Abstract

In this paper, we make contact with the field of compressive sensing and present a development and generalization of tools and results for reconstructing irregularly sampled tomographic data. In particular, we focus on denoising Spectral-Domain Optical Coherence Tomography (SDOCT) volumetric data. We take advantage of customized scanning patterns, in which, a selected number of B-scans are imaged at higher signal-to-noise ratio (SNR). We learn a sparse representation dictionary for each of these high-SNR images, and utilize such dictionaries to denoise the low-SNR B-scans. We name this method multiscale sparsity based tomographic denoising (MSBTD). We show the qualitative and quantitative superiority of the MSBTD algorithm compared to popular denoising algorithms on images from normal and age-related macular degeneration eyes of a multi-center clinical trial. We have made the corresponding data set and software freely available online.

© 2012 OSA

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2012 (4)

M. A. Mayer, A. Borsdorf, M. Wagner, J. Hornegger, C. Y. Mardin, and R. P. Tornow, “Wavelet denoising of multiframe optical coherence tomography data,” Biomed. Opt. Express3(3), 572–589 (2012).
[CrossRef] [PubMed]

S. Li, L. Fang, and H. Yin, “An efficient dictionary learning algorithm and its application to 3-D medical image denoising,” IEEE Trans. Biomed. Eng.59(2), 417–427 (2012).
[CrossRef] [PubMed]

S. Li and L. Fang, “Signal denoising with random refined orthogonal matching pursuit,” IEEE Trans. Instrum. Meas.61(1), 26–34 (2012).
[CrossRef]

S. J. Chiu, J. A. Izatt, R. V. O’Connell, K. P. Winter, C. A. Toth, and S. Farsiu, “Validated automatic segmentation of AMD pathology including drusen and geographic atrophy in SD-OCT images,” Invest. Ophthalmol. Vis. Sci.53(1), 53–61 (2012).
[CrossRef] [PubMed]

2011 (7)

W. Dong, L. Zhang, G. Shi, and X. Wu, “Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization,” IEEE Trans. Image Process.20(7), 1838–1857 (2011).
[CrossRef] [PubMed]

B. Ophir, M. Lustig, and M. Elad, “Multi-scale dictionary learning using wavelets,” IEEE J. Sel. Top. Signal Process.5(5), 1014–1024 (2011).
[CrossRef]

R. Estrada, C. Tomasi, M. T. Cabrera, D. K. Wallace, S. F. Freedman, and S. Farsiu, “Enhanced video indirect ophthalmoscopy (VIO) via robust mosaicing,” Biomed. Opt. Express2(10), 2871–2887 (2011).
[CrossRef] [PubMed]

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng.50(7), 072601–072613 (2011).
[CrossRef]

M. Young, E. Lebed, Y. Jian, P. J. Mackenzie, M. F. Beg, and M. V. Sarunic, “Real-time high-speed volumetric imaging using compressive sampling optical coherence tomography,” Biomed. Opt. Express2(9), 2690–2697 (2011).
[CrossRef] [PubMed]

W. Dong, L. Zhang, and G. Shi, “Centralized sparse representation for image restoration,” Proc. IEEEICCV, 1259–1266 (2011).

P. Chatterjee and P. Milanfar, “Practical bounds on image denoising: from estimation to information,” IEEE Trans. Image Process.20(5), 1221–1233 (2011).
[CrossRef] [PubMed]

2010 (9)

A. Wong, A. Mishra, K. Bizheva, and D. A. Clausi, “General Bayesian estimation for speckle noise reduction in optical coherence tomography retinal imagery,” Opt. Express18(8), 8338–8352 (2010).
[CrossRef] [PubMed]

Z. Jian, L. Yu, B. Rao, B. J. Tromberg, and Z. Chen, “Three-dimensional speckle suppression in Optical Coherence Tomography based on the curvelet transform,” Opt. Express18(2), 1024–1032 (2010).
[CrossRef] [PubMed]

N. Mohan, I. Stojanovic, W. C. Karl, B. E. A. Saleh, and M. C. Teich, “Compressed sensing in optical coherence tomography,” Proc. SPIE7570, 75700L, 75700L-5 (2010).
[CrossRef]

X. Liu and J. U. Kang, “Compressive SD-OCT: the application of compressed sensing in spectral domain optical coherence tomography,” Opt. Express18(21), 22010–22019 (2010).
[CrossRef] [PubMed]

E. Lebed, P. J. Mackenzie, M. V. Sarunic, and M. F. Beg, “Rapid volumetric OCT image acquisition using compressive sampling,” Opt. Express18(20), 21003–21012 (2010).
[CrossRef] [PubMed]

R. Rubinstein, M. Zibulevsky, and M. Elad, “Double sparsity: learning sparse dictionaries for sparse signal approximation,” IEEE Trans. Signal Process.58(3), 1553–1564 (2010).
[CrossRef]

I. Daubechies, R. DeVore, M. Fornasier, and C. S. Gunturk, “Iteratively reweighted least squares minimization for sparse recovery,” Commun. Pure Appl. Math.63(1), 1–38 (2010).
[CrossRef]

M. D. Robinson, C. A. Toth, J. Y. Lo, and S. Farsiu, “Efficient fourier-wavelet super-resolution,” IEEE Trans. Image Process.19(10), 2669–2681 (2010).
[CrossRef] [PubMed]

S. J. Chiu, X. T. Li, P. Nicholas, C. A. Toth, J. A. Izatt, and S. Farsiu, “Automatic segmentation of seven retinal layers in SDOCT images congruent with expert manual segmentation,” Opt. Express18(18), 19413–19428 (2010).
[CrossRef] [PubMed]

2009 (5)

G. T. Chong, S. Farsiu, S. F. Freedman, N. Sarin, A. F. Koreishi, J. A. Izatt, and C. A. Toth, “Abnormal foveal morphology in ocular albinism imaged with spectral-domain optical coherence tomography,” Arch. Ophthalmol.127(1), 37–44 (2009).
[CrossRef] [PubMed]

P. Chatterjee and P. Milanfar, “Clustering-based denoising with locally learned dictionaries,” IEEE Trans. Image Process.18(7), 1438–1451 (2009).
[CrossRef] [PubMed]

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev.51(1), 34–81 (2009).
[CrossRef]

A. W. Scott, S. Farsiu, L. B. Enyedi, D. K. Wallace, and C. A. Toth, “Imaging the infant retina with a hand-held spectral-domain optical coherence tomography device,” Am. J. Ophthalmol.147(2), 364–373.e2 (2009).
[CrossRef] [PubMed]

S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE J. Sel. Top. Signal Process.57, 2479–2493 (2009).

2008 (5)

D. Healy and D. J. Brady, “Compression at the physical interface,” IEEE Signal Process. Mag.25(2), 67–71 (2008).
[CrossRef]

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process.56(6), 2346–2356 (2008).
[CrossRef]

M. Gargesha, M. W. Jenkins, A. M. Rollins, and D. L. Wilson, “Denoising and 4D visualization of OCT images,” Opt. Express16(16), 12313–12333 (2008).
[CrossRef] [PubMed]

J. Mairal, M. Elad, and G. Sapiro, “Sparse representation for color image restoration,” IEEE Trans. Image Process.17(1), 53–69 (2008).
[CrossRef] [PubMed]

J. Mairal, G. Sapiro, and M. Elad, “Learning multiscale sparse representations for image and video restoration,” Multiscale Model. Simulation7(1), 214–241 (2008).
[CrossRef]

2007 (5)

S. Farsiu, J. Christofferson, B. Eriksson, P. Milanfar, B. Friedlander, A. Shakouri, and R. Nowak, “Statistical detection and imaging of objects hidden in turbid media using ballistic photons,” Appl. Opt.46(23), 5805–5822 (2007).
[CrossRef] [PubMed]

M. A. Neifeld and J. Ke, “Optical architectures for compressive imaging,” Appl. Opt.46(22), 5293–5303 (2007).
[CrossRef] [PubMed]

F. Luisier, T. Blu, and M. Unser, “A new SURE approach to image denoising: interscale orthonormal wavelet thresholding,” IEEE Trans. Image Process.16(3), 593–606 (2007).
[CrossRef] [PubMed]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process.16(8), 2080–2095 (2007).
[CrossRef] [PubMed]

H. Takeda, S. Farsiu, and P. Milanfar, “Kernel regression for image processing and reconstruction,” IEEE Trans. Image Process.16(2), 349–366 (2007).
[CrossRef] [PubMed]

2006 (5)

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory52(2), 489–509 (2006).
[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52(4), 1289–1306 (2006).
[CrossRef]

S. Farsiu, M. Elad, and P. Milanfar, “A practical approach to superresolution,” Proc. SPIE6077, 607703, 607703-15 (2006).
[CrossRef]

M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process.15(12), 3736–3745 (2006).
[CrossRef] [PubMed]

M. Aharon, M. Elad, and A. M. Bruckstein, “The K-SVD: an algorithm for designing of overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process.54(11), 4311–4322 (2006).
[CrossRef]

2005 (3)

2004 (2)

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math.57(11), 1413–1457 (2004).
[CrossRef]

D. C. Adler, T. H. Ko, and J. G. Fujimoto, “Speckle reduction in optical coherence tomography images by use of a spatially adaptive wavelet filter,” Opt. Lett.29(24), 2878–2880 (2004).
[CrossRef] [PubMed]

2003 (2)

M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express11(18), 2183–2189 (2003).
[CrossRef] [PubMed]

P. Bao and L. Zhang, “Noise reduction for magnetic resonance images via adaptive multiscale products thresholding,” IEEE Trans. Med. Imaging22(9), 1089–1099 (2003).
[CrossRef] [PubMed]

2001 (1)

G. Cincotti, G. Loi, and M. Pappalardo, “Frequency decomposition and compounding of ultrasound medical images with wavelet packets,” IEEE Trans. Med. Imaging20(8), 764–771 (2001).
[CrossRef] [PubMed]

2000 (1)

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process.9(9), 1532–1546 (2000).
[CrossRef] [PubMed]

1999 (1)

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt.4(1), 95–105 (1999).
[CrossRef]

1998 (1)

P. Thévenaz, U. E. Ruttimann, and M. Unser, “A pyramid approach to subpixel registration based on intensity,” IEEE Trans. Image Process.7(1), 27–41 (1998).
[CrossRef] [PubMed]

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Adler, D. C.

Aharon, M.

M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process.15(12), 3736–3745 (2006).
[CrossRef] [PubMed]

M. Aharon, M. Elad, and A. M. Bruckstein, “The K-SVD: an algorithm for designing of overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process.54(11), 4311–4322 (2006).
[CrossRef]

Bao, P.

P. Bao and L. Zhang, “Noise reduction for magnetic resonance images via adaptive multiscale products thresholding,” IEEE Trans. Med. Imaging22(9), 1089–1099 (2003).
[CrossRef] [PubMed]

Beg, M. F.

Bizheva, K.

Blu, T.

F. Luisier, T. Blu, and M. Unser, “A new SURE approach to image denoising: interscale orthonormal wavelet thresholding,” IEEE Trans. Image Process.16(3), 593–606 (2007).
[CrossRef] [PubMed]

Borsdorf, A.

Brady, D. J.

D. Healy and D. J. Brady, “Compression at the physical interface,” IEEE Signal Process. Mag.25(2), 67–71 (2008).
[CrossRef]

Bruckstein, A. M.

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev.51(1), 34–81 (2009).
[CrossRef]

M. Aharon, M. Elad, and A. M. Bruckstein, “The K-SVD: an algorithm for designing of overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process.54(11), 4311–4322 (2006).
[CrossRef]

Buades, A.

A. Buades, B. Coll, and J.-M. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Model. Simul.4(2), 490–530 (2005).
[CrossRef]

Cabrera, M. T.

Candès, E. J.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory52(2), 489–509 (2006).
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Carin, L.

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S. J. Chiu, J. A. Izatt, R. V. O’Connell, K. P. Winter, C. A. Toth, and S. Farsiu, “Validated automatic segmentation of AMD pathology including drusen and geographic atrophy in SD-OCT images,” Invest. Ophthalmol. Vis. Sci.53(1), 53–61 (2012).
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Shi, G.

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Figures (8)

Fig. 1
Fig. 1

Two classic methods for removing noise in SDOCT image. (a) Denoising by a model-based single-frame technique [7]. (b) Denoising by multi-frame averaging technique: SDOCT frames acquired from the same location are averaged to increase SNR.

Fig. 2
Fig. 2

In common scanning patterns, SDOCT B-scans acquired from adjacent (azimuthally distanced) positions (a) have similar features (b,c). (a) In the summed-voxel projection [28,29] (SVP) en face SDOCT image of a non-neovascular age-related macular degeneration (AMD) patient, (b,c) B-Scans are acquired from the location of the blue and yellow lines, respectively.

Fig. 3
Fig. 3

Dictionaries trained on (a) the original low-SNR SDOCT image by the K-SVD algorithm, (b) averaged high-SNR image by the K-SVD algorithm, and (c) averaged high-SNR image by the proposed MSBTD training algorithm (due to the limited space, we show only the first atom of each learned subdictionary).

Fig. 4
Fig. 4

Algorithmic flowchart of multiscale structural dictionary learning process.

Fig. 5
Fig. 5

The outline of the MSBTD algorithm.

Fig. 6
Fig. 6

Denoising results for two test SDOCT retinal images using the Tikhonov [58], New SURE [59], K-SVD [34], BM3D [47], and the proposed MSBTD method. The left and right columns show the foveal images from a normal subject and an AMD patient, respectively. (a, b) The averaged (high-SNR) images for the multiscale structural dictionary training. (c, d) Low-SNR noisy foveal images from the volumetric scans. (e, f) Denoising results using the Tikhonov method. (g, h) Denoising results using the New SURE method. (i, j) Denoising results using the K-SVD method. (k, l) Denoising results using the BM3D method. (m, n) Denoising results using the MSBTD method.

Fig. 7
Fig. 7

Visual comparison of denoising results from the Tikhonov [58], New SURE [59], K-SVD [34], BM3D [47], and MSBTD on two SDOCT test images. (a, b) Test SDOCT images. (c, d) Averaged images. (e, f) Denoising results using the Tikhonov method (Left: PSNR = 22.67, Right: PSNR = 24.01). (g, h) Denoising results using the New SURE method (Left: PSNR = 25.39, Right: PSNR = 25.35). (i, j) Denoising results using the K-SVD method (Left: PSNR = 27.98, Right: PSNR = 25.81). (k, l) Denoising results using the BM3D method (Left: PSNR = 27.72, Right: PSNR = 25.69). (m, n) Denoising results using the MSBTD method (Left: PSNR = 28.19, Right: PSNR = 26.06).

Fig. 8
Fig. 8

Denoising results for test images captured from four different locations processed by the same learned dictionary. (a) Summed-voxel projection (SVP) en face image of an AMD eye (~6.6mm2). (b, f, j, n) Raw noisy images acquired from the location b-e shown in (a). (c, g, k, o) Denoising results using the K-SVD [34]. (d, h, l, p) Denoising results using the BM3D [47]. (e, i, m, q) Denoising results using the MSBTD.

Tables (3)

Tables Icon

Table 1 Mean and standard deviation of the MSR and CNR results for seventeen SDOCT retinal images using the Tikhonov [58], New SURE [59], K-SVD [34], BM3D [47], and the proposed MSBTD method. The best results in the table are shown in bold.

Tables Icon

Table 2 Mean and standard deviation of the PSNR (dB) for seventeen SDOCT foveal images obtained from the Tikhonov [58], New SURE [59], K-SVD [34], BM3D [47], and the proposed MSBTD method. The best result in the table is shown in bold.

Tables Icon

Table 3 Mean and standard deviation of the MSR and CNR measures for four test images acquired from different positions using the Tikhonov [58], New SURE [59], K-SVD [34], BM3D [47], and the MSBTD method. The best results in the table are shown in bold.

Equations (7)

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

x=Dα,
α ^ =arg min α α 0   subject to   x Noise Dα 2 ω,
A=( k i , s i )=arg max k,s | c k,s , y i Hf |.
( α ^ i , β ^ i )=arg min α i , β i { y i D i A α i 2 2 + λ 1 α i 0 + λ 2 α i β i 0 },
MSR =  μ f σ f ,
CNR = | μ f μ b | 0.5( σ f 2 + σ b 2 ) ,
PSNR = 20 log 10 ( Max R 1 H h=1 H ( R h R ^ h ) 2 ),

Metrics