Abstract

Recently, compressive sensing has been introduced to confocal Raman imaging to accelerate data acquisition. In particular, unsupervised compressive imaging methods do not require a priori knowledge of an object’s spectral signatures, and they are thus applicable to unknown or dynamically changing systems. However, the current methods based on either spatial or spectral undersampling struggle between spatial and spectral fidelities at high compression ratios. By exciting a sample with an array of focused laser beams and randomly interleaving the projection locations of the scattering, we simultaneously demonstrate a single-acquisition confocal Raman hyperspectral imaging with a high fidelity and resolution in spatial and spectral domains, at a compression ratio of 40–50. The proposed method is also demonstrated with suppressed noise and a smooth transition at the boundaries.

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

1. INTRODUCTION

Raman spectroscopy is an analytical approach to detect molecules by probing the intrinsic vibrational modes of their chemical bonds. Owing to its label-free and nondestructive features, Raman spectroscopy has been widely used in drug screening, medical diagnosis, material characterization, and environmental monitoring [15]. When combined with laser scanning microscopy, the resulting confocal Raman imaging provides label-free and spatially resolved molecular distributions in cells, tissues, and organs [68]. However, the cross section of a spontaneous Raman scattering is exceedingly small and thus requires a long integration time, which significantly lowers its throughput when using a conventional raster scanning scheme. This drawback is amplified in a light-dose sensitive scenario, such as the imaging of living biological samples or nanostructured materials [4], in which a prolonged illumination with a high laser power can produce photodamage effects.

Many studies have attempted to improve the throughput of confocal Raman microscopy. One strategy is to parallelize excitation and detection by projecting the scattering from an array of foci into multiple spectral channels [813]. Compressive sensing is another strategy that has attracted significant attention in recent years, as it reduces data storage in addition to speeding up spectral acquisition [1420]. The success of compressive detection relies on the fact that a Raman spectrum usually contains only a few chemical signatures or eigenspectra, and a small number of well-designed measurements are sufficient to capture them. Although supervised compressive imaging methods that utilize these signatures a priori have been successful, they fail in scenarios where eigenspectra are unattainable in advance or dynamically changing. For this reason, unsupervised compressive Raman imaging has been receiving increasing interest [17,2124]. To date, unsupervised methods primarily undersample an object in either the spectral or spatial domain and reconstruct the hyperspectral image by solving an ill-conditioned inverse problem under minimized total variation (TV) constraints [17,22]. However, the implementation of a digital micromirror device (DMD) coded by a binary pattern for random spectral or spatial filtering always turns off half of the pixels, thereby sacrificing half of the already-starved photon budget. Moreover, these methods struggle between spatial and spectral fidelities at high compression ratios.

This study proposes an unsupervised compressive confocal Raman imaging method that allows a high-throughput data acquisition and a highly accurate hyperspectral reconstruction. Termed the scattering interleaved Raman imaging (SIRI) method, it excites a sample with an array of foci, randomly interleaves the scattering projection positions at the entrance of an imaging spectrometer, and then compresses multiple coded spectra into single spectral acquisition channels. SIRI randomly displaces the Raman spectra of adjacent foci that would otherwise be smeared on a detector because of their spectral similarities, which is crucial for an unambiguous and high-fidelity hyperspectral reconstruction. Unlike undersampling compression sensing, SIRI collects all photons. Moreover, by incorporating a Hessian regularization into the hyperspectral image reconstruction, the proposed method is demonstrated with noise suppression, smooth boundary transition, and high resolution and fidelity in both the spectral and spatial domains.

2. MATERIALS AND METHODS

A. Working Principle of SIRI

In SIRI, an object is excited by a two-dimensional (2D) array of focused laser beams. The array is generated in a time-shared manner by rapidly steering a beam with a pair of galvo mirrors [GM1 and GM2 in Fig. 1(a)] [9]. During a single spectral acquisition, the focused laser beam is rapidly scanned over the object several times, which allows the accumulation of sufficient Raman photons, while mitigating photodamage effects. When staircase waveforms (${{\rm V}_1}$, ${{\rm V}_2}$) of a constant step size are applied, the array samples the object uniformly [see Fig. 1(a)]. The descanned Raman scattering from the focus array is then rescanned by a second pair of galvo mirrors (GMx, GMy). When projection waveforms (${{\rm V}_x}$, ${{\rm V}_y}$) with changing step sizes are applied, these galvo mirrors randomly project the scattering onto the entrance of an imaging spectrometer. In more detail, the projected positions of the Raman scattering are still organized in a 2D array at the entrance plane; however, the horizontally projected coordinates of the foci in the same rows are randomly swapped with each other by the projection pattern as shown in Fig. 1(a). Inside the spectrometer, the Raman scattering is dispersed by the grating, and the signals arriving at the detector are encoded by both the wavenumber and the projection pattern. In this way, the Raman spectra from the same row foci are recorded in the same spectral channels, which significantly improves the data acquisition throughput. The Raman scattering recorded by an array detector, such as a charge-coupled device (CCD), exhibits a number of evenly spaced spectral stripes as long as the space is larger than the width of the stripes (see the experimental results below). After binning each stripe, a number of superimposed spectra are obtained, each consisting of randomly translated spectra of all foci in the same row.

 figure: Fig. 1.

Fig. 1. Principle of SIRI compressive Raman imaging. (a) Focus array generation and randomized Raman scattering projection via synchronized beam steering. (b) Image formation and reconstruction in SIRI. Note, the detection of a 3D data cube with a 2D detector results in a compression ratio of ${N_x}$.

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The image formation process can be modeled as shown in Fig. 1(b) and is described in more detail in the Supplement 1. In brief, the spectra $\boldsymbol{y}$ obtained from multiple spectral stripes (or spectral channels) can be mathematically written as

$$\boldsymbol{y} = \boldsymbol{CSPu}= \boldsymbol{Ku}{\rm ,}$$
where $\boldsymbol{u}$ is the 3D hyperspectral data cube of ${N_x} \times {N_y} \times {N_\lambda}$ dimensions, $\boldsymbol{P}$ represents the random projection of the Raman scattering at the entrance plane of the spectrometer, $\boldsymbol{S}$ is a shearing operator because of the grating dispersion, and $\boldsymbol{C}$ is a compression operator representing the CCD integration. The operator $\boldsymbol{K}$ represents a successive application of the operators $\boldsymbol{P}$, $\boldsymbol{S}$, and $\boldsymbol{C}$.

B. Hyperspectral Image Reconstruction

The reconstruction of the data cube solves the inverse problem in Eq. (1), which is converted into the following optimization problem:

$$\boldsymbol{{\hat u}} = \arg {\min}_{\boldsymbol{u}} \frac{1}{2}\left\| {\boldsymbol{y - Ku}} \right\|_2^2 + \gamma \phi (\boldsymbol{u}),$$
where $\phi (\boldsymbol{u})$ is a function that regularizes the data cube’s continuity along the spatial and/or spectral dimensions. In this study, we use two different regularization functions, TV and Hessian penalty (HP), which explore the sparsity in first- and second-order gradient spaces, respectively. The TV function is defined as
$${\phi _{{\rm TV}}}(\boldsymbol{u}) = \sum\limits_{i = 1,j = 1,k = 1}^{i = {N_x},j = {N_y},k = {N_\lambda}} {\sqrt {\left({{\nabla _x}\boldsymbol{u}} \right)_{i,j,k}^2 + \left({{\nabla _y}\boldsymbol{u}} \right)_{i,j,k}^2 + \left({\sigma {\nabla _\lambda}\boldsymbol{u}} \right)_{i,j,k}^2}} ,$$
where ${\nabla _x},{\nabla _y},{\nabla _\lambda}$ are the first-order differentiation operators defined along the $x$, $y$, and $\lambda$ dimensions, respectively, and $\sigma$ is a parameter to tune the continuity along the wavelength dimension. Constraints are imposed only on the spatial dimension if $\sigma$ is zero. The HP in this study is defined as follows [25]:
$$\begin{split}{\phi _{{\rm HP}}}(\boldsymbol{u}) &= {\left\| {{\nabla _{\textit{xx}}}\boldsymbol{u}} \right\|_1} + {\left\| {{\nabla _{\textit{yy}}}\boldsymbol{u}} \right\|_1} + {\left\| {\sigma {\nabla _{\lambda \lambda}}\boldsymbol{u}} \right\|_1} + {\left\| {2{\nabla _{\textit{xy}}}\boldsymbol{u}} \right\|_1} \\&\quad+ {\left\| {2\sqrt \sigma {\nabla _{{x\lambda}}}\boldsymbol{u}} \right\|_1} + {\left\| {2\sqrt \sigma {\nabla _{{y\lambda}}}\boldsymbol{u}} \right\|_1}\\ &= \sum\limits_{i = 1,j = 1,k = 1}^{i = {N_x},j = {N_y},k = {N_\lambda}} {\left(\vphantom{{\left| {{{\left({2\sqrt \sigma {\nabla _{{x\lambda}}}\boldsymbol{u}} \right)}_{i,j,k}}} \right| + \left| {{{\left({2\sqrt \sigma {\nabla _{{y\lambda}}}\boldsymbol{u}} \right)}_{i,j,k}}} \right|}}{\left| {{{\left({{\nabla _{\textit{xx}}}\boldsymbol{u}} \right)}_{i,j,k}}} \right|+ } \right.\left| {{{\left({{\nabla _{\textit{yy}}}\boldsymbol{u}} \right)}_{i,j,k}}} \right| }\\&\quad+ {\left| {{{\left({\sigma {\nabla _{\lambda \lambda}}\boldsymbol{u}} \right)}_{i,j,k}}} \right| + \left| {{{\left({2{\nabla _{\textit{xy}}}\boldsymbol{u}} \right)}_{i,j,k}}} \right|} \\ &\quad+ \left. {\left| {{{\left({2\sqrt \sigma {\nabla _{{x\lambda}}}\boldsymbol{u}} \right)}_{i,j,k}}} \right| + \left| {{{\left({2\sqrt \sigma {\nabla _{{y\lambda}}}\boldsymbol{u}} \right)}_{i,j,k}}} \right|} \right),\end{split}$$
where ${\nabla _{\textit{xx}}},{\nabla _{\textit{yy}}},{\nabla _{\lambda \lambda}},{\nabla _{\textit{xy}}},{\nabla _{{x\lambda}}},{\nabla _{{y\lambda}}}$ are the second-order differentiation operators. Again, $\sigma$ is used to adjust the continuity along the $\lambda$ direction. The unconstrained optimization problem in Eq. (2) is solved by a two-step iterative shrinkage/thresholding (TwIST) algorithm [26] as detailed in the Supplement 1.

C. Fidelity of Hyperspectral Image Reconstruction

There are several methods to characterize the fidelity of a hyperspectral image reconstruction. Spatial fidelity is defined by the mean squared error in the spatial domain as follows:

$${{\rm MSE}_{{\rm spatial}}} = \frac{1}{{{N_x} \times {N_y}}}{\sum\limits_{i,j,m} {\left({{{\boldsymbol{{\hat u}}}_{i,j,{k_m}}} - {\boldsymbol{u}_{i,j,{k_m}}}} \right)} ^2},$$
where ${k_m}$ is the index of the wavenumber, where a band is used to generate the Raman image. The summation is performed over all spatial pixels and Raman bands. Spectral fidelity is characterized in two ways. One of them is the spectral similarity between the reconstructed and true spectra, which is evaluated by the correlation coefficient $r$ as follows:
$${r_{i,j}} = \frac{{{{\left({{{\boldsymbol{{\hat u}}}_{i,j}} - {{\boldsymbol{{\bar {\hat u}}}}_{i,j}}} \right)}^T} \cdot \left({{\boldsymbol{u}_{i,j}} - {{\boldsymbol{{\bar u}}}_{i,j}}} \right)}}{{\sqrt {{{\left({{{\boldsymbol{{\hat u}}}_{i,j}} - {{{\boldsymbol{ \bar {\hat u}}}}_{i,j}}} \right)}^T} \cdot \left({{{\boldsymbol{{\hat u}}}_{i,j}} - {{\boldsymbol{{\bar{ \hat u}}}}_{i,j}}} \right) \times {{\left({{\boldsymbol{u}_{i,j}} - {{\boldsymbol{{\bar u}}}_{i,j}}} \right)}^T} \cdot \left({{\boldsymbol{u}_{i,j}} - {{\boldsymbol{{\bar u}}}_{i,j}}} \right)}}},$$
where ${\boldsymbol{u}_{i,j}}$ is the true spectrum at the spatial pixel ($i,\;j$), $\boldsymbol{\hat u}_{i,j}$ is the reconstructed spectrum at the corresponding pixel, and ${{\boldsymbol{ \bar u}}_{i,j}}$ and ${\boldsymbol{{\bar{ \hat u}}}_{i,j}}$ are their corresponding mean values. The correlation coefficients are suitable for characterizing spectral distortions, especially in the band locations, line shapes, and linewidths. However, they do not consider the changes in the absolute Raman scattering intensities. Another way to characterize spectral fidelity is through the mean squared error in the spectral domain, which is expressed as follows:
$${{\rm MSE}_{{\rm spectral}}} = \frac{1}{{{N_\lambda}}}{\sum\limits_{m,k} {\left({{{\boldsymbol{{\hat u}}}_{{i_m},{j_m},k}} - {\boldsymbol{u}_{{i_m},{j_m},k}}} \right)} ^2},$$
where (${i_m}$, ${j_m}$) are the indices of the $m$th spatial pixel where the spectrum is evaluated. Usually, the pixels are selected at locations with specific molecular distributions. Moreover, we define the overall fidelity of the reconstructed data cube as
$${{\rm MSE}_{{\rm overall}}} = \frac{1}{{{N_x} \times {N_y} \times {N_\lambda}}}{\sum\limits_{i,j,k} {\left({{{\boldsymbol{{\hat u}}}_{i,j,k}} - {\boldsymbol{u}_{i,j,k}}} \right)} ^2}.$$

D. Materials

The materials used to demonstrate the SIRI method are monodisperse polystyrene (PS) microspheres with a mean diameter of 4 µm (Wuxi Ruige Technology Co., Ltd., China) and industry-graded polypropylene (PP) powder (Zhonglian Plastic Chemical Industry Co., Ltd., China).

E. Optical Setup

The Raman excitation source was provided by a volume-holographic-grating-stabilized single-frequency laser diode at 785 nm (LD785-SEV300, Thorlabs). The collimated laser beam was filtered by a laser line filter (LL01-785-12.5, Semrock) and focused onto a sample by a high-numerical-aperture (high-NA) objective (${100} \times$ oil-immersed, NA of 1.3, RMS100X-PFO, Olympus). The Raman scattering was separated from the excitation beam by a dichroic mirror (LPD02-785RU-25, Semrock) prior to being introduced to a homemade imaging spectrometer. The spectrometer adopted a Czerny–Turner configuration and was equipped with a sensitive CCD camera (PIXIS 400BR, Princeton Instrument) as detailed in Supplement 1. In the compressive hyperspectral imaging mode, the spectrometer slit was widely opened (${\sim}{5}\;{\rm mm}$), such that the scatterings at all projection locations could be collected. Two pairs of galvo mirrors (GVS002, Thorlabs) were respectively used for the focus array generation and Raman scattering projection.

3. RESULTS AND DISCUSSION

A. Numerical Simulations

We first demonstrate the capability of our compressive Raman spectral imaging method using a numerical simulation. We assume the object under investigation consists of three types of molecules, and their spatial distribution produces flower-like structures as shown in Fig. 2(a) by different colors. The Raman spectrum of each type of molecule contains a number of Lorentzian-line-shaped bands, with their locations, widths, and heights being randomly assigned [see the black curves in Figs. 2(e) and 2(g)]. The Raman image of the object is acquired by following the procedure in the Methods section. We assume that within the camera integration time, the object sees a time-averaged laser beam array with ${50} \times {50}$ foci, and the spectrum excited at each focus has 1024 pixels along the wavenumber dimension. This way, we obtain a Raman hyperspectral image with dimensions of ${50} \times {50} \times {1024}$. According to our compressive imaging scheme, the 3D data cube is first randomly permutated in the $x$ dimension (see Fig. S1(b)), sheared along the $\lambda$ dimension by 6 pixels per focus, and finally summed along the $x$ dimension, resulting in a 2D compressed hyperspectral image with dimensions of ${50} \times {1024}$ as shown in Fig. 2(b). Therefore, the compression ratio is 50. A Gaussian noise is then added to yield a signal-to-noise ratio of 100.

 figure: Fig. 2.

Fig. 2. Numerical simulation of the SIRI compressive Raman imaging. (a) Object containing three types of molecules represented by different colors. (b) Compressed hyperspectral image using randomly interleaved scattering projection. (c) Superimposed spectrum in the spectral channel indicated by the dashed line in (b) under randomized (red) and continuous (black) scattering projections. (d) Reconstructed Raman image using Hessian regularization. (e) Spectra reconstructed using Hessian regularization at the pixels indicated by the dots in (d) as well as their ground truth (black curves). The baselines are shifted for display purposes only. (f), (g) Same as (d) and (e), but using TV regularization. The regularization parameter used here is $\gamma = {1} \times {{10}^{- 2}}$, and the spectral smoothness parameter is $\sigma = {0.05}$. The images are color-coded by the intensities of the bands at 179 (blue), 554 (green), and ${1298}\;{{\rm cm}^{- 1}}$ (red), respectively. The brightness of different channels is scaled by these bands’ peak intensities in the true spectra. Notably, although random noises are not shown in the ground truth, they are present in the synthetic hyperspectrum with a SNR of 100.

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 figure: Fig. 3.

Fig. 3. Reconstruction accuracy of simulated hyperspectral image using Hessian penalty under different regularization parameters. (a) Correlation coefficients between the reconstructed and true spectra of the three types of molecules as functions of $\gamma$. (b) Spatial, spectral, and overall mean squared errors at different values of $\gamma$.

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Each row of the compressed hyperspectral image is a superimposed spectrum of 50 foci in the same row. For example, the intensity profile along the dashed line in Fig. 2(b) represents the superimposed spectrum of the foci along the dashed line in Fig. 2(a). The spectra from adjacent foci are usually similar because of a continuity in the molecular distribution. Under a continuous projection with unmodulated scattering, the shearing and integration operations on the data cube smear the Raman bands in the spectra of different foci. As shown by the black curve in Fig. 2(c), the narrow bands in the spectrum of molecule 2 are smeared into broad bands. In contrast, the projection positions of scattering are randomly interleaved in SIRI. The spectra from the adjacent foci in the same rows are no longer adjacent to the CCD, but it is highly possible that they are spaced by distances large enough to avoid smearing, as evidenced by several narrow peaks in the superimposed spectrum [red curve in Fig. 2(c)]. The randomized scattering projection significantly compresses the solution space to the inverse problem in Eq. (1), as the presence of narrow peaks in the mixed spectra ensures their existence in the spectra of the individual foci, which is not guaranteed if the bands are smeared into wide distributions. Searching for an estimate of the hyperspectral image in a compressed subspace removes ambiguity and allows a high spectral resolution and fidelity.

To recover the 3D data cube from the compressed 2D image, we solve the inverse problem in Eq. (2) using a TwIST algorithm [26], which involves a denoising subproblem and a two-step iterative update, as detailed in the Supplement 1. Reconstruction of the hyperspectrum on a standard laptop with one 1.8 GHz dual-core processor (Intel, Xeon) takes approximately 1 h; this speed can be improved using graphics processing unit (GPU) computing. Figures 2(d) and 2(f) show the reconstructed Raman images encoded by the band intensities at 179 (blue), 554 (green), and ${1298}\;{{\rm cm}^{- 1}}$ (red). These bands correspond to the three types of molecules as indicated by the arrows in Fig. 2(e). As can be seen, the SIRI method with both Hessian and TV regularizations perfectly recovers the object’s flower-like structures. A drawback of TV regularization is that it oversharpens the boundaries, resulting in staircase-like transitions [see Fig. 2(f)]. This is because the TV regularization searches for a solution to the inverse problem in Eq. (1) with maximum sparsity in the gradient space, that is, a solution with piecewise smoothness. In contrast to the TV regularization, the Hessian regularization penalizes the second-order differentiation and thus maximizes the sparsity in linear ramps, yielding smooth transitions at the boundaries [see Fig. 2(d)]. It is counterintuitive that replacing the first-order differentiation with the second-order differentiation in the regularization function will not compromise the spatial resolution. In contrast, the region indicated by arrows in Figs. 2(d) and 2(f) is resolved better by the Hessian regularization.

In addition to high spatial fidelity, SIRI provides a high spectral fidelity. The spectra of the three types of molecules are extracted at spatial pixels #1, #2, and #3 as labeled by the dots in Figs. 2(d) and 2(f), which are then compared to the ground truth. As shown in Figs. 2(e) and 2(g), the spectra of all types of molecules are recovered perfectly, in terms of either band shapes or band intensities. Again, the Hessian regularization outperforms the TV regularization, as it recovers the bands at 885 and ${943}\;{{\rm cm}^{- 1}}$ in the spectrum of molecule #3 with a higher accuracy. Regardless of which regularization function is used, the perfect recovery of sharp peaks, especially the closely located peaks at 712 and ${748}\;{{\rm cm}^{- 1}}$ in the spectrum of molecule #1, suggests the high spectral resolution of SIRI.

It should be noted that the parameter $\gamma$ plays an important role in the reconstruction accuracy. A previous study using random undersampling and TV regularization suggested that a decrease in $\gamma$ improves the spatial resolution but at the expense of a reduced spectral resolution [22]. As shown in Fig. S2, a smaller regularization parameter improves the spatial resolution, which agrees with our prediction. It is interesting that SIRI with a Hessian regularization does not sacrifice the spectral resolution at a smaller $\gamma$. The closely located peaks at 712 and ${748}\;{{\rm cm}^{- 1}}$ in the spectrum of molecule #1 are always resolved well, and the overall spectral shapes are preserved at smaller $\gamma$ values. We extract the Raman spectra of the three types of molecules in the same way as mentioned above and calculate their correlation coefficients with the ground truth [Eq. (6)]. The coefficients characterize the spectral similarities, ignoring their absolute intensities. As shown in Fig. 3(a), the proposed method perfectly recovers the spectra of molecules #1 and #2, with the correlation coefficients approaching 1 for all values of $\gamma$. Although the correlation coefficient is slightly lower for molecule #3, a moderately small $\gamma$ still yields very high spectral similarities.

Despite the minor effects on spectral similarities, a varied $\gamma$ does change the absolute spectral intensities and thus affects the reconstruction fidelities. We characterize the spatial, spectral, and overall fidelities of the reconstructed hyperspectral image at different $\gamma$ values by calculating the corresponding mean squared errors as detailed in the Materials and Methods sections. As shown in Fig. 3(b), the spatial and spectral fidelities have similar tendencies at various $\gamma$ values, suggesting that the highest spatial and spectral fidelities can be obtained simultaneously. The above observations show the advantages of SIRI over the previous undersampling methods, that is, we do not have to find a trade-off between spatial fidelity and spectral fidelity [22]. It can also be seen that the spatial and spectral fidelities, and consequently the overall fidelity, increase at moderately smaller $\gamma$ values until reaching a threshold below which all of them decrease rapidly.

B. Experimental Results

We experimentally demonstrated the excellent performance of our proposed technique by imaging microplastics. A drop (5 µL) of monodisperse PS microsphere suspension (4 µm in diameter, ${4} \times {{10}^{10}}\;/{\rm mL}$ in concentration) was placed on a quartz coverslip (0.1 mm in thickness) that was sealed onto an acrylic sample chamber from the bottom. The drop was naturally dried at room temperature (25°C), leaving a film of microspheres on the slip. A cotton swab sticking PP powder was gently applied on the coverslip such that some PP particles were also adhered onto its surface. Water was then filled into the chamber prior to the imaging. Because industry-grade PP particles have irregular shapes, they can be well distinguished from the monodisperse PS microspheres under a microscope. We selected a region with the presence of both types of microplastics. As shown in the bright-field image in Fig. 4(a), there are a few PS microspheres surrounding a large PP particle. This region was excited using a ${40} \times {40}$ focused laser array. The array was generated in a time-shared manner, that is, during the exposure time of the spectral acquisition CCD, a focused laser beam was quickly scanned over the region several times, as described in Methods. Thus, during the exposure time, the object saw a “time-averaged” 2D focused array. The array had a grid size of 0.5 µm and thus covered a ${20} \times {20}\;\unicode{x00B5}{\rm m}^2$ sampling region. The dwell time at each focus was 1 ms, and the integration time of the CCD was 64 s, suggesting that each sampling point was visited by the focused laser 40 times during each exposure. The total laser power was 250 mW. In a light-dose-sensitive scenario, such as living cell imaging, a lower laser power is expected to mitigate the phototoxic effect, which requires a longer integration time and thus more laser visits to accumulate sufficient Raman photons.

 figure: Fig. 4.

Fig. 4. Experimental demonstration of the SIRI method in a single acquisition. (a) Bright-field image of microplastics. The microspheres are made of polystyrene, and the irregular object is made of polypropylene. The scale bar is 5 µm. (b) Raman scattering recorded by the spectral acquisition CCD in a single exposure. (c), (d) Raman images encoded by the intensity of the band at 1001 (c) and ${1459}\;{{\rm cm}^{- 1}}$ (d), respectively. A Hessian regularization function was used. (e) Combined image using the band intensities in (c) and (d) as the red and green channels, respectively. The brightness in the green channel had been multiplied by a factor of 4 because of the weaker Raman scattering of the PP particle. (f)–(h) Same as (c)–(e), but with TV regularization. (i), (j) Spectra of the PS and PP reconstructed using (i) Hessian and (j) TV regularizations. The spectra are extracted at the pixels indicated by the arrows in (c) and (d), respectively. The ground truth obtained by single-focus Raman is also present (black curves).

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To realize a randomized scattering projection, the galvo mirror for the horizontal projection of Raman scattering was applied with a staircase waveform of random step sizes (${-}{1.0}$ to 1.0 V) as detailed in Materials and Methods. Meanwhile, the galvo mirror for the vertical projection of Raman scattering was applied with a staircase waveform of a constant step size (90 mV) to determine the space between adjacent spectral stripes as shown below. Figure 4(b) shows the Raman scattering recorded by the spectrometer in a single exposure. As can be seen, the Raman scattering exhibited 40 well-separated spectral stripes (some were too weak to be visible), each consisting of 40 spectra from the same row foci. Thus, the compression ratio in the experimental demonstration was 40. The dot-like structures in the stripes indicated that SIRI interleaved the spectral projection, which otherwise would have smeared the Raman bands because of the spectral similarities of the adjacent foci. Breaking the continuity of spectral projection was crucial for an unambiguous and high-fidelity reconstruction as emphasized in the simulation section.

As the spectral stripes were separated by 7 pixels, we binned each stripe over 5 pixels along the vertical dimension, resulting in 40 cross-talk-free spectra. Equation (2) was then solved to retrieve the 3D hyperspectral image. Figures 4(c)–4(h) show the reconstructed Raman images encoded by the band intensities at 1001 and ${1459}\;{{\rm cm}^{- 1}}$, which are associated with the breathing mode of the aromatic carbon ring in PS and the bending mode of the ${{\rm CH}_2}$-group in PP [see Figs. 4(i) and 4(j)], respectively [27]. SIRI with Hessian and TV regularizations accurately identified these two types of microplastics. The shapes and spatial distributions of the microplastics measured by SIRI agreed well with those obtained from the bright-field imaging, although the structures too close (${\sim}{2}$ pixels) to the edges of the imaging region did not recover very well. Again, SIRI with the TV regularization resulted in over-sharpened boundaries, even at the edges of the regular microspheres [see Figs. 4(f)–4(h)]. The Hessian regularization avoided this effect and provided exceptionally smooth transitions at the edges. The smooth boundaries were not achieved at the expense of a reduced spatial resolution. The multiple microspheres stuck together could be distinguished by the Hessian regularization [Figs. 4(c) and 4(e)]; however, they were not resolved by the TV regularization [Figs. 4(f) and 4(h)]. Raman images encoded by the intensities of the other bands provided similar results (see Fig. S3). This advantage is more apparent when a higher sampling resolution is used as shown in Fig. S4, in which a ${20} \times {20}\;\unicode{x00B5}{\rm m}^2$ region is imaged with four frames, but at a sampling resolution of 0.25 µm.

We also experimentally investigated the spectral fidelity and resolution of SIRI with both Hessian and TV regularizations. We extracted the spectra of PS and PP from the reconstructed hyperspectral image at the spatial pixels indicated by the arrows in Figs. 4(c) and 4(d), respectively. The extracted spectra were then compared to the ground truth obtained at the same locations by single-focus confocal Raman spectroscopy under the same laser power and equivalent integration time (40 ms). As shown in Figs. 4(i) and 4(j), the compressive Raman imaging method accurately recovered the spectra of PS and PP, and the Hessian regularization provided a higher fidelity than the TV regularization. The closely located Raman bands of polystyrene at 1182 and ${1199}\;{{\rm cm}^{- 1}}$ could be resolved by both regularizations, demonstrating the SIRI imaging technique’s high spectral resolution. These two bands are related to the in-plane bending and stretching modes of the aromatic ring, respectively [28]. In addition to the high spectral fidelity and resolution, the reconstructed spectra had much higher SNRs than those of the ground truth, which is an additional advantage of SIRI. The improvement in SNR is not surprising. By compressing multiple spectra into one spectral channel, more Raman photons were collected, while the read noise of the CCD was the same as that of the single-focus acquisition mode.

In this study, we have experimentally demonstrated that 40 spectra from a row of foci can be recorded in one spectral channel, resulting in a 40-fold improvement in the imaging throughput and a ${40} \times$ compression ratio in the data acquisition, in comparison to the previous multiplexing schemes [912]. As a comparison, the state-of-the-art confocal-based methods usually achieve a compression ratio of ${\sim}{10} \times$ with a reasonable reconstruction fidelity [17,2124]. A compression ratio of ${80} \times$ is possible in a spectral-multiplexed detection method, but a priori knowledge is required [17]. Unsupervised compressive Raman imaging also reports a maximum compression ratio of ${64} \times$; however, the fidelity of this method drops significantly at a moderate compression ratio (${8} \times$) [24]. Methods using wide-illumination and spatial undersampling usually have higher compression ratios. For example, a compression ratio of up to ${83} \times$ has been reported in a variant of the coded aperture snapshot spectral imaging (CASSI) method [22,29]. However, these methods lose their depth-sectioning capabilities. In addition, their spectral resolution is very low, even with a large regularization parameter, at which the spatial resolution is significantly reduced [22].

Considering that 40 spectral channels were used in one CCD exposure and 40 spectra were recorded in each spectral channel, the throughput was improved by more than 3 orders of magnitude when compared to a conventional confocal Raman microscope. Obtaining a 3D data cube with the same resolution using a single-point mode requires 1600 individual acquisitions. The compression ratio in this study was primarily limited by the field of view of the homemade imaging spectrometer. The small sizes of the concave mirrors and grating reduced the light throughput when the projected scattering deviated significantly from the axis of the system; however, this can be improved in the future. The developed technique has already demonstrated single-shot Raman imaging of a ${20} \times {20}\;\unicode{x00B5}{\rm m}^2$ region with a submicrometer spatial resolution, making it a promising tool for the label-free imaging of living biological cells or tissues. However, in biomedical applications, a fluorescent background may pose some challenges to the hyperspectrum reconstruction, which is present not only in SIRI but also in other compressive Raman imaging methods. As fluorescence usually creates a broad baseline in the Raman spectrum, the regularization term in Eq. (2) produces fewer constraints. Consequently, a broad baseline may not be recovered uniquely. Fortunately, as the fluorescent background carries little molecular information, it can be removed by algorithms either prior to or posterior to the data reconstruction.

The performance of the SIRI reconstruction algorithm can be improved in several ways in the future. For example, a hyperspectrum usually exhibits a high sparsity under a wavelet transformation. Thus, incorporating the L1 norm of the wavelet coefficients into the regularization function could improve the reconstruction accuracy. Moreover, although not demonstrated in this study, SIRI adopts a confocal configuration and thus allows the depth sectioning of biological cells or tissues, provided a pinhole is placed at an intermediate plane prior to rescanning the scattering light. In this case, the ${ z}$-stacking of hyperspectra can be acquired by moving the sample along the axial direction. If a forward model is built on the 4D data (x-y-z-$\lambda$) and smoothness constraints are imposed along the ${ z}$ dimension, an improved reconstruction accuracy can also be expected from the inverse problem’s solution.

4. CONCLUSION

In summary, we proposed an unsupervised compressive technique to accelerate the data acquisition of confocal Raman hyperspectral imaging. The proposed SIRI method excites a sample with an array of focused laser beams and randomly interleaves the scattering projection positioned at the entrance of an imaging spectrometer. The multiple spectra from the same row foci are thus recorded in one spectral channel, significantly improving the data acquisition throughput. The performance of the developed technique was substantiated with both numerically simulated and experimental data, demonstrating an excellent fidelity and resolution at a high compression ratio (40–50) simultaneously in spatial and spectral domains, without any compromise between them. SIRI also exhibited excellent noise suppression performance in the reconstructed spectra. It is important to note that, because a priori knowledge about an object’s eigenspectra is not required, our developed technique does not need model training and can be implemented in any scenario, including unknown or dynamically changing systems in which supervised compressive Raman imaging methods may fail [1420]. In addition to the novel data acquisition scheme, we used a Hessian regularization function in the compressive sensing algorithm instead of a TV regularization, which is usually used in image processing and restoration [17,22]. Hyperspectral image reconstructions with both simulated and experimental data demonstrated that the Hessian regularization provides smoother transitions at the boundaries without sacrificing the spatial resolution.

Funding

National Key Research and Development Program of China (2019YFC1605500).

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.

Supplemental document

See Supplement 1 for supporting content.

REFERENCES

1. C. H. Camp Jr., Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014). [CrossRef]  

2. L. J. Livermore, M. Isabelle, I. M. Bell, C. Scott, J. Walsby-Tickle, J. Gannon, P. Plaha, C. Vallance, and O. Ansorge, “Rapid intraoperative molecular genetic classification of gliomas using Raman spectroscopy,” Neuro-Oncol. Adv. 1, vdz008 (2019). [CrossRef]  

3. Z. Farhane, F. Bonnier, A. Casey, and H. J. Byrne, “Raman micro spectroscopy for in vitro drug screening: subcellular localisation and interactions of doxorubicin,” Analyst 140, 4212–4223 (2015). [CrossRef]  

4. S. Nair, J. Gao, Q. Yao, M. H. G. Duits, C. Otto, and F. Mugele, “Algorithm-improved high-speed and non-invasive confocal Raman imaging of 2D materials,” Natl. Sci. Rev. 7, 620–628 (2019). [CrossRef]  

5. D. Schymanski, C. Goldbeck, H.-U. Humpf, and P. Fürst, “Analysis of microplastics in water by micro-Raman spectroscopy: release of plastic particles from different packaging into mineral water,” Water Res. 129, 154–162 (2018). [CrossRef]  

6. S. Keren, C. Zavaleta, Z. Cheng, A. de la Zerda, O. Gheysens, and S. S. Gambhir, “Noninvasive molecular imaging of small living subjects using Raman spectroscopy,” Proc. Natl. Acad. Sci. USA 105, 5844–5849 (2008). [CrossRef]  

7. J. W. Kang, P. T. C. So, R. R. Dasari, and D.-K. Lim, “High resolution live cell Raman imaging using subcellular organelle-targeting SERS-sensitive gold nanoparticles with highly narrow intra-nanogap,” Nano Lett. 15, 1766–1772 (2015). [CrossRef]  

8. L. Kong, P. Zhang, J. Yu, P. Setlow, and Y.-Q. Li, “Rapid confocal Raman imaging using a synchro multifoci-scan scheme for dynamic monitoring of single living cells,” Appl. Phys. Lett. 98, 213703 (2011). [CrossRef]  

9. P. Zhang, L. Kong, P. Setlow, and Y.-Q. Li, “Multiple-trap laser tweezers Raman spectroscopy for simultaneous monitoring of the biological dynamics of multiple individual cells,” Opt. Lett. 35, 3321–3323 (2010). [CrossRef]  

10. R. Liu, D. S. Taylor, D. L. Matthews, and J. W. Chan, “Parallel analysis of individual biological cells using multifocal laser tweezers Raman spectroscopy,” Appl. Spectrosc. 64, 1308–1310 (2010). [CrossRef]  

11. M. Okuno and H.-O. Hamaguchi, “Multifocus confocal Raman microspectroscopy for fast multimode vibrational imaging of living cells,” Opt. Lett. 35, 4096–4098 (2010). [CrossRef]  

12. S. Yabumoto and H.-O. Hamaguchi, “Tilted two-dimensional array multifocus confocal Raman microspectroscopy,” Anal. Chem. 89, 7291–7296 (2017). [CrossRef]  

13. H. Ji, V. Nava, Y. Yang, and J. W. Chan, “Multifocal 1064 nm Raman imaging of carbon nanotubes,” Opt. Lett. 45, 5132–5135 (2020). [CrossRef]  

14. N. Uzunbajakava, P. de Peinder, G. W’t Hoof, and A. T. M. van Gogh, “Low-cost spectroscopy with a variable multivariate optical element,” Anal. Chem. 78, 7302–7308 (2006). [CrossRef]  

15. B. M. Davis, A. J. Hemphill, D. C. Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, “Multivariate hyperspectral Raman imaging using compressive detection,” Anal. Chem. 83, 5086–5092 (2011). [CrossRef]  

16. D. S. Wilcox, G. T. Buzzard, B. J. Lucier, P. Wang, and D. Ben-Amotz, “Photon level chemical classification using digital compressive detection,” Anal. Chim. Acta 755, 17–27 (2012). [CrossRef]  

17. B. Sturm, F. Soldevila, E. Tajahuerce, S. Gigan, H. Rigneault, and H. B. de Aguiar, “High-sensitivity high-speed compressive spectrometer for Raman imaging,” ACS Photon. 6, 1409–1415 (2019). [CrossRef]  

18. C. Scotté, H. B. de Aguiar, D. Marguet, E. M. Green, P. Bouzy, S. Vergnole, C. P. Winlove, N. Stone, and H. Rigneault, “Assessment of compressive Raman versus hyperspectral Raman for microcalcification chemical imaging,” Anal. Chem. 90, 7197–7203 (2018). [CrossRef]  

19. P. Zhang, G. Wang, X. Zhang, and Y.-Q. Li, “Single-acquisition 2-D multifocal Raman spectroscopy using compressive sensing,” Anal. Chem. 92, 1326–1332 (2020). [CrossRef]  

20. P. Zhang, G. Wang, and S. Huang, “Parallel micro-Raman spectroscopy of multiple cells in a single acquisition using hierarchical sparsity,” Analyst 145, 6032–6037 (2020). [CrossRef]  

21. N. Pavillon and N. I. Smith, “Compressed sensing laser scanning microscopy,” Opt. Express 24, 30038–30052 (2016). [CrossRef]  

22. J. V. Thompson, J. N. Bixler, B. H. Hokr, G. D. Noojin, M. O. Scully, and V. V. Yakovlev, “Single-shot chemical detection and identification with compressed hyperspectral Raman imaging,” Opt. Lett. 42, 2169–2172 (2017). [CrossRef]  

23. C. Hu, X. Wang, L. Liu, C. Fu, K. Chu, and Z. J. Smith, “Fast confocal Raman imaging via context-aware compressive sensing,” Analyst 146, 2348–2357 (2021). [CrossRef]  

24. F. Soldevila, J. Dong, E. Tajahuerce, S. Gigan, and H. B. de Aguiar, “Fast compressive Raman bio-imaging via matrix completion,” Optica 6,341–346 (2019). [CrossRef]  

25. X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Nanotechnol. 36, 451–459 (2018). [CrossRef]  

26. J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007). [CrossRef]  

27. T. Furukawa, H. Sato, Y. Kita, K. Matsukawa, H. Yamaguchi, S. Ochiai, H. W. Siesler, and Y. Ozaki, “Molecular structure, crystallinity and morphology of polyethylene/polypropylene blends studied by Raman mapping, scanning electron microscopy, wide angle X-ray diffraction, and differential scanning calorimetry,” Polym. J. 38, 1127–1136 (2006). [CrossRef]  

28. L. Noda and O. Sala, “A resonance Raman investigation on the interaction of styrene and 4-methyl styrene oligomers on sulphated titanium oxide,” Spectrochim. Acta A 56, 145–155 (2000). [CrossRef]  

29. A. Wagadarikar, R. John, R. Willett, and D. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008). [CrossRef]  

References

  • View by:

  1. C. H. Camp, Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014).
    [Crossref]
  2. L. J. Livermore, M. Isabelle, I. M. Bell, C. Scott, J. Walsby-Tickle, J. Gannon, P. Plaha, C. Vallance, and O. Ansorge, “Rapid intraoperative molecular genetic classification of gliomas using Raman spectroscopy,” Neuro-Oncol. Adv. 1, vdz008 (2019).
    [Crossref]
  3. Z. Farhane, F. Bonnier, A. Casey, and H. J. Byrne, “Raman micro spectroscopy for in vitro drug screening: subcellular localisation and interactions of doxorubicin,” Analyst 140, 4212–4223 (2015).
    [Crossref]
  4. S. Nair, J. Gao, Q. Yao, M. H. G. Duits, C. Otto, and F. Mugele, “Algorithm-improved high-speed and non-invasive confocal Raman imaging of 2D materials,” Natl. Sci. Rev. 7, 620–628 (2019).
    [Crossref]
  5. D. Schymanski, C. Goldbeck, H.-U. Humpf, and P. Fürst, “Analysis of microplastics in water by micro-Raman spectroscopy: release of plastic particles from different packaging into mineral water,” Water Res. 129, 154–162 (2018).
    [Crossref]
  6. S. Keren, C. Zavaleta, Z. Cheng, A. de la Zerda, O. Gheysens, and S. S. Gambhir, “Noninvasive molecular imaging of small living subjects using Raman spectroscopy,” Proc. Natl. Acad. Sci. USA 105, 5844–5849 (2008).
    [Crossref]
  7. J. W. Kang, P. T. C. So, R. R. Dasari, and D.-K. Lim, “High resolution live cell Raman imaging using subcellular organelle-targeting SERS-sensitive gold nanoparticles with highly narrow intra-nanogap,” Nano Lett. 15, 1766–1772 (2015).
    [Crossref]
  8. L. Kong, P. Zhang, J. Yu, P. Setlow, and Y.-Q. Li, “Rapid confocal Raman imaging using a synchro multifoci-scan scheme for dynamic monitoring of single living cells,” Appl. Phys. Lett. 98, 213703 (2011).
    [Crossref]
  9. P. Zhang, L. Kong, P. Setlow, and Y.-Q. Li, “Multiple-trap laser tweezers Raman spectroscopy for simultaneous monitoring of the biological dynamics of multiple individual cells,” Opt. Lett. 35, 3321–3323 (2010).
    [Crossref]
  10. R. Liu, D. S. Taylor, D. L. Matthews, and J. W. Chan, “Parallel analysis of individual biological cells using multifocal laser tweezers Raman spectroscopy,” Appl. Spectrosc. 64, 1308–1310 (2010).
    [Crossref]
  11. M. Okuno and H.-O. Hamaguchi, “Multifocus confocal Raman microspectroscopy for fast multimode vibrational imaging of living cells,” Opt. Lett. 35, 4096–4098 (2010).
    [Crossref]
  12. S. Yabumoto and H.-O. Hamaguchi, “Tilted two-dimensional array multifocus confocal Raman microspectroscopy,” Anal. Chem. 89, 7291–7296 (2017).
    [Crossref]
  13. H. Ji, V. Nava, Y. Yang, and J. W. Chan, “Multifocal 1064 nm Raman imaging of carbon nanotubes,” Opt. Lett. 45, 5132–5135 (2020).
    [Crossref]
  14. N. Uzunbajakava, P. de Peinder, G. W’t Hoof, and A. T. M. van Gogh, “Low-cost spectroscopy with a variable multivariate optical element,” Anal. Chem. 78, 7302–7308 (2006).
    [Crossref]
  15. B. M. Davis, A. J. Hemphill, D. C. Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, “Multivariate hyperspectral Raman imaging using compressive detection,” Anal. Chem. 83, 5086–5092 (2011).
    [Crossref]
  16. D. S. Wilcox, G. T. Buzzard, B. J. Lucier, P. Wang, and D. Ben-Amotz, “Photon level chemical classification using digital compressive detection,” Anal. Chim. Acta 755, 17–27 (2012).
    [Crossref]
  17. B. Sturm, F. Soldevila, E. Tajahuerce, S. Gigan, H. Rigneault, and H. B. de Aguiar, “High-sensitivity high-speed compressive spectrometer for Raman imaging,” ACS Photon. 6, 1409–1415 (2019).
    [Crossref]
  18. C. Scotté, H. B. de Aguiar, D. Marguet, E. M. Green, P. Bouzy, S. Vergnole, C. P. Winlove, N. Stone, and H. Rigneault, “Assessment of compressive Raman versus hyperspectral Raman for microcalcification chemical imaging,” Anal. Chem. 90, 7197–7203 (2018).
    [Crossref]
  19. P. Zhang, G. Wang, X. Zhang, and Y.-Q. Li, “Single-acquisition 2-D multifocal Raman spectroscopy using compressive sensing,” Anal. Chem. 92, 1326–1332 (2020).
    [Crossref]
  20. P. Zhang, G. Wang, and S. Huang, “Parallel micro-Raman spectroscopy of multiple cells in a single acquisition using hierarchical sparsity,” Analyst 145, 6032–6037 (2020).
    [Crossref]
  21. N. Pavillon and N. I. Smith, “Compressed sensing laser scanning microscopy,” Opt. Express 24, 30038–30052 (2016).
    [Crossref]
  22. J. V. Thompson, J. N. Bixler, B. H. Hokr, G. D. Noojin, M. O. Scully, and V. V. Yakovlev, “Single-shot chemical detection and identification with compressed hyperspectral Raman imaging,” Opt. Lett. 42, 2169–2172 (2017).
    [Crossref]
  23. C. Hu, X. Wang, L. Liu, C. Fu, K. Chu, and Z. J. Smith, “Fast confocal Raman imaging via context-aware compressive sensing,” Analyst 146, 2348–2357 (2021).
    [Crossref]
  24. F. Soldevila, J. Dong, E. Tajahuerce, S. Gigan, and H. B. de Aguiar, “Fast compressive Raman bio-imaging via matrix completion,” Optica 6,341–346 (2019).
    [Crossref]
  25. X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Nanotechnol. 36, 451–459 (2018).
    [Crossref]
  26. J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).
    [Crossref]
  27. T. Furukawa, H. Sato, Y. Kita, K. Matsukawa, H. Yamaguchi, S. Ochiai, H. W. Siesler, and Y. Ozaki, “Molecular structure, crystallinity and morphology of polyethylene/polypropylene blends studied by Raman mapping, scanning electron microscopy, wide angle X-ray diffraction, and differential scanning calorimetry,” Polym. J. 38, 1127–1136 (2006).
    [Crossref]
  28. L. Noda and O. Sala, “A resonance Raman investigation on the interaction of styrene and 4-methyl styrene oligomers on sulphated titanium oxide,” Spectrochim. Acta A 56, 145–155 (2000).
    [Crossref]
  29. A. Wagadarikar, R. John, R. Willett, and D. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008).
    [Crossref]

2021 (1)

C. Hu, X. Wang, L. Liu, C. Fu, K. Chu, and Z. J. Smith, “Fast confocal Raman imaging via context-aware compressive sensing,” Analyst 146, 2348–2357 (2021).
[Crossref]

2020 (3)

P. Zhang, G. Wang, X. Zhang, and Y.-Q. Li, “Single-acquisition 2-D multifocal Raman spectroscopy using compressive sensing,” Anal. Chem. 92, 1326–1332 (2020).
[Crossref]

P. Zhang, G. Wang, and S. Huang, “Parallel micro-Raman spectroscopy of multiple cells in a single acquisition using hierarchical sparsity,” Analyst 145, 6032–6037 (2020).
[Crossref]

H. Ji, V. Nava, Y. Yang, and J. W. Chan, “Multifocal 1064 nm Raman imaging of carbon nanotubes,” Opt. Lett. 45, 5132–5135 (2020).
[Crossref]

2019 (4)

B. Sturm, F. Soldevila, E. Tajahuerce, S. Gigan, H. Rigneault, and H. B. de Aguiar, “High-sensitivity high-speed compressive spectrometer for Raman imaging,” ACS Photon. 6, 1409–1415 (2019).
[Crossref]

L. J. Livermore, M. Isabelle, I. M. Bell, C. Scott, J. Walsby-Tickle, J. Gannon, P. Plaha, C. Vallance, and O. Ansorge, “Rapid intraoperative molecular genetic classification of gliomas using Raman spectroscopy,” Neuro-Oncol. Adv. 1, vdz008 (2019).
[Crossref]

S. Nair, J. Gao, Q. Yao, M. H. G. Duits, C. Otto, and F. Mugele, “Algorithm-improved high-speed and non-invasive confocal Raman imaging of 2D materials,” Natl. Sci. Rev. 7, 620–628 (2019).
[Crossref]

F. Soldevila, J. Dong, E. Tajahuerce, S. Gigan, and H. B. de Aguiar, “Fast compressive Raman bio-imaging via matrix completion,” Optica 6,341–346 (2019).
[Crossref]

2018 (3)

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Nanotechnol. 36, 451–459 (2018).
[Crossref]

D. Schymanski, C. Goldbeck, H.-U. Humpf, and P. Fürst, “Analysis of microplastics in water by micro-Raman spectroscopy: release of plastic particles from different packaging into mineral water,” Water Res. 129, 154–162 (2018).
[Crossref]

C. Scotté, H. B. de Aguiar, D. Marguet, E. M. Green, P. Bouzy, S. Vergnole, C. P. Winlove, N. Stone, and H. Rigneault, “Assessment of compressive Raman versus hyperspectral Raman for microcalcification chemical imaging,” Anal. Chem. 90, 7197–7203 (2018).
[Crossref]

2017 (2)

2016 (1)

2015 (2)

Z. Farhane, F. Bonnier, A. Casey, and H. J. Byrne, “Raman micro spectroscopy for in vitro drug screening: subcellular localisation and interactions of doxorubicin,” Analyst 140, 4212–4223 (2015).
[Crossref]

J. W. Kang, P. T. C. So, R. R. Dasari, and D.-K. Lim, “High resolution live cell Raman imaging using subcellular organelle-targeting SERS-sensitive gold nanoparticles with highly narrow intra-nanogap,” Nano Lett. 15, 1766–1772 (2015).
[Crossref]

2014 (1)

C. H. Camp, Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014).
[Crossref]

2012 (1)

D. S. Wilcox, G. T. Buzzard, B. J. Lucier, P. Wang, and D. Ben-Amotz, “Photon level chemical classification using digital compressive detection,” Anal. Chim. Acta 755, 17–27 (2012).
[Crossref]

2011 (2)

B. M. Davis, A. J. Hemphill, D. C. Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, “Multivariate hyperspectral Raman imaging using compressive detection,” Anal. Chem. 83, 5086–5092 (2011).
[Crossref]

L. Kong, P. Zhang, J. Yu, P. Setlow, and Y.-Q. Li, “Rapid confocal Raman imaging using a synchro multifoci-scan scheme for dynamic monitoring of single living cells,” Appl. Phys. Lett. 98, 213703 (2011).
[Crossref]

2010 (3)

2008 (2)

S. Keren, C. Zavaleta, Z. Cheng, A. de la Zerda, O. Gheysens, and S. S. Gambhir, “Noninvasive molecular imaging of small living subjects using Raman spectroscopy,” Proc. Natl. Acad. Sci. USA 105, 5844–5849 (2008).
[Crossref]

A. Wagadarikar, R. John, R. Willett, and D. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008).
[Crossref]

2007 (1)

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).
[Crossref]

2006 (2)

T. Furukawa, H. Sato, Y. Kita, K. Matsukawa, H. Yamaguchi, S. Ochiai, H. W. Siesler, and Y. Ozaki, “Molecular structure, crystallinity and morphology of polyethylene/polypropylene blends studied by Raman mapping, scanning electron microscopy, wide angle X-ray diffraction, and differential scanning calorimetry,” Polym. J. 38, 1127–1136 (2006).
[Crossref]

N. Uzunbajakava, P. de Peinder, G. W’t Hoof, and A. T. M. van Gogh, “Low-cost spectroscopy with a variable multivariate optical element,” Anal. Chem. 78, 7302–7308 (2006).
[Crossref]

2000 (1)

L. Noda and O. Sala, “A resonance Raman investigation on the interaction of styrene and 4-methyl styrene oligomers on sulphated titanium oxide,” Spectrochim. Acta A 56, 145–155 (2000).
[Crossref]

Ansorge, O.

L. J. Livermore, M. Isabelle, I. M. Bell, C. Scott, J. Walsby-Tickle, J. Gannon, P. Plaha, C. Vallance, and O. Ansorge, “Rapid intraoperative molecular genetic classification of gliomas using Raman spectroscopy,” Neuro-Oncol. Adv. 1, vdz008 (2019).
[Crossref]

Bell, I. M.

L. J. Livermore, M. Isabelle, I. M. Bell, C. Scott, J. Walsby-Tickle, J. Gannon, P. Plaha, C. Vallance, and O. Ansorge, “Rapid intraoperative molecular genetic classification of gliomas using Raman spectroscopy,” Neuro-Oncol. Adv. 1, vdz008 (2019).
[Crossref]

Ben-Amotz, D.

D. S. Wilcox, G. T. Buzzard, B. J. Lucier, P. Wang, and D. Ben-Amotz, “Photon level chemical classification using digital compressive detection,” Anal. Chim. Acta 755, 17–27 (2012).
[Crossref]

B. M. Davis, A. J. Hemphill, D. C. Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, “Multivariate hyperspectral Raman imaging using compressive detection,” Anal. Chem. 83, 5086–5092 (2011).
[Crossref]

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).
[Crossref]

Bixler, J. N.

Bonnier, F.

Z. Farhane, F. Bonnier, A. Casey, and H. J. Byrne, “Raman micro spectroscopy for in vitro drug screening: subcellular localisation and interactions of doxorubicin,” Analyst 140, 4212–4223 (2015).
[Crossref]

Bouzy, P.

C. Scotté, H. B. de Aguiar, D. Marguet, E. M. Green, P. Bouzy, S. Vergnole, C. P. Winlove, N. Stone, and H. Rigneault, “Assessment of compressive Raman versus hyperspectral Raman for microcalcification chemical imaging,” Anal. Chem. 90, 7197–7203 (2018).
[Crossref]

Brady, D.

Buzzard, G. T.

D. S. Wilcox, G. T. Buzzard, B. J. Lucier, P. Wang, and D. Ben-Amotz, “Photon level chemical classification using digital compressive detection,” Anal. Chim. Acta 755, 17–27 (2012).
[Crossref]

Byrne, H. J.

Z. Farhane, F. Bonnier, A. Casey, and H. J. Byrne, “Raman micro spectroscopy for in vitro drug screening: subcellular localisation and interactions of doxorubicin,” Analyst 140, 4212–4223 (2015).
[Crossref]

Camp, C. H.

C. H. Camp, Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014).
[Crossref]

Casey, A.

Z. Farhane, F. Bonnier, A. Casey, and H. J. Byrne, “Raman micro spectroscopy for in vitro drug screening: subcellular localisation and interactions of doxorubicin,” Analyst 140, 4212–4223 (2015).
[Crossref]

Chan, J. W.

Chen, L.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Nanotechnol. 36, 451–459 (2018).
[Crossref]

Cheng, Z.

S. Keren, C. Zavaleta, Z. Cheng, A. de la Zerda, O. Gheysens, and S. S. Gambhir, “Noninvasive molecular imaging of small living subjects using Raman spectroscopy,” Proc. Natl. Acad. Sci. USA 105, 5844–5849 (2008).
[Crossref]

Chu, K.

C. Hu, X. Wang, L. Liu, C. Fu, K. Chu, and Z. J. Smith, “Fast confocal Raman imaging via context-aware compressive sensing,” Analyst 146, 2348–2357 (2021).
[Crossref]

Cicerone, M. T.

C. H. Camp, Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014).
[Crossref]

Dasari, R. R.

J. W. Kang, P. T. C. So, R. R. Dasari, and D.-K. Lim, “High resolution live cell Raman imaging using subcellular organelle-targeting SERS-sensitive gold nanoparticles with highly narrow intra-nanogap,” Nano Lett. 15, 1766–1772 (2015).
[Crossref]

Davis, B. M.

B. M. Davis, A. J. Hemphill, D. C. Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, “Multivariate hyperspectral Raman imaging using compressive detection,” Anal. Chem. 83, 5086–5092 (2011).
[Crossref]

de Aguiar, H. B.

F. Soldevila, J. Dong, E. Tajahuerce, S. Gigan, and H. B. de Aguiar, “Fast compressive Raman bio-imaging via matrix completion,” Optica 6,341–346 (2019).
[Crossref]

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C. H. Camp, Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014).
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C. H. Camp, Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014).
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X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Nanotechnol. 36, 451–459 (2018).
[Crossref]

Li, Y.-Q.

P. Zhang, G. Wang, X. Zhang, and Y.-Q. Li, “Single-acquisition 2-D multifocal Raman spectroscopy using compressive sensing,” Anal. Chem. 92, 1326–1332 (2020).
[Crossref]

L. Kong, P. Zhang, J. Yu, P. Setlow, and Y.-Q. Li, “Rapid confocal Raman imaging using a synchro multifoci-scan scheme for dynamic monitoring of single living cells,” Appl. Phys. Lett. 98, 213703 (2011).
[Crossref]

P. Zhang, L. Kong, P. Setlow, and Y.-Q. Li, “Multiple-trap laser tweezers Raman spectroscopy for simultaneous monitoring of the biological dynamics of multiple individual cells,” Opt. Lett. 35, 3321–3323 (2010).
[Crossref]

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J. W. Kang, P. T. C. So, R. R. Dasari, and D.-K. Lim, “High resolution live cell Raman imaging using subcellular organelle-targeting SERS-sensitive gold nanoparticles with highly narrow intra-nanogap,” Nano Lett. 15, 1766–1772 (2015).
[Crossref]

Liu, H.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Nanotechnol. 36, 451–459 (2018).
[Crossref]

Liu, L.

C. Hu, X. Wang, L. Liu, C. Fu, K. Chu, and Z. J. Smith, “Fast confocal Raman imaging via context-aware compressive sensing,” Analyst 146, 2348–2357 (2021).
[Crossref]

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Liu, Y.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Nanotechnol. 36, 451–459 (2018).
[Crossref]

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L. J. Livermore, M. Isabelle, I. M. Bell, C. Scott, J. Walsby-Tickle, J. Gannon, P. Plaha, C. Vallance, and O. Ansorge, “Rapid intraoperative molecular genetic classification of gliomas using Raman spectroscopy,” Neuro-Oncol. Adv. 1, vdz008 (2019).
[Crossref]

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D. S. Wilcox, G. T. Buzzard, B. J. Lucier, P. Wang, and D. Ben-Amotz, “Photon level chemical classification using digital compressive detection,” Anal. Chim. Acta 755, 17–27 (2012).
[Crossref]

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B. M. Davis, A. J. Hemphill, D. C. Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, “Multivariate hyperspectral Raman imaging using compressive detection,” Anal. Chem. 83, 5086–5092 (2011).
[Crossref]

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X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Nanotechnol. 36, 451–459 (2018).
[Crossref]

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C. Scotté, H. B. de Aguiar, D. Marguet, E. M. Green, P. Bouzy, S. Vergnole, C. P. Winlove, N. Stone, and H. Rigneault, “Assessment of compressive Raman versus hyperspectral Raman for microcalcification chemical imaging,” Anal. Chem. 90, 7197–7203 (2018).
[Crossref]

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T. Furukawa, H. Sato, Y. Kita, K. Matsukawa, H. Yamaguchi, S. Ochiai, H. W. Siesler, and Y. Ozaki, “Molecular structure, crystallinity and morphology of polyethylene/polypropylene blends studied by Raman mapping, scanning electron microscopy, wide angle X-ray diffraction, and differential scanning calorimetry,” Polym. J. 38, 1127–1136 (2006).
[Crossref]

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Mugele, F.

S. Nair, J. Gao, Q. Yao, M. H. G. Duits, C. Otto, and F. Mugele, “Algorithm-improved high-speed and non-invasive confocal Raman imaging of 2D materials,” Natl. Sci. Rev. 7, 620–628 (2019).
[Crossref]

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S. Nair, J. Gao, Q. Yao, M. H. G. Duits, C. Otto, and F. Mugele, “Algorithm-improved high-speed and non-invasive confocal Raman imaging of 2D materials,” Natl. Sci. Rev. 7, 620–628 (2019).
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Noda, L.

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Ochiai, S.

T. Furukawa, H. Sato, Y. Kita, K. Matsukawa, H. Yamaguchi, S. Ochiai, H. W. Siesler, and Y. Ozaki, “Molecular structure, crystallinity and morphology of polyethylene/polypropylene blends studied by Raman mapping, scanning electron microscopy, wide angle X-ray diffraction, and differential scanning calorimetry,” Polym. J. 38, 1127–1136 (2006).
[Crossref]

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Otto, C.

S. Nair, J. Gao, Q. Yao, M. H. G. Duits, C. Otto, and F. Mugele, “Algorithm-improved high-speed and non-invasive confocal Raman imaging of 2D materials,” Natl. Sci. Rev. 7, 620–628 (2019).
[Crossref]

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T. Furukawa, H. Sato, Y. Kita, K. Matsukawa, H. Yamaguchi, S. Ochiai, H. W. Siesler, and Y. Ozaki, “Molecular structure, crystallinity and morphology of polyethylene/polypropylene blends studied by Raman mapping, scanning electron microscopy, wide angle X-ray diffraction, and differential scanning calorimetry,” Polym. J. 38, 1127–1136 (2006).
[Crossref]

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Plaha, P.

L. J. Livermore, M. Isabelle, I. M. Bell, C. Scott, J. Walsby-Tickle, J. Gannon, P. Plaha, C. Vallance, and O. Ansorge, “Rapid intraoperative molecular genetic classification of gliomas using Raman spectroscopy,” Neuro-Oncol. Adv. 1, vdz008 (2019).
[Crossref]

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C. H. Camp, Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014).
[Crossref]

Rigneault, H.

B. Sturm, F. Soldevila, E. Tajahuerce, S. Gigan, H. Rigneault, and H. B. de Aguiar, “High-sensitivity high-speed compressive spectrometer for Raman imaging,” ACS Photon. 6, 1409–1415 (2019).
[Crossref]

C. Scotté, H. B. de Aguiar, D. Marguet, E. M. Green, P. Bouzy, S. Vergnole, C. P. Winlove, N. Stone, and H. Rigneault, “Assessment of compressive Raman versus hyperspectral Raman for microcalcification chemical imaging,” Anal. Chem. 90, 7197–7203 (2018).
[Crossref]

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L. Noda and O. Sala, “A resonance Raman investigation on the interaction of styrene and 4-methyl styrene oligomers on sulphated titanium oxide,” Spectrochim. Acta A 56, 145–155 (2000).
[Crossref]

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T. Furukawa, H. Sato, Y. Kita, K. Matsukawa, H. Yamaguchi, S. Ochiai, H. W. Siesler, and Y. Ozaki, “Molecular structure, crystallinity and morphology of polyethylene/polypropylene blends studied by Raman mapping, scanning electron microscopy, wide angle X-ray diffraction, and differential scanning calorimetry,” Polym. J. 38, 1127–1136 (2006).
[Crossref]

Schymanski, D.

D. Schymanski, C. Goldbeck, H.-U. Humpf, and P. Fürst, “Analysis of microplastics in water by micro-Raman spectroscopy: release of plastic particles from different packaging into mineral water,” Water Res. 129, 154–162 (2018).
[Crossref]

Scott, C.

L. J. Livermore, M. Isabelle, I. M. Bell, C. Scott, J. Walsby-Tickle, J. Gannon, P. Plaha, C. Vallance, and O. Ansorge, “Rapid intraoperative molecular genetic classification of gliomas using Raman spectroscopy,” Neuro-Oncol. Adv. 1, vdz008 (2019).
[Crossref]

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C. Scotté, H. B. de Aguiar, D. Marguet, E. M. Green, P. Bouzy, S. Vergnole, C. P. Winlove, N. Stone, and H. Rigneault, “Assessment of compressive Raman versus hyperspectral Raman for microcalcification chemical imaging,” Anal. Chem. 90, 7197–7203 (2018).
[Crossref]

Scully, M. O.

Setlow, P.

L. Kong, P. Zhang, J. Yu, P. Setlow, and Y.-Q. Li, “Rapid confocal Raman imaging using a synchro multifoci-scan scheme for dynamic monitoring of single living cells,” Appl. Phys. Lett. 98, 213703 (2011).
[Crossref]

P. Zhang, L. Kong, P. Setlow, and Y.-Q. Li, “Multiple-trap laser tweezers Raman spectroscopy for simultaneous monitoring of the biological dynamics of multiple individual cells,” Opt. Lett. 35, 3321–3323 (2010).
[Crossref]

Siesler, H. W.

T. Furukawa, H. Sato, Y. Kita, K. Matsukawa, H. Yamaguchi, S. Ochiai, H. W. Siesler, and Y. Ozaki, “Molecular structure, crystallinity and morphology of polyethylene/polypropylene blends studied by Raman mapping, scanning electron microscopy, wide angle X-ray diffraction, and differential scanning calorimetry,” Polym. J. 38, 1127–1136 (2006).
[Crossref]

Smith, N. I.

Smith, Z. J.

C. Hu, X. Wang, L. Liu, C. Fu, K. Chu, and Z. J. Smith, “Fast confocal Raman imaging via context-aware compressive sensing,” Analyst 146, 2348–2357 (2021).
[Crossref]

So, P. T. C.

J. W. Kang, P. T. C. So, R. R. Dasari, and D.-K. Lim, “High resolution live cell Raman imaging using subcellular organelle-targeting SERS-sensitive gold nanoparticles with highly narrow intra-nanogap,” Nano Lett. 15, 1766–1772 (2015).
[Crossref]

Soldevila, F.

F. Soldevila, J. Dong, E. Tajahuerce, S. Gigan, and H. B. de Aguiar, “Fast compressive Raman bio-imaging via matrix completion,” Optica 6,341–346 (2019).
[Crossref]

B. Sturm, F. Soldevila, E. Tajahuerce, S. Gigan, H. Rigneault, and H. B. de Aguiar, “High-sensitivity high-speed compressive spectrometer for Raman imaging,” ACS Photon. 6, 1409–1415 (2019).
[Crossref]

Stone, N.

C. Scotté, H. B. de Aguiar, D. Marguet, E. M. Green, P. Bouzy, S. Vergnole, C. P. Winlove, N. Stone, and H. Rigneault, “Assessment of compressive Raman versus hyperspectral Raman for microcalcification chemical imaging,” Anal. Chem. 90, 7197–7203 (2018).
[Crossref]

Sturm, B.

B. Sturm, F. Soldevila, E. Tajahuerce, S. Gigan, H. Rigneault, and H. B. de Aguiar, “High-sensitivity high-speed compressive spectrometer for Raman imaging,” ACS Photon. 6, 1409–1415 (2019).
[Crossref]

Tajahuerce, E.

B. Sturm, F. Soldevila, E. Tajahuerce, S. Gigan, H. Rigneault, and H. B. de Aguiar, “High-sensitivity high-speed compressive spectrometer for Raman imaging,” ACS Photon. 6, 1409–1415 (2019).
[Crossref]

F. Soldevila, J. Dong, E. Tajahuerce, S. Gigan, and H. B. de Aguiar, “Fast compressive Raman bio-imaging via matrix completion,” Optica 6,341–346 (2019).
[Crossref]

Tan, S.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Nanotechnol. 36, 451–459 (2018).
[Crossref]

Tang, L.

X. Huang, J. Fan, L. Li, H. Liu, R. Wu, Y. Wu, L. Wei, H. Mao, A. Lal, P. Xi, L. Tang, Y. Zhang, Y. Liu, S. Tan, and L. Chen, “Fast, long-term, super-resolution imaging with Hessian structured illumination microscopy,” Nat. Nanotechnol. 36, 451–459 (2018).
[Crossref]

Taylor, D. S.

Thompson, J. V.

Uzunbajakava, N.

N. Uzunbajakava, P. de Peinder, G. W’t Hoof, and A. T. M. van Gogh, “Low-cost spectroscopy with a variable multivariate optical element,” Anal. Chem. 78, 7302–7308 (2006).
[Crossref]

Vallance, C.

L. J. Livermore, M. Isabelle, I. M. Bell, C. Scott, J. Walsby-Tickle, J. Gannon, P. Plaha, C. Vallance, and O. Ansorge, “Rapid intraoperative molecular genetic classification of gliomas using Raman spectroscopy,” Neuro-Oncol. Adv. 1, vdz008 (2019).
[Crossref]

van Gogh, A. T. M.

N. Uzunbajakava, P. de Peinder, G. W’t Hoof, and A. T. M. van Gogh, “Low-cost spectroscopy with a variable multivariate optical element,” Anal. Chem. 78, 7302–7308 (2006).
[Crossref]

Vergnole, S.

C. Scotté, H. B. de Aguiar, D. Marguet, E. M. Green, P. Bouzy, S. Vergnole, C. P. Winlove, N. Stone, and H. Rigneault, “Assessment of compressive Raman versus hyperspectral Raman for microcalcification chemical imaging,” Anal. Chem. 90, 7197–7203 (2018).
[Crossref]

W’t Hoof, G.

N. Uzunbajakava, P. de Peinder, G. W’t Hoof, and A. T. M. van Gogh, “Low-cost spectroscopy with a variable multivariate optical element,” Anal. Chem. 78, 7302–7308 (2006).
[Crossref]

Wagadarikar, A.

Walker, A. R. H.

C. H. Camp, Y. J. Lee, J. M. Heddleston, C. M. Hartshorn, A. R. H. Walker, J. N. Rich, J. D. Lathia, and M. T. Cicerone, “High-speed coherent Raman fingerprint imaging of biological tissues,” Nat. Photonics 8, 627–634 (2014).
[Crossref]

Walsby-Tickle, J.

L. J. Livermore, M. Isabelle, I. M. Bell, C. Scott, J. Walsby-Tickle, J. Gannon, P. Plaha, C. Vallance, and O. Ansorge, “Rapid intraoperative molecular genetic classification of gliomas using Raman spectroscopy,” Neuro-Oncol. Adv. 1, vdz008 (2019).
[Crossref]

Wang, G.

P. Zhang, G. Wang, X. Zhang, and Y.-Q. Li, “Single-acquisition 2-D multifocal Raman spectroscopy using compressive sensing,” Anal. Chem. 92, 1326–1332 (2020).
[Crossref]

P. Zhang, G. Wang, and S. Huang, “Parallel micro-Raman spectroscopy of multiple cells in a single acquisition using hierarchical sparsity,” Analyst 145, 6032–6037 (2020).
[Crossref]

Wang, P.

D. S. Wilcox, G. T. Buzzard, B. J. Lucier, P. Wang, and D. Ben-Amotz, “Photon level chemical classification using digital compressive detection,” Anal. Chim. Acta 755, 17–27 (2012).
[Crossref]

B. M. Davis, A. J. Hemphill, D. C. Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, “Multivariate hyperspectral Raman imaging using compressive detection,” Anal. Chem. 83, 5086–5092 (2011).
[Crossref]

Wang, X.

C. Hu, X. Wang, L. Liu, C. Fu, K. Chu, and Z. J. Smith, “Fast confocal Raman imaging via context-aware compressive sensing,” Analyst 146, 2348–2357 (2021).
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Supplementary Material (1)

NameDescription
Supplement 1       supplementary method

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 (4)

Fig. 1.
Fig. 1. Principle of SIRI compressive Raman imaging. (a) Focus array generation and randomized Raman scattering projection via synchronized beam steering. (b) Image formation and reconstruction in SIRI. Note, the detection of a 3D data cube with a 2D detector results in a compression ratio of ${N_x}$.
Fig. 2.
Fig. 2. Numerical simulation of the SIRI compressive Raman imaging. (a) Object containing three types of molecules represented by different colors. (b) Compressed hyperspectral image using randomly interleaved scattering projection. (c) Superimposed spectrum in the spectral channel indicated by the dashed line in (b) under randomized (red) and continuous (black) scattering projections. (d) Reconstructed Raman image using Hessian regularization. (e) Spectra reconstructed using Hessian regularization at the pixels indicated by the dots in (d) as well as their ground truth (black curves). The baselines are shifted for display purposes only. (f), (g) Same as (d) and (e), but using TV regularization. The regularization parameter used here is $\gamma = {1} \times {{10}^{- 2}}$, and the spectral smoothness parameter is $\sigma = {0.05}$. The images are color-coded by the intensities of the bands at 179 (blue), 554 (green), and ${1298}\;{{\rm cm}^{- 1}}$ (red), respectively. The brightness of different channels is scaled by these bands’ peak intensities in the true spectra. Notably, although random noises are not shown in the ground truth, they are present in the synthetic hyperspectrum with a SNR of 100.
Fig. 3.
Fig. 3. Reconstruction accuracy of simulated hyperspectral image using Hessian penalty under different regularization parameters. (a) Correlation coefficients between the reconstructed and true spectra of the three types of molecules as functions of $\gamma$. (b) Spatial, spectral, and overall mean squared errors at different values of $\gamma$.
Fig. 4.
Fig. 4. Experimental demonstration of the SIRI method in a single acquisition. (a) Bright-field image of microplastics. The microspheres are made of polystyrene, and the irregular object is made of polypropylene. The scale bar is 5 µm. (b) Raman scattering recorded by the spectral acquisition CCD in a single exposure. (c), (d) Raman images encoded by the intensity of the band at 1001 (c) and ${1459}\;{{\rm cm}^{- 1}}$ (d), respectively. A Hessian regularization function was used. (e) Combined image using the band intensities in (c) and (d) as the red and green channels, respectively. The brightness in the green channel had been multiplied by a factor of 4 because of the weaker Raman scattering of the PP particle. (f)–(h) Same as (c)–(e), but with TV regularization. (i), (j) Spectra of the PS and PP reconstructed using (i) Hessian and (j) TV regularizations. The spectra are extracted at the pixels indicated by the arrows in (c) and (d), respectively. The ground truth obtained by single-focus Raman is also present (black curves).

Equations (8)

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y = C S P u = K u ,
u ^ = arg min u 1 2 y K u 2 2 + γ ϕ ( u ) ,
ϕ T V ( u ) = i = 1 , j = 1 , k = 1 i = N x , j = N y , k = N λ ( x u ) i , j , k 2 + ( y u ) i , j , k 2 + ( σ λ u ) i , j , k 2 ,
ϕ H P ( u ) = xx u 1 + yy u 1 + σ λ λ u 1 + 2 xy u 1 + 2 σ x λ u 1 + 2 σ y λ u 1 = i = 1 , j = 1 , k = 1 i = N x , j = N y , k = N λ ( | ( 2 σ x λ u ) i , j , k | + | ( 2 σ y λ u ) i , j , k | | ( xx u ) i , j , k | + | ( yy u ) i , j , k | + | ( σ λ λ u ) i , j , k | + | ( 2 xy u ) i , j , k | + | ( 2 σ x λ u ) i , j , k | + | ( 2 σ y λ u ) i , j , k | ) ,
M S E s p a t i a l = 1 N x × N y i , j , m ( u ^ i , j , k m u i , j , k m ) 2 ,
r i , j = ( u ^ i , j u ^ ¯ i , j ) T ( u i , j u ¯ i , j ) ( u ^ i , j u ^ ¯ i , j ) T ( u ^ i , j u ^ ¯ i , j ) × ( u i , j u ¯ i , j ) T ( u i , j u ¯ i , j ) ,
M S E s p e c t r a l = 1 N λ m , k ( u ^ i m , j m , k u i m , j m , k ) 2 ,
M S E o v e r a l l = 1 N x × N y × N λ i , j , k ( u ^ i , j , k u i , j , k ) 2 .