Abstract

Compressive measurements benefit low-light-level imaging (L3-imaging) due to the significantly improved measurement signal-to-noise ratio (SNR). However, as with other compressive imaging (CI) systems, compressive L3-imaging is slow. To accelerate the data acquisition, we develop an algorithm to compute the optimal binary sensing matrix that can minimize the image reconstruction error. First, we make use of the measurement SNR and the reconstruction mean square error (MSE) to define the optimal gray-value sensing matrix. Then, we construct an equality-constrained optimization problem to solve for a binary sensing matrix. From several experimental results, we show that the latter delivers a similar reconstruction performance as the former, while having a smaller dynamic range requirement to system sensors.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
  3. A. Kirmani, A. Colaço, F. N. C. Wong, and V. K. Goyal, “Exploiting sparsity in time-of-flight range acquisition using a single time-resolved sensor,” Opt. Express 19(22): 21485–21507 (2011).
    [Crossref] [PubMed]
  4. G. A. Howland, D. J. Lum, M. R. Ware, and J. C. Howell, “Photon counting compressive depth mapping,” Opt. Express 21(20): 23822–23837 (2013).
    [Crossref] [PubMed]
  5. Z. Xu and E. Y. Lam, “Image reconstruction using spectroscopic and hyperspectral information for compressive terahertz imaging,” J. Opt. Soc. Am. A 27: (7)1638–1646 (2010).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  11. D. Sui, J. Ke, and P. Wei, “Implementing two compressed sensing algorithms on GPU,” Proc. SPIE 9273, 92730J (2014).
    [Crossref]
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    [Crossref]
  14. G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 604–615 (2012).
    [Crossref]
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    [Crossref] [PubMed]
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  21. M. Elad, “Optimized projections for compressed sensing,” IEEE Trans. Signal Process. 55(12): 5695–5702 (2007).
    [Crossref]
  22. J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: Simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7): 395–1408 (2009).
    [Crossref]
  23. J. Xu, Y. Pi, and Z. Cao, “Optimized projection matrix for compressive sensing,” EURASIP Journal on Advances in Signal Processing 2010, 43 (2010).
    [Crossref]
  24. G. Li, Z. Zhu, D. Yang, L. Chang, and H. Bai, “On projection matrix optimization for compressive sensing systems,” IEEE Trans. Signal Process. 61(11): 2887–2898 (2013).
    [Crossref]
  25. W. Chen, M. R. D. Rodrigues, and I. J. Wassell, “On the use of unit-norm tight frames to improve the average mse performance in compressive sensing applications,” IEEE Signal Process. Lett. 19(1): 8–11 (2012).
    [Crossref]
  26. W. Chen, M. R. D. Rodrigues, and I. J. Wassell, “Projection design for statistical compressive sensing: A tight frame based approach,” IEEE Trans. Signal Process. 61(8): 2016–2029 (2013).
    [Crossref]
  27. A. Yang, J. Zhang, and Z. Hou, “Optimized sensing matrix design based on parseval tight frame and matrix decomposition,” Journal of Communications 8(7): 456–462 (2013).
    [Crossref]
  28. D. L. Donoho, A. Javanmard, and A. Montanari, “Information-theoretically optimal compressed sensing via spatial coupling and approximate message passing,” in Proceedings of IEEE International Symposium on Information Theory Proceedings (IEEE, 2012), 1231–1235.
  29. A. Ashok, L. Huang, and M. A. Neifeld, “Information optimal compressive sensing: static measurement design,” J. Opt. Soc. Am. A 30: (5): 831–853 (2013).
    [Crossref]
  30. W. R. Carson, M. Chen, M. R. D. Rodrigues, R. Calderbank, and L. Carin, “Communications-inspired projection design with application to compressive sensing,” SIAM Journal on Imaging Sciences 5(4): 1185–1212 (2012).
    [Crossref]
  31. Y. Gu and N. A. Goodman, “Compressed sensing kernel design for radar range profiling,” in Proceedings of 2013 IEEE Radar Conference (RADAR) (IEEE, 2013), 1–5.
  32. A. Mahalanobis and M. A. Neifeld, “Optimizing measurements for feature-specific compressive sensing,” Appl. Opt. 53(26): 6108–6118 (2014).
    [Crossref] [PubMed]
  33. J. Ke and E. Y. Lam, “Object reconstruction in block-based compressive imaging,” Opt. Express 20(20): 22102–22117 (2012).
    [Crossref] [PubMed]
  34. J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12): 4655–4666 (2007).
    [Crossref]
  35. 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(12): 2992–3004 (2007).
    [Crossref] [PubMed]
  36. J. Haupt and R. Nowak, “Signal reconstruction from noisy random projections,” IEEE Trans. Inf. Theory 52(9): 4036–4048 (2006).
    [Crossref]
  37. J. Xia, R. D. Miller, and Y. Xu, “Data-resolution matrix and model-resolution matrix for rayleigh-wave inversion using a damped least-squares method,” Pure and Applied Geophysics 165(7): 1227–1248 (2008).
    [Crossref]
  38. D. Karkala and P. K. Yalavarthy, “Data-resolution based optimization of the data-collection strategy for near infrared diffuse optical tomography,” Medical Physics 39(8): 4715–4725 (2012).
    [Crossref] [PubMed]
  39. J. Prakash, H. Dehghani, B. W. Pogue, and P. K. Yalavarthy, “Model-resolution-based basis pursuit deconvolution improves diffuse optical tomographic imaging,” IEEE Trans. Med. Imag. 33(4): 891–901 (2014).
    [Crossref]
  40. J. Ke, M. D. Stenner, and M. A. Neifeld, “Minimum reconstruction error in feature-specific imaging,” Proc. SPIE 5817, 7–12 (2005).
    [Crossref]
  41. R. Baldick, Applied Optimization: Formulation and Algorithms for Engineering Systems(Cambridge University, 2006).
    [Crossref]
  42. P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic Press, 1981).
  43. A. Saxena, S. H. Chung, and A. Y. Ng, “Learning depth from single monocular images,” Advances in Neural Information Processing Systems 18: 1161–1168 (2005).
  44. A. Saxena, M. Sun, and A. Y. Ng, “Make3D: Learning 3D scene structure from a single still image,” IEEE Trans. Pattern Anal. Mach. Intell. 30(5): 824–840 (2009).
    [Crossref]

2015 (2)

M. E. Gehm and D. J. Brady, “Compressive sensing in the EO/IR,” Appl. Opt. 54(8): C14–C22 (2015).
[Crossref] [PubMed]

X. Yuan, T. Tsai, R. Zhu, P. Llull, D. Brady, and L. Carin, “Compressive hyperspectral imaging with side information,” IEEE J. Sel. Topics Signal Process. 9(6): 964–976 (2015).
[Crossref]

2014 (6)

J. Ke, D. Sui, and P. Wei, “Fast object reconstruction in block-based compressive low-light-level imagin,” Proc. SPIE 9301, 930136 (2014).
[Crossref]

D. Xu, Y. Huang, and J. U. Kang, “GPU-accelerated non-uniform fast fourier transform-based compressive sensing spectral domain optical coherence tomography,” Opt. Express 22(12): 14871–14884 (2014).
[Crossref] [PubMed]

D. Sui, J. Ke, and P. Wei, “Implementing two compressed sensing algorithms on GPU,” Proc. SPIE 9273, 92730J (2014).
[Crossref]

P. Li, J. Ke, D. Sui, and P. Wei, “Linear bregman algorithm implemented in parallel GPU,” Proc. SPIE 9622, 962216 (2014).

A. Mahalanobis and M. A. Neifeld, “Optimizing measurements for feature-specific compressive sensing,” Appl. Opt. 53(26): 6108–6118 (2014).
[Crossref] [PubMed]

J. Prakash, H. Dehghani, B. W. Pogue, and P. K. Yalavarthy, “Model-resolution-based basis pursuit deconvolution improves diffuse optical tomographic imaging,” IEEE Trans. Med. Imag. 33(4): 891–901 (2014).
[Crossref]

2013 (6)

G. Li, Z. Zhu, D. Yang, L. Chang, and H. Bai, “On projection matrix optimization for compressive sensing systems,” IEEE Trans. Signal Process. 61(11): 2887–2898 (2013).
[Crossref]

W. Chen, M. R. D. Rodrigues, and I. J. Wassell, “Projection design for statistical compressive sensing: A tight frame based approach,” IEEE Trans. Signal Process. 61(8): 2016–2029 (2013).
[Crossref]

A. Yang, J. Zhang, and Z. Hou, “Optimized sensing matrix design based on parseval tight frame and matrix decomposition,” Journal of Communications 8(7): 456–462 (2013).
[Crossref]

A. Ashok, L. Huang, and M. A. Neifeld, “Information optimal compressive sensing: static measurement design,” J. Opt. Soc. Am. A 30: (5): 831–853 (2013).
[Crossref]

J. Ke and P. Wei, “Using compressive measurement to obtain images at ultra low-light-level,” Proc. SPIE 8908, 89081O (2013).
[Crossref]

G. A. Howland, D. J. Lum, M. R. Ware, and J. C. Howell, “Photon counting compressive depth mapping,” Opt. Express 21(20): 23822–23837 (2013).
[Crossref] [PubMed]

2012 (7)

Y. Kashter, O. Levi, and A. Stern, “Optical compressive change and motion detection,” Appl. Opt. 51(13): 2491–2496 (2012).
[Crossref] [PubMed]

P. Maechler, C. Studer, D. E. Bellasi, A. Maleki, A. Burg, N. Felber, H. Kaeslin, and R. G. Baraniuk, “VLSI design of approximate message passing for signal restoration and compressive sensing,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 579–590 (2012).
[Crossref]

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 604–615 (2012).
[Crossref]

W. R. Carson, M. Chen, M. R. D. Rodrigues, R. Calderbank, and L. Carin, “Communications-inspired projection design with application to compressive sensing,” SIAM Journal on Imaging Sciences 5(4): 1185–1212 (2012).
[Crossref]

W. Chen, M. R. D. Rodrigues, and I. J. Wassell, “On the use of unit-norm tight frames to improve the average mse performance in compressive sensing applications,” IEEE Signal Process. Lett. 19(1): 8–11 (2012).
[Crossref]

D. Karkala and P. K. Yalavarthy, “Data-resolution based optimization of the data-collection strategy for near infrared diffuse optical tomography,” Medical Physics 39(8): 4715–4725 (2012).
[Crossref] [PubMed]

J. Ke and E. Y. Lam, “Object reconstruction in block-based compressive imaging,” Opt. Express 20(20): 22102–22117 (2012).
[Crossref] [PubMed]

2011 (3)

A. Kirmani, A. Colaço, F. N. C. Wong, and V. K. Goyal, “Exploiting sparsity in time-of-flight range acquisition using a single time-resolved sensor,” Opt. Express 19(22): 21485–21507 (2011).
[Crossref] [PubMed]

Y. Yu, A. P. Petropulu, and H. V. Poor, “Measurement matrix design for compressive sensing–based MIMO radar,” IEEE Trans. Signal Process. 59(11): 5338–5352 (2011).
[Crossref]

L. Zelnik-Manor, K. Rosenblum, and Y. C. Eldar, “Sensing matrix optimization for block-sparse decoding,” IEEE Trans. Signal Process. 59(9): 4300–4312 (2011).
[Crossref]

2010 (2)

Z. Xu and E. Y. Lam, “Image reconstruction using spectroscopic and hyperspectral information for compressive terahertz imaging,” J. Opt. Soc. Am. A 27: (7)1638–1646 (2010).
[Crossref]

J. Xu, Y. Pi, and Z. Cao, “Optimized projection matrix for compressive sensing,” EURASIP Journal on Advances in Signal Processing 2010, 43 (2010).
[Crossref]

2009 (2)

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: Simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7): 395–1408 (2009).
[Crossref]

A. Saxena, M. Sun, and A. Y. Ng, “Make3D: Learning 3D scene structure from a single still image,” IEEE Trans. Pattern Anal. Mach. Intell. 30(5): 824–840 (2009).
[Crossref]

2008 (3)

J. Xia, R. D. Miller, and Y. Xu, “Data-resolution matrix and model-resolution matrix for rayleigh-wave inversion using a damped least-squares method,” Pure and Applied Geophysics 165(7): 1227–1248 (2008).
[Crossref]

E. J. Candès, “The restricted isometry property and its implications for compressed sensing,” Comptes Rendus Mathematique 346(9): 589–592 (2008).
[Crossref]

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation 28(3): 253–263 (2008).
[Crossref]

2007 (4)

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

M. Elad, “Optimized projections for compressed sensing,” IEEE Trans. Signal Process. 55(12): 5695–5702 (2007).
[Crossref]

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12): 4655–4666 (2007).
[Crossref]

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(12): 2992–3004 (2007).
[Crossref] [PubMed]

2006 (1)

J. Haupt and R. Nowak, “Signal reconstruction from noisy random projections,” IEEE Trans. Inf. Theory 52(9): 4036–4048 (2006).
[Crossref]

2005 (2)

J. Ke, M. D. Stenner, and M. A. Neifeld, “Minimum reconstruction error in feature-specific imaging,” Proc. SPIE 5817, 7–12 (2005).
[Crossref]

A. Saxena, S. H. Chung, and A. Y. Ng, “Learning depth from single monocular images,” Advances in Neural Information Processing Systems 18: 1161–1168 (2005).

Ashok, A.

Bai, H.

G. Li, Z. Zhu, D. Yang, L. Chang, and H. Bai, “On projection matrix optimization for compressive sensing systems,” IEEE Trans. Signal Process. 61(11): 2887–2898 (2013).
[Crossref]

Baldick, R.

R. Baldick, Applied Optimization: Formulation and Algorithms for Engineering Systems(Cambridge University, 2006).
[Crossref]

Baraniuk, R.

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation 28(3): 253–263 (2008).
[Crossref]

Baraniuk, R. G.

P. Maechler, C. Studer, D. E. Bellasi, A. Maleki, A. Burg, N. Felber, H. Kaeslin, and R. G. Baraniuk, “VLSI design of approximate message passing for signal restoration and compressive sensing,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 579–590 (2012).
[Crossref]

Bellasi, D. E.

P. Maechler, C. Studer, D. E. Bellasi, A. Maleki, A. Burg, N. Felber, H. Kaeslin, and R. G. Baraniuk, “VLSI design of approximate message passing for signal restoration and compressive sensing,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 579–590 (2012).
[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(12): 2992–3004 (2007).
[Crossref] [PubMed]

Brady, D.

X. Yuan, T. Tsai, R. Zhu, P. Llull, D. Brady, and L. Carin, “Compressive hyperspectral imaging with side information,” IEEE J. Sel. Topics Signal Process. 9(6): 964–976 (2015).
[Crossref]

Brady, D. J.

Burg, A.

P. Maechler, C. Studer, D. E. Bellasi, A. Maleki, A. Burg, N. Felber, H. Kaeslin, and R. G. Baraniuk, “VLSI design of approximate message passing for signal restoration and compressive sensing,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 579–590 (2012).
[Crossref]

Calderbank, R.

W. R. Carson, M. Chen, M. R. D. Rodrigues, R. Calderbank, and L. Carin, “Communications-inspired projection design with application to compressive sensing,” SIAM Journal on Imaging Sciences 5(4): 1185–1212 (2012).
[Crossref]

Candès, E. J.

E. J. Candès, “The restricted isometry property and its implications for compressed sensing,” Comptes Rendus Mathematique 346(9): 589–592 (2008).
[Crossref]

Cao, Z.

J. Xu, Y. Pi, and Z. Cao, “Optimized projection matrix for compressive sensing,” EURASIP Journal on Advances in Signal Processing 2010, 43 (2010).
[Crossref]

Carin, L.

X. Yuan, T. Tsai, R. Zhu, P. Llull, D. Brady, and L. Carin, “Compressive hyperspectral imaging with side information,” IEEE J. Sel. Topics Signal Process. 9(6): 964–976 (2015).
[Crossref]

W. R. Carson, M. Chen, M. R. D. Rodrigues, R. Calderbank, and L. Carin, “Communications-inspired projection design with application to compressive sensing,” SIAM Journal on Imaging Sciences 5(4): 1185–1212 (2012).
[Crossref]

Carson, W. R.

W. R. Carson, M. Chen, M. R. D. Rodrigues, R. Calderbank, and L. Carin, “Communications-inspired projection design with application to compressive sensing,” SIAM Journal on Imaging Sciences 5(4): 1185–1212 (2012).
[Crossref]

Chang, H. S.

Y. Weiss, H. S. Chang, and W. T. Freeman, “Learning compressed sensing,” In Snowbird Learning Workshop, Allerton, CA (2007).

Chang, L.

G. Li, Z. Zhu, D. Yang, L. Chang, and H. Bai, “On projection matrix optimization for compressive sensing systems,” IEEE Trans. Signal Process. 61(11): 2887–2898 (2013).
[Crossref]

Chen, M.

W. R. Carson, M. Chen, M. R. D. Rodrigues, R. Calderbank, and L. Carin, “Communications-inspired projection design with application to compressive sensing,” SIAM Journal on Imaging Sciences 5(4): 1185–1212 (2012).
[Crossref]

Chen, W.

W. Chen, M. R. D. Rodrigues, and I. J. Wassell, “Projection design for statistical compressive sensing: A tight frame based approach,” IEEE Trans. Signal Process. 61(8): 2016–2029 (2013).
[Crossref]

W. Chen, M. R. D. Rodrigues, and I. J. Wassell, “On the use of unit-norm tight frames to improve the average mse performance in compressive sensing applications,” IEEE Signal Process. Lett. 19(1): 8–11 (2012).
[Crossref]

Chin, S.

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 604–615 (2012).
[Crossref]

Chung, S. H.

A. Saxena, S. H. Chung, and A. Y. Ng, “Learning depth from single monocular images,” Advances in Neural Information Processing Systems 18: 1161–1168 (2005).

Colaço, A.

Dao, M.

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 604–615 (2012).
[Crossref]

Davenport, M.

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation 28(3): 253–263 (2008).
[Crossref]

Dehghani, H.

J. Prakash, H. Dehghani, B. W. Pogue, and P. K. Yalavarthy, “Model-resolution-based basis pursuit deconvolution improves diffuse optical tomographic imaging,” IEEE Trans. Med. Imag. 33(4): 891–901 (2014).
[Crossref]

DeVore, R.

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation 28(3): 253–263 (2008).
[Crossref]

Donoho, D. L.

D. L. Donoho, A. Javanmard, and A. Montanari, “Information-theoretically optimal compressed sensing via spatial coupling and approximate message passing,” in Proceedings of IEEE International Symposium on Information Theory Proceedings (IEEE, 2012), 1231–1235.

Duarte-Carvajalino, J. M.

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: Simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7): 395–1408 (2009).
[Crossref]

Elad, M.

M. Elad, “Optimized projections for compressed sensing,” IEEE Trans. Signal Process. 55(12): 5695–5702 (2007).
[Crossref]

Eldar, Y. C.

L. Zelnik-Manor, K. Rosenblum, and Y. C. Eldar, “Sensing matrix optimization for block-sparse decoding,” IEEE Trans. Signal Process. 59(9): 4300–4312 (2011).
[Crossref]

Etienne-Cummings, R.

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 604–615 (2012).
[Crossref]

Felber, N.

P. Maechler, C. Studer, D. E. Bellasi, A. Maleki, A. Burg, N. Felber, H. Kaeslin, and R. G. Baraniuk, “VLSI design of approximate message passing for signal restoration and compressive sensing,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 579–590 (2012).
[Crossref]

Figueiredo, M. A. T.

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(12): 2992–3004 (2007).
[Crossref] [PubMed]

Freeman, W. T.

Y. Weiss, H. S. Chang, and W. T. Freeman, “Learning compressed sensing,” In Snowbird Learning Workshop, Allerton, CA (2007).

Gehm, M. E.

Gilbert, A. C.

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12): 4655–4666 (2007).
[Crossref]

Gill, P. E.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic Press, 1981).

Goodman, N. A.

Y. Gu and N. A. Goodman, “Compressed sensing kernel design for radar range profiling,” in Proceedings of 2013 IEEE Radar Conference (RADAR) (IEEE, 2013), 1–5.

Goyal, V. K.

Gu, Y.

Y. Gu and N. A. Goodman, “Compressed sensing kernel design for radar range profiling,” in Proceedings of 2013 IEEE Radar Conference (RADAR) (IEEE, 2013), 1–5.

Haupt, J.

J. Haupt and R. Nowak, “Signal reconstruction from noisy random projections,” IEEE Trans. Inf. Theory 52(9): 4036–4048 (2006).
[Crossref]

Hou, Z.

A. Yang, J. Zhang, and Z. Hou, “Optimized sensing matrix design based on parseval tight frame and matrix decomposition,” Journal of Communications 8(7): 456–462 (2013).
[Crossref]

Howell, J. C.

Howland, G. A.

Huang, L.

Huang, Y.

Javanmard, A.

D. L. Donoho, A. Javanmard, and A. Montanari, “Information-theoretically optimal compressed sensing via spatial coupling and approximate message passing,” in Proceedings of IEEE International Symposium on Information Theory Proceedings (IEEE, 2012), 1231–1235.

Kaeslin, H.

P. Maechler, C. Studer, D. E. Bellasi, A. Maleki, A. Burg, N. Felber, H. Kaeslin, and R. G. Baraniuk, “VLSI design of approximate message passing for signal restoration and compressive sensing,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 579–590 (2012).
[Crossref]

Kang, J. U.

Karkala, D.

D. Karkala and P. K. Yalavarthy, “Data-resolution based optimization of the data-collection strategy for near infrared diffuse optical tomography,” Medical Physics 39(8): 4715–4725 (2012).
[Crossref] [PubMed]

Kashter, Y.

Ke, J.

D. Sui, J. Ke, and P. Wei, “Implementing two compressed sensing algorithms on GPU,” Proc. SPIE 9273, 92730J (2014).
[Crossref]

J. Ke, D. Sui, and P. Wei, “Fast object reconstruction in block-based compressive low-light-level imagin,” Proc. SPIE 9301, 930136 (2014).
[Crossref]

P. Li, J. Ke, D. Sui, and P. Wei, “Linear bregman algorithm implemented in parallel GPU,” Proc. SPIE 9622, 962216 (2014).

J. Ke and P. Wei, “Using compressive measurement to obtain images at ultra low-light-level,” Proc. SPIE 8908, 89081O (2013).
[Crossref]

J. Ke and E. Y. Lam, “Object reconstruction in block-based compressive imaging,” Opt. Express 20(20): 22102–22117 (2012).
[Crossref] [PubMed]

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

J. Ke, M. D. Stenner, and M. A. Neifeld, “Minimum reconstruction error in feature-specific imaging,” Proc. SPIE 5817, 7–12 (2005).
[Crossref]

J. Ke, P. Wei, X. Zhang, and E. Y. Lam, “Block-based compressive low-light-level imaging,” in Proceedings of IEEE International Conference on Imaging Systems and Techneques (IEEE2013), 311–316.

Kirmani, A.

Lam, E. Y.

Levi, O.

Li, G.

G. Li, Z. Zhu, D. Yang, L. Chang, and H. Bai, “On projection matrix optimization for compressive sensing systems,” IEEE Trans. Signal Process. 61(11): 2887–2898 (2013).
[Crossref]

Li, P.

P. Li, J. Ke, D. Sui, and P. Wei, “Linear bregman algorithm implemented in parallel GPU,” Proc. SPIE 9622, 962216 (2014).

Llull, P.

X. Yuan, T. Tsai, R. Zhu, P. Llull, D. Brady, and L. Carin, “Compressive hyperspectral imaging with side information,” IEEE J. Sel. Topics Signal Process. 9(6): 964–976 (2015).
[Crossref]

Lum, D. J.

Maechler, P.

P. Maechler, C. Studer, D. E. Bellasi, A. Maleki, A. Burg, N. Felber, H. Kaeslin, and R. G. Baraniuk, “VLSI design of approximate message passing for signal restoration and compressive sensing,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 579–590 (2012).
[Crossref]

Mahalanobis, A.

Maleki, A.

P. Maechler, C. Studer, D. E. Bellasi, A. Maleki, A. Burg, N. Felber, H. Kaeslin, and R. G. Baraniuk, “VLSI design of approximate message passing for signal restoration and compressive sensing,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 579–590 (2012).
[Crossref]

Miller, R. D.

J. Xia, R. D. Miller, and Y. Xu, “Data-resolution matrix and model-resolution matrix for rayleigh-wave inversion using a damped least-squares method,” Pure and Applied Geophysics 165(7): 1227–1248 (2008).
[Crossref]

Montanari, A.

D. L. Donoho, A. Javanmard, and A. Montanari, “Information-theoretically optimal compressed sensing via spatial coupling and approximate message passing,” in Proceedings of IEEE International Symposium on Information Theory Proceedings (IEEE, 2012), 1231–1235.

Murray, W.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic Press, 1981).

Neifeld, M. A.

Ng, A. Y.

A. Saxena, M. Sun, and A. Y. Ng, “Make3D: Learning 3D scene structure from a single still image,” IEEE Trans. Pattern Anal. Mach. Intell. 30(5): 824–840 (2009).
[Crossref]

A. Saxena, S. H. Chung, and A. Y. Ng, “Learning depth from single monocular images,” Advances in Neural Information Processing Systems 18: 1161–1168 (2005).

Nguyen, D. T.

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 604–615 (2012).
[Crossref]

Nowak, R.

J. Haupt and R. Nowak, “Signal reconstruction from noisy random projections,” IEEE Trans. Inf. Theory 52(9): 4036–4048 (2006).
[Crossref]

Orchard, G.

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 604–615 (2012).
[Crossref]

Petropulu, A. P.

Y. Yu, A. P. Petropulu, and H. V. Poor, “Measurement matrix design for compressive sensing–based MIMO radar,” IEEE Trans. Signal Process. 59(11): 5338–5352 (2011).
[Crossref]

Pi, Y.

J. Xu, Y. Pi, and Z. Cao, “Optimized projection matrix for compressive sensing,” EURASIP Journal on Advances in Signal Processing 2010, 43 (2010).
[Crossref]

Pogue, B. W.

J. Prakash, H. Dehghani, B. W. Pogue, and P. K. Yalavarthy, “Model-resolution-based basis pursuit deconvolution improves diffuse optical tomographic imaging,” IEEE Trans. Med. Imag. 33(4): 891–901 (2014).
[Crossref]

Poor, H. V.

Y. Yu, A. P. Petropulu, and H. V. Poor, “Measurement matrix design for compressive sensing–based MIMO radar,” IEEE Trans. Signal Process. 59(11): 5338–5352 (2011).
[Crossref]

Posch, C.

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 604–615 (2012).
[Crossref]

Prakash, J.

J. Prakash, H. Dehghani, B. W. Pogue, and P. K. Yalavarthy, “Model-resolution-based basis pursuit deconvolution improves diffuse optical tomographic imaging,” IEEE Trans. Med. Imag. 33(4): 891–901 (2014).
[Crossref]

Rodrigues, M. R. D.

W. Chen, M. R. D. Rodrigues, and I. J. Wassell, “Projection design for statistical compressive sensing: A tight frame based approach,” IEEE Trans. Signal Process. 61(8): 2016–2029 (2013).
[Crossref]

W. Chen, M. R. D. Rodrigues, and I. J. Wassell, “On the use of unit-norm tight frames to improve the average mse performance in compressive sensing applications,” IEEE Signal Process. Lett. 19(1): 8–11 (2012).
[Crossref]

W. R. Carson, M. Chen, M. R. D. Rodrigues, R. Calderbank, and L. Carin, “Communications-inspired projection design with application to compressive sensing,” SIAM Journal on Imaging Sciences 5(4): 1185–1212 (2012).
[Crossref]

Rosenblum, K.

L. Zelnik-Manor, K. Rosenblum, and Y. C. Eldar, “Sensing matrix optimization for block-sparse decoding,” IEEE Trans. Signal Process. 59(9): 4300–4312 (2011).
[Crossref]

Sapiro, G.

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: Simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7): 395–1408 (2009).
[Crossref]

Saxena, A.

A. Saxena, M. Sun, and A. Y. Ng, “Make3D: Learning 3D scene structure from a single still image,” IEEE Trans. Pattern Anal. Mach. Intell. 30(5): 824–840 (2009).
[Crossref]

A. Saxena, S. H. Chung, and A. Y. Ng, “Learning depth from single monocular images,” Advances in Neural Information Processing Systems 18: 1161–1168 (2005).

Stenner, M. D.

J. Ke, M. D. Stenner, and M. A. Neifeld, “Minimum reconstruction error in feature-specific imaging,” Proc. SPIE 5817, 7–12 (2005).
[Crossref]

Stern, A.

Studer, C.

P. Maechler, C. Studer, D. E. Bellasi, A. Maleki, A. Burg, N. Felber, H. Kaeslin, and R. G. Baraniuk, “VLSI design of approximate message passing for signal restoration and compressive sensing,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 579–590 (2012).
[Crossref]

Sui, D.

P. Li, J. Ke, D. Sui, and P. Wei, “Linear bregman algorithm implemented in parallel GPU,” Proc. SPIE 9622, 962216 (2014).

D. Sui, J. Ke, and P. Wei, “Implementing two compressed sensing algorithms on GPU,” Proc. SPIE 9273, 92730J (2014).
[Crossref]

J. Ke, D. Sui, and P. Wei, “Fast object reconstruction in block-based compressive low-light-level imagin,” Proc. SPIE 9301, 930136 (2014).
[Crossref]

Sun, M.

A. Saxena, M. Sun, and A. Y. Ng, “Make3D: Learning 3D scene structure from a single still image,” IEEE Trans. Pattern Anal. Mach. Intell. 30(5): 824–840 (2009).
[Crossref]

Suo, Y.

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 604–615 (2012).
[Crossref]

Tran, T. D.

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 604–615 (2012).
[Crossref]

Tropp, J. A.

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12): 4655–4666 (2007).
[Crossref]

Tsai, T.

X. Yuan, T. Tsai, R. Zhu, P. Llull, D. Brady, and L. Carin, “Compressive hyperspectral imaging with side information,” IEEE J. Sel. Topics Signal Process. 9(6): 964–976 (2015).
[Crossref]

Wakin, M.

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation 28(3): 253–263 (2008).
[Crossref]

Ware, M. R.

Wassell, I. J.

W. Chen, M. R. D. Rodrigues, and I. J. Wassell, “Projection design for statistical compressive sensing: A tight frame based approach,” IEEE Trans. Signal Process. 61(8): 2016–2029 (2013).
[Crossref]

W. Chen, M. R. D. Rodrigues, and I. J. Wassell, “On the use of unit-norm tight frames to improve the average mse performance in compressive sensing applications,” IEEE Signal Process. Lett. 19(1): 8–11 (2012).
[Crossref]

Wei, P.

J. Ke, D. Sui, and P. Wei, “Fast object reconstruction in block-based compressive low-light-level imagin,” Proc. SPIE 9301, 930136 (2014).
[Crossref]

D. Sui, J. Ke, and P. Wei, “Implementing two compressed sensing algorithms on GPU,” Proc. SPIE 9273, 92730J (2014).
[Crossref]

P. Li, J. Ke, D. Sui, and P. Wei, “Linear bregman algorithm implemented in parallel GPU,” Proc. SPIE 9622, 962216 (2014).

J. Ke and P. Wei, “Using compressive measurement to obtain images at ultra low-light-level,” Proc. SPIE 8908, 89081O (2013).
[Crossref]

J. Ke, P. Wei, X. Zhang, and E. Y. Lam, “Block-based compressive low-light-level imaging,” in Proceedings of IEEE International Conference on Imaging Systems and Techneques (IEEE2013), 311–316.

Weiss, Y.

Y. Weiss, H. S. Chang, and W. T. Freeman, “Learning compressed sensing,” In Snowbird Learning Workshop, Allerton, CA (2007).

Wong, F. N. C.

Wright, M. H.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic Press, 1981).

Xia, J.

J. Xia, R. D. Miller, and Y. Xu, “Data-resolution matrix and model-resolution matrix for rayleigh-wave inversion using a damped least-squares method,” Pure and Applied Geophysics 165(7): 1227–1248 (2008).
[Crossref]

Xu, D.

Xu, J.

J. Xu, Y. Pi, and Z. Cao, “Optimized projection matrix for compressive sensing,” EURASIP Journal on Advances in Signal Processing 2010, 43 (2010).
[Crossref]

Xu, Y.

J. Xia, R. D. Miller, and Y. Xu, “Data-resolution matrix and model-resolution matrix for rayleigh-wave inversion using a damped least-squares method,” Pure and Applied Geophysics 165(7): 1227–1248 (2008).
[Crossref]

Xu, Z.

Yalavarthy, P. K.

J. Prakash, H. Dehghani, B. W. Pogue, and P. K. Yalavarthy, “Model-resolution-based basis pursuit deconvolution improves diffuse optical tomographic imaging,” IEEE Trans. Med. Imag. 33(4): 891–901 (2014).
[Crossref]

D. Karkala and P. K. Yalavarthy, “Data-resolution based optimization of the data-collection strategy for near infrared diffuse optical tomography,” Medical Physics 39(8): 4715–4725 (2012).
[Crossref] [PubMed]

Yang, A.

A. Yang, J. Zhang, and Z. Hou, “Optimized sensing matrix design based on parseval tight frame and matrix decomposition,” Journal of Communications 8(7): 456–462 (2013).
[Crossref]

Yang, D.

G. Li, Z. Zhu, D. Yang, L. Chang, and H. Bai, “On projection matrix optimization for compressive sensing systems,” IEEE Trans. Signal Process. 61(11): 2887–2898 (2013).
[Crossref]

Yu, Y.

Y. Yu, A. P. Petropulu, and H. V. Poor, “Measurement matrix design for compressive sensing–based MIMO radar,” IEEE Trans. Signal Process. 59(11): 5338–5352 (2011).
[Crossref]

Yuan, X.

X. Yuan, T. Tsai, R. Zhu, P. Llull, D. Brady, and L. Carin, “Compressive hyperspectral imaging with side information,” IEEE J. Sel. Topics Signal Process. 9(6): 964–976 (2015).
[Crossref]

Zelnik-Manor, L.

L. Zelnik-Manor, K. Rosenblum, and Y. C. Eldar, “Sensing matrix optimization for block-sparse decoding,” IEEE Trans. Signal Process. 59(9): 4300–4312 (2011).
[Crossref]

Zhang, J.

A. Yang, J. Zhang, and Z. Hou, “Optimized sensing matrix design based on parseval tight frame and matrix decomposition,” Journal of Communications 8(7): 456–462 (2013).
[Crossref]

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 604–615 (2012).
[Crossref]

Zhang, X.

J. Ke, P. Wei, X. Zhang, and E. Y. Lam, “Block-based compressive low-light-level imaging,” in Proceedings of IEEE International Conference on Imaging Systems and Techneques (IEEE2013), 311–316.

Zhu, R.

X. Yuan, T. Tsai, R. Zhu, P. Llull, D. Brady, and L. Carin, “Compressive hyperspectral imaging with side information,” IEEE J. Sel. Topics Signal Process. 9(6): 964–976 (2015).
[Crossref]

Zhu, Z.

G. Li, Z. Zhu, D. Yang, L. Chang, and H. Bai, “On projection matrix optimization for compressive sensing systems,” IEEE Trans. Signal Process. 61(11): 2887–2898 (2013).
[Crossref]

Advances in Neural Information Processing Systems (1)

A. Saxena, S. H. Chung, and A. Y. Ng, “Learning depth from single monocular images,” Advances in Neural Information Processing Systems 18: 1161–1168 (2005).

Appl. Opt. (4)

Comptes Rendus Mathematique (1)

E. J. Candès, “The restricted isometry property and its implications for compressed sensing,” Comptes Rendus Mathematique 346(9): 589–592 (2008).
[Crossref]

Constructive Approximation (1)

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” Constructive Approximation 28(3): 253–263 (2008).
[Crossref]

EURASIP Journal on Advances in Signal Processing (1)

J. Xu, Y. Pi, and Z. Cao, “Optimized projection matrix for compressive sensing,” EURASIP Journal on Advances in Signal Processing 2010, 43 (2010).
[Crossref]

IEEE J. Emerg. Sel. Topic Circuits Syst. (2)

P. Maechler, C. Studer, D. E. Bellasi, A. Maleki, A. Burg, N. Felber, H. Kaeslin, and R. G. Baraniuk, “VLSI design of approximate message passing for signal restoration and compressive sensing,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 579–590 (2012).
[Crossref]

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE J. Emerg. Sel. Topic Circuits Syst. 2(3): 604–615 (2012).
[Crossref]

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

X. Yuan, T. Tsai, R. Zhu, P. Llull, D. Brady, and L. Carin, “Compressive hyperspectral imaging with side information,” IEEE J. Sel. Topics Signal Process. 9(6): 964–976 (2015).
[Crossref]

IEEE Signal Process. Lett. (1)

W. Chen, M. R. D. Rodrigues, and I. J. Wassell, “On the use of unit-norm tight frames to improve the average mse performance in compressive sensing applications,” IEEE Signal Process. Lett. 19(1): 8–11 (2012).
[Crossref]

IEEE Trans. Image Process. (2)

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: Simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18(7): 395–1408 (2009).
[Crossref]

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(12): 2992–3004 (2007).
[Crossref] [PubMed]

IEEE Trans. Inf. Theory (2)

J. Haupt and R. Nowak, “Signal reconstruction from noisy random projections,” IEEE Trans. Inf. Theory 52(9): 4036–4048 (2006).
[Crossref]

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12): 4655–4666 (2007).
[Crossref]

IEEE Trans. Med. Imag. (1)

J. Prakash, H. Dehghani, B. W. Pogue, and P. K. Yalavarthy, “Model-resolution-based basis pursuit deconvolution improves diffuse optical tomographic imaging,” IEEE Trans. Med. Imag. 33(4): 891–901 (2014).
[Crossref]

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

A. Saxena, M. Sun, and A. Y. Ng, “Make3D: Learning 3D scene structure from a single still image,” IEEE Trans. Pattern Anal. Mach. Intell. 30(5): 824–840 (2009).
[Crossref]

IEEE Trans. Signal Process. (5)

W. Chen, M. R. D. Rodrigues, and I. J. Wassell, “Projection design for statistical compressive sensing: A tight frame based approach,” IEEE Trans. Signal Process. 61(8): 2016–2029 (2013).
[Crossref]

G. Li, Z. Zhu, D. Yang, L. Chang, and H. Bai, “On projection matrix optimization for compressive sensing systems,” IEEE Trans. Signal Process. 61(11): 2887–2898 (2013).
[Crossref]

Y. Yu, A. P. Petropulu, and H. V. Poor, “Measurement matrix design for compressive sensing–based MIMO radar,” IEEE Trans. Signal Process. 59(11): 5338–5352 (2011).
[Crossref]

L. Zelnik-Manor, K. Rosenblum, and Y. C. Eldar, “Sensing matrix optimization for block-sparse decoding,” IEEE Trans. Signal Process. 59(9): 4300–4312 (2011).
[Crossref]

M. Elad, “Optimized projections for compressed sensing,” IEEE Trans. Signal Process. 55(12): 5695–5702 (2007).
[Crossref]

J. Opt. Soc. Am. A (2)

Journal of Communications (1)

A. Yang, J. Zhang, and Z. Hou, “Optimized sensing matrix design based on parseval tight frame and matrix decomposition,” Journal of Communications 8(7): 456–462 (2013).
[Crossref]

Medical Physics (1)

D. Karkala and P. K. Yalavarthy, “Data-resolution based optimization of the data-collection strategy for near infrared diffuse optical tomography,” Medical Physics 39(8): 4715–4725 (2012).
[Crossref] [PubMed]

Opt. Express (4)

Proc. SPIE (5)

J. Ke, M. D. Stenner, and M. A. Neifeld, “Minimum reconstruction error in feature-specific imaging,” Proc. SPIE 5817, 7–12 (2005).
[Crossref]

J. Ke and P. Wei, “Using compressive measurement to obtain images at ultra low-light-level,” Proc. SPIE 8908, 89081O (2013).
[Crossref]

J. Ke, D. Sui, and P. Wei, “Fast object reconstruction in block-based compressive low-light-level imagin,” Proc. SPIE 9301, 930136 (2014).
[Crossref]

D. Sui, J. Ke, and P. Wei, “Implementing two compressed sensing algorithms on GPU,” Proc. SPIE 9273, 92730J (2014).
[Crossref]

P. Li, J. Ke, D. Sui, and P. Wei, “Linear bregman algorithm implemented in parallel GPU,” Proc. SPIE 9622, 962216 (2014).

Pure and Applied Geophysics (1)

J. Xia, R. D. Miller, and Y. Xu, “Data-resolution matrix and model-resolution matrix for rayleigh-wave inversion using a damped least-squares method,” Pure and Applied Geophysics 165(7): 1227–1248 (2008).
[Crossref]

SIAM Journal on Imaging Sciences (1)

W. R. Carson, M. Chen, M. R. D. Rodrigues, R. Calderbank, and L. Carin, “Communications-inspired projection design with application to compressive sensing,” SIAM Journal on Imaging Sciences 5(4): 1185–1212 (2012).
[Crossref]

Other (6)

Y. Gu and N. A. Goodman, “Compressed sensing kernel design for radar range profiling,” in Proceedings of 2013 IEEE Radar Conference (RADAR) (IEEE, 2013), 1–5.

R. Baldick, Applied Optimization: Formulation and Algorithms for Engineering Systems(Cambridge University, 2006).
[Crossref]

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic Press, 1981).

J. Ke, P. Wei, X. Zhang, and E. Y. Lam, “Block-based compressive low-light-level imaging,” in Proceedings of IEEE International Conference on Imaging Systems and Techneques (IEEE2013), 311–316.

Y. Weiss, H. S. Chang, and W. T. Freeman, “Learning compressed sensing,” In Snowbird Learning Workshop, Allerton, CA (2007).

D. L. Donoho, A. Javanmard, and A. Montanari, “Information-theoretically optimal compressed sensing via spatial coupling and approximate message passing,” in Proceedings of IEEE International Symposium on Information Theory Proceedings (IEEE, 2012), 1231–1235.

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Figures (12)

Fig. 1
Fig. 1 A system diagram for compressive L3-imaging.
Fig. 2
Fig. 2 Object examples of size (a) (196 × 128) [43,44], and (b) (1056 × 1920).
Fig. 3
Fig. 3 Reconstruction RMSE for objects of size (a) (196×128) and (b) (1056×1920), when M = 32 Hadamard, DCT, and PCA features are collected for (32×32) object blocks.
Fig. 4
Fig. 4 (a) The Hadamard vectors sorted using measurement SNR, (b) the optimal binary vector set or the optimal solution for problem P3, (c) the suboptimal solution for P3 which has the minimal feature measurement dynamic range, when M is 8 for 32 × 32 blocks.
Fig. 5
Fig. 5 When M = 8 features are collected for 32×32 blocks, the normalized RMSE using (a) the sorted Hadamard, DCT, PCA, Frmse, and Fdyn matrices, and (b) the standard Hadamard, random binary, and Frmse matrices.
Fig. 6
Fig. 6 When M = 8 features are collected for 32×32 blocks, the normalized Fourier transforms of the vectors in (a) the standard Hadamard matrix, (b) Hsnr, and (c) Fdyn.
Fig. 7
Fig. 7 (a) The optimal binary vector set or the optimal solution for problem P3, (b) the suboptimal solution for P3 which has the minimal feature measurement dynamic range, (c) the normalized RMSE for sorted Hadamard, DCT, PCA matrices, Frmse, and Fdyn, and the normalized Fourier transforms of the vectors in (d) Hsnr and (e) Fdyn, when M is 16 for 32 × 32 blocks.
Fig. 8
Fig. 8 The object reconstruction using (a) conventional imaging, (b) Hmean, (c) Hsnr, and (d) Fdyn, when M = 16 features are collected for 32 × 32 blocks and σ is 148.67.
Fig. 9
Fig. 9 The object reconstructions (a)&(b) using Hsnr, and (c)&(d) using Fdyn when M = 16 features are collected for 32 × 32 blocks and σ is 148.67.
Fig. 10
Fig. 10 Normalized RMSE for different sets of nonnegative sensing vectors when M = 16 features are collected for 32 × 32 block.
Fig. 11
Fig. 11 Normalized RMSE for different sets of nonnegative sensing vectors when M = 16 features are collected for 32 × 32 blocks. The object blocks are sparse in the wavelet domain. The sparsity is K = 64.
Fig. 12
Fig. 12 (a) The original object which is sparse in the wavelet domain. The sparsity for each 32 × 32 block is K = 4. The object reconstructions using (b) the fast linearized Bregman iterative method with a binary random matrix, (c) the fast linearized Bregman iterative method with Fdyn, and (d) Wiener operator with Fdyn, when M = 16 features are collected for each block and σ is 148.67.

Tables (4)

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Table 1 The cost function ε(F) = Tr{FRxFT} in P1 when M = 32 features are obtained using PCA, DCT, and Hadamard matrices. (*The values listed in the table are ε(F)/106.)

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Table 2 The dynamic ranges of M = 8 features obtained using different sensing matrices. (*The values listed in the table are the actual values divided by 104.)

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Table 3 The dynamic ranges of M = 16 features obtained using different nonnegative matrices. (*The values listed in the table are the actual values divided by 104.)

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Table 4 The (measurement collection time, reconstruction time) for different kinds of sensing matrices and linear/nonlinear methods. 16 feature are collected for each block. The DMD working frequency is set as 32kHz.

Equations (26)

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y = F x + n ,
S N R CS = E { F x 2 } E { n 2 } = Tr { FR x F T } M σ 2 .
P 1 : max F subject to Tr { FR x F T } FF T = I .
P 1 a : max H subject to Tr { HDH T } HH T = I .
F = [ q 1 q 2 q M 1 α q M + 1 α 2 q M + 1 ] T
W = R x F T ( FR x F T + σ 2 I ) 1 .
M S E CS = E { x est x 2 } = Tr { R x } Tr { FR x 2 F T ( FR x F T + σ 2 I ) 1 } .
P 2 : max F subject to Tr { FR x 2 F T ( FR x F T + σ 2 I ) 1 } FF T = I .
F = [ q 1 q 2 q M 1 α q M + 1 α 2 q M + 1 ] T ,
Tr { FR x 2 F T ( FR x F T + σ 2 I ) 1 } = j = 1 M d i 2 d i + σ 2 + d M 2 α 2 + d M + 1 2 ( 1 α 2 ) d M α 2 + d M + 1 ( 1 α 2 ) + σ 2 d M 2 d M + σ 2 = j = 1 M d i 2 d i + σ 2 + ( 1 α 2 ) [ σ 2 ( d M + 1 2 d M 2 ) + d m d M + 1 ( d M + 1 d M ) ] ( d M α 2 + d M + 1 ( 1 α 2 ) + σ 2 ) ( d M + σ 2 ) j = 1 M d i 2 d i + σ 2 ,
P 3 : min A subject to ε ( A ) = N AQ P C A T sgn ( AQ PCA T ) F 2 AA T = 1 ,
G i j = { k = 1 M A i k 2 1 , i = j k = 1 M A i k A j k , otherwise .
( A , λ ) = i = 1 M j = 1 N [ N AQ PCA T sgn ( AQ PCA T ) ] i j 2 + i = 1 M j = i M [ λ . G ] i j ,
[ AA 2 ( a ( ν ) , λ ( ν ) ) J ( a ( ν ) ) T J ( a ( ν ) ) 0 ] [ Δ a ( ν ) Δ λ ( ν ) ] = [ ε ( a ( ν ) ) + J ( a ( ν ) ) T λ ( ν ) g ( a ( ν ) ) ] ,
[ a ( ν + 1 ) λ ( ν + 1 ) ] = [ Δ a ( ν ) Δ λ ( ν ) ] + α [ a ( ν ) λ ( ν ) ] .
2 ( a , λ ) A i j A i j = 2 N δ ( i i ) δ ( j j ) + 2 λ i i δ ( j j ) .
G i j A i j = δ ( i i ) A j j + δ ( j i ) A i j .
ε A i j = 2 N A i j 2 N [ sgn ( XQ PCA T ) Q PCA ] i j .
ε A i j = 2 k = 1 N [ N [ AQ PCA T ] i k s g n ( [ AQ PCA T ] i k ) ] [ N [ Q PCA T ] j k δ ( [ AQ PCA T ] i k ) [ Q PCA T ] j k ]
ε A i j = 2 k = 1 N [ N [ AQ PCA T ] i k s g n ( [ AQ PCA T ] i k ) ] N [ Q PCA T ] j k = 2 N [ AQ PCA T Q PCA ] i j 2 N [ s g n ( AQ PCA T ) Q PCA ] i j = 2 N [ A ] i j 2 N [ s g n ( AQ PCA T ) Q PCA ] i j ,
2 ε A i j A i j = 2 N δ ( i i ) δ ( j j ) 2 N A i j [ k = 1 N s g n ( [ AQ PCA T ] i k ) [ Q PCA ] k j ] = 2 N δ ( i i ) δ ( j j ) 2 N δ ( i i ) k = 1 N δ ( [ AQ PCA T ] i k ) [ Q PCA T ] i k [ Q PCA ] k j = 2 N δ ( i i ) δ ( j j )
ε λ A i j = k , k = 1 M [ λ . * A i j ( AA T 1 ) ] k k = k , k = 1 M λ k k G k k A i j
C k k A i j = δ ( k i ) A k j + δ ( k i ) A k j .
ε λ A i j = k , k = 1 M λ k k ( δ ( k i ) A k j + δ ( k i ) A k j ) = k = 1 M 2 λ i k A k j
2 ε λ A i j A i j = ( k = 1 M 2 λ i k A k j ) A i j = 2 λ i i δ ( j j )
2 A i j A i j = 2 ε A i j A i j + 2 ε λ A i j A i j = 2 N δ ( i i ) δ ( j j ) + 2 λ i i δ ( j j )

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