative Experiments

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

g = F 3 D 1 { H { F 2 D ( S ) E } } = A 1 S ,
g = F 2 D , k x , k y 1 { { F N U , k z 1 { F 2 D , x , y ( S ) } } E } = A _ 1 S .
S = F 2 D , x , y 1 { { F N U , z { F 2 D , k x , k y ( g ) } } E } = A _ g ,
A _ = F 2 D , x , y 1 { { F N U , z { F 2 D , k x , k y ( ) } } E } = F 2 D , x , y 1 × ( F N U , z × ( F 2 D , k x , k y E ) ) ,
F 2 D = F 1 D X F 1 D Y ,
F 1 D X = 1 M [ 1 1 1 1 1 f f 2 f ( M 1 ) 1 f 2 f 4 f 2 ( M 1 ) 1 f ( M 1 ) f 2 ( M 1 ) f ( M 1 ) ( M 1 ) ] ,
{ E = e ¯ [ 1 1 1 ] 1 × ( N M L ) e ¯ = [ e ( 1 , 1 ) H e ( 1 , 2 ) H e ( 1 , n ) H e ( 1 , N ) H e ( M , 1 ) H e ( M , 2 ) H e ( M , n ) H e ( M , N ) H ] ,
e = [ e x p ( j k z z 0 ) ] M N L ,
F N U = 1 L [ 1 1 1 1 1 f n u f n u 2 f n u L 1 1 f n u 2 f n u 4 f n u 2 ( L 1 ) 1 f n u L 1 f n u 2 ( L 1 ) f n u ( L 1 ) ( L 1 ) ] ,
F ( k ) = 1 N i = 0 N 1 f i e j k x i , k = M 2 , , M 2 1 ,
f ( x ) = i = 0 N 1 f i δ ( x x i ) .
g η ( x ) = l = e ( x 2 l π ) 2 / 4 η .
f η ( x ) = f ( x ) g η ( x ) = 0 2 π f ( s ) g n ( x s ) d s .
F η ( k ) m = 0 M r 1 f η ( 2 π m / M r ) e j k 2 π m / M r ,
f η ( 2 π m / M r ) = i = 0 N 1 f i g η ( 2 π m / M r x i ) = i = 0 N 1 f i l = e ( x i 2 π m / M r 2 l π ) 2 / 4 η .
f n [ m + m ] f n [ m + m ] + f i e ( x i 2 π m / M r 2 π m / M r ) / 4 η ,
{ F 2 D F 2 D H = I F 2 D 1 ( F 2 D 1 ) H = I F N U F N U H = I
E E H = d i a g ( e 1 , e 2 , , e M N L × P Q T )
A _ A _ H = F 2 D 1 F N U E F 2 D ( F 2 D 1 F N U E F 2 D ) H = F 2 D 1 ( F N U ( E ( F 2 D F 2 D H ) E H ) F N U H ) ( F 2 D 1 ) H = d i a g ( e 1 , e 2 , , e M N L × P Q T )
f ( g ) = 1 2 S A _ g 2 2 + λ g 1 .
f ( g ) = 1 2 S A _ g 2 2 + λ g 1 = k = 1 m [ 1 2 ( g 0 ( k ) g ( k ) ) 2 + λ | g ( k ) | ] .
TCR = ( 1 / N t ) ( x , y , z ) D t | I ( x , y , z ) | 2 ( 1 / N c ) ( x , y , z ) D c | I ( x , y , z ) | 2 ,
M i s h = x tanh ( ln ( 1 + e x ) ) .