Compressed sensing for practical optical imaging systems: A tutorial

Optical Engineering

Volumn 50, Issue 7, 2011, Pages

  Willet, Rebecca M ^a   Mareia, Roummel F ^b   Nichols, Jonathan M ^c  

^a DUKE UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c NAVAL RESEARCH LABORATORY   (United States)

Author keywords

Co mpressed sensing; Coded aperture imaging; Computational imaging; Image reconstruction; Infrared; Inverse problems; Optimization; Sampling

Indexed keywords

CODED APERTURE IMAGING; COMPRESSED SENSING; COMPUTATIONAL IMAGING; HIGHER RESOLUTION; LARGE-FORMAT FOCAL PLANE ARRAYS; OPTICAL IMAGING; OPTICAL IMAGING SYSTEM; PRACTICAL ISSUES;

FOCUSING; IMAGE RECONSTRUCTION; IMAGING TECHNIQUES; INFRARED RADIATION; INVERSE PROBLEMS; OPTICAL IMAGE STORAGE; OPTIMIZATION; SAMPLING;

THERMOGRAPHY (IMAGING);

EID: 80053407766     PISSN: 00913286     EISSN: 15602303     Source Type: Journal    
DOI: 10.1117/1.3596602     Document Type: Article

References (105)

1. E. J. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory 51(12), 4203-4215 (2005).
2. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory 52(4), 1289-1306 (2006).
3. E. Candes, "Compressive sampling," in Proc. Int. Congress of Mathematicians, Madrid, Spain Vol. 3, pp. 1433-1452 (2006).
4. R. Baraniuk, "Compressive sensing," IEEE Signal Process. Mag. 24(4), 118-121 (2007).
5. E. J. Candes and M. B. Wakin, "An introduction to compressive sampling," IEEE Signal Process. Mag. 25(2), 21-30 (2008).
6. J. Romberg, "Imaging via compressive sampling," IEEE Signal Process. Mag. 25(2), 14-20 (2008).
7. M. Fornasier and H. Rauhut, "Compressive sensing," in Handbook of Mathematical Methods in Imaging, Springer, Heidelberg, Germany, (2011).
8. H. Yuan, G. Apgar, J. Kim, J. Laquindanum, V. Nalavade, P. Beer, J. Kimchi, and T. Wong, "FPA development: from InGaAs, InSb, to HgCdTe," in Infrared Technology and Applications XXXIV, B. F. Andresen, G. F. Fulop, and P. R. Norton, Eds., Proc. SPIE Defense, Security, and Sensing Symposium Vol. 6940 (2008).
9. J. M. Nichols, J. R. Waterman, R. Menon, and J. Devitt, "Modeling and analysis of a high performance midwave infrared panoramic periscope," Opt. Eng. 49(11) (2010).
10. M. Carmody, J. G. Pasko, D. Edwall, E. Piquette, M. Kangas, S. Freeman, J. Arias, R. Jacobs, W. Mason, A. Stoltz, Y. Chen, and N. K. Dhar, "Status of LWIR HgCdTe-on-Silicon FPA Technology," J. Electron. Mater. 37(9), 1184-1188 (2008).
11. E. J. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory 15(12), 4203-4215 (2005).
12. J. Haupt and R. Nowak, "Signal reconstruction from noisy random projections," IEEE Trans. Inf. Theory 52(9), 4036-4048 (2006).
13. E. J. Candes, J. Romberg, and T Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory 52(2), 489-509 (2006).
14. R. G. Baraniuk, M. Davenport, R. A. DeVore, and M. B. Wakin, "A simple proof of the restricted isometry property for random matrices," Constructive Approx. 28(3), 253-263 (2008).
15. E. J. Candes, J. K. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math. 59(8), 1207-1223 (2006).
16. E. J. Candes and T. Tao, "The Dantzig selector: Statistical estimation when p is much larger than n," Ann. Stat. 35, 2313-2351 (2007).
17. J. A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory 50(10), 2231-2242 (2004).
18. 1 minimization," Ann. Stat. 37, 2145-2177 (2009).
19. 1 minimization," Proc. Natl. Acad. Sci. U.S.A 100(5), 2191-2202 (2003).
20. T. Strohmer and R. W. Heath Jr., "Grassmannian frames with applications to coding and communications," Appl. Comput. Harmon. Anal. 14(3), 257-275 (2003).
21. D. L. Donoho, M. Elad, and V N. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Trans. Inf. Theory 52(1), 6-18 (2006).
22. D. L. Donoho and X. Huo, "Uncertainty principles and ideal atomic decomposition," IEEE Trans. Inf. Theory 47(7), 2845-2862 (2001).
23. 1 minimization," Proc. Natl. Acad. Sci. U.SA. 100(5), 2197-2202 (2003).
24. R. Gribonval and M. Nielsen, "Sparse representations in unions of bases," IEEE Trans. Inf. Theory 49(12), 3320-3325 (2003).
25. J. A. Tropp, "Just relax: convex programming methods for identifying sparse signals in noise," IEEE Trans. Inf. Theory 52(3), 1030-1051 (2006).
26. A. C. Gilbert, S. Muthukrishnan, and M. J. Strauss, "Approximation of functions over redundant dictionaries using coherence," in Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD (2003).
27. R. Varga, Geršgorin and His Circles, Springer-Verlag, Berlin, Germany (2004).
28. J. A. Tropp, A. C. Gilbert, S. Muthukrishnan, and M. J. Strauss, "Improved sparse approximation over quasiincoherent dictionaries," in IEEE International Conference on Image Processing, Barcelona, Spain (2003).
29. J. A. Tropp, "On the conditioning of random subdictionaries," Appl. Comput. Harmon. Anal. 25, 1-24 (2008).
30. D. L. Donoho and J. Tanner, "Precise undersampling theorems," Proc. IEEE 98(6), 913-924 (2010).
31. D. L. Donoho and J. Tanner, "Exponential bounds implying construction of compressed sensing matrices, error-correcting codes, and neighborly polytopes by random sampling," IEEE Trans. Inf. Theory, 56(4), 2002-2016 (2010).
32. M. Neifeld and J. Ke, "Optical architectures for compressive imaging," Appl. Opt. 46, 5293-5303 (2007).
33. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, "Single-pixel imaging via compressive sampling," IEEE Signal Process. Mag. 25(2), 83-91 (2008).
34. W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, "A single-pixel terahertz imaging system based on compressed sensing," Appl. Phys. Lett. 93, 121105 (2008).
35. 1C. Chen, P Ye, G. R. Arce, and D. W. Prather, "Development of a compressive programmable array microscope," Proceedings of the Conference on Lasers and Electro-opticslQuantum Electronics and Laser Science Conference, Baltimore, MD, Vol. 1-5, pp. 3135-3136 (2009).
36. R. F. Mareia and R. M. Willett, "Compressive coded aperture superresolution image reconstruction," in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 833-836, Las Vegas, NV (2008).
37. R. F. Mareia, Z. T. Harmany, and R. M. Willett, "Compressive coded aperture imaging," in Proceedings of the 2009 IS&TISPIE Electronic Imaging: Computational Imaging VII, San Jose, CA (2009).
38. J. Romberg, "Compressive sampling by random convolution," SIAM J. Imaging Sci. 2(4), 1098-1128 (2009).
39. A. Stern and B. Javidi, "Random projections imaging with extended space-bandwidth product," J. Disp. Tech. 3(3), 315-320 (2007).
40. W. Yin, S. P Morgan, J. Yang, and Y Zhang, "Practical compressive sensing with Toeplitz and circulant matrices," in Proceedings of Visual Communications and Image Processing (VCIP), SPIE, San Jose, CA (2010).
41. R. Fergus, A. Torralba, and W. T Freeman, "Random lens imaging," Tech. Rep. MIT-CSAIL-TR-2006-058, MIT Computer Science and Artificial Intelligence Laboratory (2006).
42. R. Robucci, J. D. Gray, L. K. Chiu, J. Romberg, and P Hasler, "Compressive sensing on a CMOS separable-transform image sensor," Proc. IEEE 98(6), 1089-1101 (2010).
43. V Majidzadeh, L. Jacques, A. Schmid, P Vandergheynst, and Y Leblebici, "A (256*256) pixel 76.7mW CMOS imager/compressor based on real-time in-pixel compressive sensing," in IEEE International Symposium on Circuits and Systems, Paris, France, pp. 29562959 (2010).
44. M. E. Gehm, R. John, D. J. Brady, R. M. Willett, and T J. Schultz, "Single-shot compressive spectral imaging with a dual-disperser architecture," Opt. Express 15(21), 14013-14027 (2007).
45. A. Wagadarikar, R. John, R. Willett, and D. Brady, "Single disperser design for coded aperture snapshot spectral imaging," Appl. Opt. 47(10), B44-B51 (2008).
46. M. Maggioni.G.L. Davis, F. J. Warner, F. B. Geshwind, A. C. Coppi, R. A. DeVerse, and R. R. Coifman, "Hyperspectral microscopic analysis of normal, benign and carcinoma microarray tissue sections," Proc. SPIE 6091 (2006).
47. J. Gu, S. K. Nayar, E. Grinspun, P N. Belhumeur, and R. Ramamoorthi, "Compressive Structured Light for Recovering Inho-mogeneous Participating Media," in European Conference on Computer Vision (ECCV), Marseille-France (2008).
48. M. A. Golub, M. Nathan, A. Averbuch, E. Lavi, V. A. Zheludev, and A. Scholar, "Spectral multiplexing method for digital snapshot spectral imaging," Appl. Opt. 48, 1520-1526 (2009).
49. M. Shankar, R. Willett, N. Pitsianis, T. Schulz, R. Gibbons, R. T. Kolste, J. Carriere, C. Chen, D. Prather, and D. Brady, "Thin infrared imaging systems through multichannel sampling," Appl. Opt. 47(10), B1-B10 (2008).
50. A. F. Coskun, I. Sencan, T-W. Su, and A. Ozcan, "Lensless widefield flourescent imaging on a chip using compressive decoding of sparse objects," Opt. Express 18(10), 10510-10523 (2010).
51. L. C. Potter, E. Ertin, J. T. Parker, and M. Cetin, "Sparsity and compressed sensing in radar imaging," Proc. IEEE 98(6), 1006-1020 (2010).
52. J. Gu, S. K. Nayar, E. Grinspun, P. N. Belhumeur, and R. Ramamoorthi, "Compressive structured light for recovering inhomogeneous participating media," in Proceedings of the European Conference on Computer Vision, Marseille, France (2008).
53. M. Mohtashemi, H. Smith, D. Walburger, F. Sutton, and J. Diggans, "Sparse sensing DNA microarray-based biosensor: Is it feasible?," in 2010 IEEE Sensors Applications Symposium, Limerick, Ireland, pp. 127-130 (2010).
54. M. Sheikh, O. Milenkovic, and R. Baraniuk, "Designing compressive sensing DNA microarrays," in 2nd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, St. Thomas, VI, USA 2007, pp. 141-144 (2007).
55. M. Lustig, D. Donoho, and J. M. Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magn. Reson. Med. 58,1182-1195(2007).
56. A. C. Gurbuz, J. H. McClellan, and W. R. Scott, "A compressive sensing data acquisition and imaging method for stepped frequency GPRs," IEEE Trans. Signal Process. 57, 2640-2650 (2009).
57. P. Ye, J. L. Paredes, G. Arce, Y Wu, C. Chen, and D. Prather, "Compressive confocal microscopy," in IEEE International Conference on Acoustics, Speech and Signal Processing, Taipei, Taiwan, pp. 429-432 (2009).
58. J. Bobin, J.-L. Starek, and R. Ottensamer, "Compressed sensing in astronomy," IEEE J. Sel. Top. Signal Process. 2, 718-726 (2008).
59. M. Raginsky, R. M. Willett, Z. T. Harmany, and R. F. Mareia, "Compressed sensing performance bounds under Poisson noise," IEEE Trans. Signal Process. 58(8), 3990-4002 (2010).
60. M. Raginsky, S. Jafarpour, Z. Harmany, R. Mareia, R. Willett, and R. Calderbank, "Performance bounds for expander-based compressed sensing in Poisson noise," accepted to IEEE Transactions on Signal Processing, 2011.
61. W. Dai, H. V. Pham, and O. Milenkovic, "Distortion-rate functions for quantized compressive sensing," in IEEE Information Theory Workshop on Networking and Information Theory, 2009, ITW 2009, pp. 171-175 (2009).
62. L. Jacques, D. K. Hammond, and M. J. Fadili, "Dequantizing compressed sensing: When oversampling and non-gaussian constraints combine," IEEE Trans. Inf. Theory 57(1), 559-571 (2011).
63. J. N. Laska, P. T. Boufounos, M. A. Davenport, and R. G. Baraniuk, "Democracy in action: Quantization, saturation, and compressive sensing," in Applied and Computational Harmonic Analysis, (2011) (in press).
64. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE J. Sel. Top. Signal Process. 1(4), 586-597 (2007).
65. E. van den Berg and M. P. Friedlander, "Probing the pareto frontier for basis pursuit solutions," SIAM J. Sci. Comput. 31(2), 890-912 (2008).
66. S. Wright, R. Nowak, and M. Figueiredo, "Sparse reconstruction by separable approximation," IEEE Trans. Signal Process. 57, 2479-2493 (2009).
67. P. L. Combettes and V. R. Wajs, "Signal recovery by proximal forward-backward splitting," Multiscale Model. Simul. 4(4), 1168-1200 (2005).
68. I. Daubechies, M. Defrise, and C. De Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Math. LVII, 1413-1457 (2004).
69. J. M. Bioucas-Dias and M. A. Figueiredo, "A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration," IEEE Trans. Image Process. 16(12), 2992-3004 (2007).
70. G. Davis, S. Mallat, and M. Avellaneda, "Greedy adaptive approximation," J. Constructive Approximation 13, 57-98 (1997).
71. D. L. Donoho, M. Elad, and V N. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Trans. Inf. Theory 52(1), 6-18 (2006).
72. J. A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory 50, 2231-2242 (2004).
73. T. Chan and J. Shen, Image Processing And Analysis: Variational, PDE, Wavelet, and Stochastic Methods, Society for Industrial and Applied Mathematics, Philadelphia, PA (2005).
74. W. Yin, S. Osher, D. Goldfarb, and J. Darbon, "Bregman iterative algorithms for 11-minimization with applications to compressed sensing," SIAM J. Imag. Sci. 1(1), 143-168 (2008).
75. J. P. Oliveira, J. M. Bioucas-Dias, and M. A. T. Figueiredo, "Review: Adaptive total variation image deblurring: A majorizationminimization approach," Signal Process. 89(9), 1683-1693 (2009).
76. A. Chambolle, "An algorithm for total variation minimization and applications," J. Math. Imaging Vision 20(1-2), 89-97 (2004).
77. J. Darbon and M. Sigelle, "Image restoration with discrete constrained total variation part i: Fast and exact optimization," J. Math. Imaging Vision 26(3), 261-276 (2006).
78. J. B. Tenenbaum, V. de Silva, and J. C. Langford, "A global geometric framework for nonlinear dimensionality reduction," Science 290(5500), 2319-2323 (2000).
79. S. Roweis and L. Saul, "Nonlinear dimensionality reduction by locally linear embedding," Science 22(5500), 2323-2326 (2000).
80. M. Belkin, P. Niyogi, and V. Singhwani, "Manifold regularization: A geometric framework for learning from labeled and unlabeled examples," J. Mach. Learn. Res. 7, 2399-2434 (2006).
81. M. B. Wakin, "Manifold-based signal recovery and parameter estimation from compressive measurements," (2009), (submitted) http://arxiv.org/abs/1002.1247.
82. M. Davenport, M. Duarte, M. Wakin, J. Laska, D. Takhar, K. Kelly, and R. Baraniuk, "The smashed filter for compressive classification and target recognition," in Proc. of SPIE Computational Imaging V, San Jose, CA (2007).
83. Y. C. Eldar and M. Mishali, "Robust recovery of signals from a structured union of subspaces," IEEE Trans. Info. Theory 55(11), 5302-5316(2009).
84. R. Baraniuk, V. Cevher, M. Duarte, and C. Hegde, "Model-based compressive sensing," IEEE Trans. Inf. Theory 56(4), 1982-2001 (2010).
85. E. Candes and B. Recht, "Exact matrix completion via convex optimization," Found. Comput. Math. 9(6), 717-772 (2009).
86. E. J. Candes, X. Li, Y. Ma, and J. Wright, "Robust principal component analysis?" arXiv:0912.3599vl (2009).
87. M. Zhou.H. Chen, J. Paisley, L. Ren, L. Li, Z. Xing, D. Dunson, G. Sapiro, and L. Carin, "Nonparametric bayesian dictionary learning for analysis of noisy and incomplete images," IEEE Trans. Image Process. (2010) (submitted).
88. Z. T. Harmany, D. O. Thompson, R. M. Willett, and R. F. Mareia, "Gradient projection for linearly constrained convex optimization in sparse signal recovery," in IEEE International Conference on Image Processing, Hong Kong, China (2010).
89. D. Snyder, Random Point Processes, Wiley-Interscience, New York, (1975).
90. S. Ahn and J. Fessier, "Globally convergent image reconstruction for emission tomography using relaxed ordered subsets algorithms," IEEE Trans. Med. Imaging 22, 613-626 (2003).
91. R. Willett and R. Nowak, "Multiscale Poisson intensity and density estimation," IEEE Trans. Inf. Theory 53(9), 3171-3187 (2007).
92. Z.T. Harmany, R. F. Mareia, and R. M. Willett, "SPIRAL out of convexity: Sparsity-regularized algorithms for photon-limited imaging," in Proc. of SPIE Computational Imaging VIII, San Jose, CA (2010).
93. R. M. Willett, Z. T. Harmany, and R. F. Mareia, "Poisson image reconstruction with total variation regularization," in Proceedings of IEEE International Conference on Image Processing, Hong Kong, China (2010).
94. Z. T. Harmany, R. F. Mareia, and R. M. Willett, "Sparse Poisson intensity reconstruction algorithms," in IEEE Workshop on Statistical Signal Processing, Cardiff, Wales, UK (2009).
95. F-X. Dupe, J. M. Fadili, and J.-L. Starek, "A proximal iteration for deconvolving Poisson noisy images using sparse representations," IEEE Trans. Image Process. 18(2), 310-321 (2009).
96. M. Figueiredo and J. Bioucas-Dias, "Deconvolution of Poissonian images using variable splitting and augmented Lagrangian optimization," in IEEE Workshop on Statistical Signal Processing, Cardiff, United Kingdom (2009). Available at http://arxiv.org/abs/0904.4868.
97. J.Y Park and M.B. Wakin, "A multiscale framework for compressive sensing of video," in Picture Coding Symposium (PCS), Chicago, IL (2009).
98. R. F. Mareia and R. M. Willett, "Compressive coded aperture video reconstruction," in Proceedings 16th European Signal Processing Conference, 2008, Lausanne, Switzerland (2008).
99. N. Jacobs, S. Schuh, and R. Pless, "Compressive sensing and differential image motion," in IEEE International Conference on Acoustics, Speech, and Signal Processing, Dallas, TX (2010).
100. D. O. Thompson, Z. T. Harmany, and R. F. Mareia, "Sparse video recovery using linearly constrained gradient projection," in IEEE International Conference on Acoustics, Speech, and Signal Processing, Prague, Czech Republic (2011).
101. R. F. Mareia, Z. T Harmany, and R. M. Willett, "Compressive coded apertures for high-resolution imaging," in Proceedings of the 2010 SPIE Photonics Europe, Brussels, Belgium (2010).
102. Y. Rivenson, A. Stern, and B. Javidi, "Single exposure superresolution compressive imaging by double phase encoding," Opt. Express 18(14), 15094-15103 (2010).
103. J.W. Stayman, N. Subotic, and W. Buller, "An analysis of coded aperture acquisition and reconstruction using multiframe code sequences for relaxed optical design constraints," in Proc. SPIE 7468 (2009).
104. N. Savage, "Digital spatial light modulators," Nature Photonics 3, 170-172 (2009).
105. http://www.bnonlinear.com/products/xyslm/xy.htm.