Abstract

The tendency of natural scenes to cluster around low frequencies is not only useful in image compression, it also can prove advantageous in novel infrared and hyperspectral image acquisition. In this paper, we exploit this signal model with two approaches to enhance the quality of compressive imaging as implemented in a single-pixel compressive camera and compare these results against purely random acquisition. We combine projection patterns that can efficiently extract the model-based information with subsequent random projections to form the hybrid pattern sets. With the first approach, we generate low-frequency patterns via a direct transform. As an alternative, we also used principal component analysis of an image library to identify the low-frequency components. We present the first (to the best of our knowledge) experimental validation of this hybrid signal model on real data. For both methods, we acquire comparable quality of reconstructions while acquiring only half the number of measurements needed by traditional random sequences. The optimal combination of hybrid patterns and the effects of noise on image reconstruction are also discussed.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Baron, M. F. Duarte, S. Sarvotham, M. B. Wakin, and R. G. Baraniuk, “An information-theoretic approach to distributed compressed sensing,” in Proceedings of 45rd Annual Allerton Conference on Communication, Control, and Computing, Allerton, Illinois,2005.
  2. D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Electronic Imaging 2006 (International Society for Optics and Photonics, 2006), p. 606509.
  3. 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).
    [CrossRef]
  4. M. A. Davenport, J. N. Laska, P. T. Boufounos, and R. G. Baraniuk, “A simple proof that random matrices are democratic,” arXiv:0911.0736 (2009).
  5. T. Goldstein and S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).
    [CrossRef]
  6. R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56, 1982–2001 (2010).
    [CrossRef]
  7. Y. C. Eldar, P. Kuppinger, and H. Bolcskei, “Block-sparse signals: uncertainty relations and efficient recovery,” IEEE Trans. Signal Process. 58, 3042–3054 (2010).
    [CrossRef]
  8. J. Huang and T. Zhang, “The benefit of group sparsity,” Annals Stat. 38, 1978–2004 (2010).
  9. V. Cevher, P. Indyk, C. Hegde, and R. G. Baraniuk, “Recovery of clustered sparse signals from compressive measurements,” (2009).
  10. A. Ashok and M. A. Neifeld, “Compressive imaging: hybrid measurement basis design,” J. Opt. Soc. Am. A 28, 1041–1050 (2011).
    [CrossRef]
  11. B. Adcock, A. C. Hansen, C. Poon, and B. Roman, “Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing,” arXiv:1302.0561 (2013).
  12. A. Ashok, L. Huang, and M. A. Neifeld, “Information optimal compressive sensing: static measurement design,” J. Opt. Soc. Am. A 30, 831–853 (2013).
    [CrossRef]
  13. E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
    [CrossRef]
  14. R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
    [CrossRef]
  15. E. Van Den Berg and M. P. Friedlander, “SPGL1: a solver for large-scale sparse reconstruction,” http://www.cs.ubc.ca/labs/scl/spgl1 , 2007.
  16. C. Tsai and D. G. Nishimura, “Reduced aliasing artifacts using variable-density k-space sampling trajectories,” Magn. Reson. Med. 43, 452–458 (2000).
    [CrossRef]
  17. M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).
    [CrossRef]
  18. A. E. Waters, A. C. Sankaranarayanan, and R. G. Baraniuk, “SpaRCS: recovering low-rank and sparse matrices from compressive measurements,” in Advances in Neural Information Processing Systems (2011), pp. 1089–1097.
  19. “Columbus large image format (CLIF) 2007 dataset,” https://www.sdms.afrl.af.mil/index.php?collection=clif2007 .
  20. J. Liang and T. D. Tran, “Fast multiplierless approximations of the DCT with the lifting scheme,” IEEE Trans. Signal Process. 49, 3032–3044 (2001).
    [CrossRef]
  21. D. Bottisti and R. Muise, “Tree-based adaptive measurement design for compressive imaging under device constraints,” Proc. SPIE 8748, 874802 (2013).
    [CrossRef]
  22. A. C. Sankaranarayanan, C. Studer, and R. G. Baraniuk, “CS-MUVI: video compressive sensing for spatial-multiplexing cameras,” in IEEE International Conference on Computational Photography (ICCP) (2012), pp. 1–10.
  23. L. Xu, A. C. Sankaranarayanan, C. Studer, Y. Li, R. G. Baraniuk, and K. F. Kelly, “Multi-scale compressive video acquisition,” in Computational Optical Sensing and Imaging (Optical Society of America, 2013), paper CW2C.4.
  24. T. Goldstein, L. Xu, K. F. Kelly, and R. G. Baraniuk, “The STONE transform: multi-resolution image enhancement and real-time compressive video,” arXiv:1311.34056 (2013).

2013

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

D. Bottisti and R. Muise, “Tree-based adaptive measurement design for compressive imaging under device constraints,” Proc. SPIE 8748, 874802 (2013).
[CrossRef]

2011

2010

R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56, 1982–2001 (2010).
[CrossRef]

Y. C. Eldar, P. Kuppinger, and H. Bolcskei, “Block-sparse signals: uncertainty relations and efficient recovery,” IEEE Trans. Signal Process. 58, 3042–3054 (2010).
[CrossRef]

J. Huang and T. Zhang, “The benefit of group sparsity,” Annals Stat. 38, 1978–2004 (2010).

2009

T. Goldstein and S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).
[CrossRef]

2008

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).
[CrossRef]

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).
[CrossRef]

2007

R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
[CrossRef]

2006

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

2001

J. Liang and T. D. Tran, “Fast multiplierless approximations of the DCT with the lifting scheme,” IEEE Trans. Signal Process. 49, 3032–3044 (2001).
[CrossRef]

2000

C. Tsai and D. G. Nishimura, “Reduced aliasing artifacts using variable-density k-space sampling trajectories,” Magn. Reson. Med. 43, 452–458 (2000).
[CrossRef]

Adcock, B.

B. Adcock, A. C. Hansen, C. Poon, and B. Roman, “Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing,” arXiv:1302.0561 (2013).

Ashok, A.

Baraniuk, R. G.

R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56, 1982–2001 (2010).
[CrossRef]

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).
[CrossRef]

R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
[CrossRef]

V. Cevher, P. Indyk, C. Hegde, and R. G. Baraniuk, “Recovery of clustered sparse signals from compressive measurements,” (2009).

A. E. Waters, A. C. Sankaranarayanan, and R. G. Baraniuk, “SpaRCS: recovering low-rank and sparse matrices from compressive measurements,” in Advances in Neural Information Processing Systems (2011), pp. 1089–1097.

A. C. Sankaranarayanan, C. Studer, and R. G. Baraniuk, “CS-MUVI: video compressive sensing for spatial-multiplexing cameras,” in IEEE International Conference on Computational Photography (ICCP) (2012), pp. 1–10.

M. A. Davenport, J. N. Laska, P. T. Boufounos, and R. G. Baraniuk, “A simple proof that random matrices are democratic,” arXiv:0911.0736 (2009).

D. Baron, M. F. Duarte, S. Sarvotham, M. B. Wakin, and R. G. Baraniuk, “An information-theoretic approach to distributed compressed sensing,” in Proceedings of 45rd Annual Allerton Conference on Communication, Control, and Computing, Allerton, Illinois,2005.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Electronic Imaging 2006 (International Society for Optics and Photonics, 2006), p. 606509.

L. Xu, A. C. Sankaranarayanan, C. Studer, Y. Li, R. G. Baraniuk, and K. F. Kelly, “Multi-scale compressive video acquisition,” in Computational Optical Sensing and Imaging (Optical Society of America, 2013), paper CW2C.4.

T. Goldstein, L. Xu, K. F. Kelly, and R. G. Baraniuk, “The STONE transform: multi-resolution image enhancement and real-time compressive video,” arXiv:1311.34056 (2013).

Baron, D.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Electronic Imaging 2006 (International Society for Optics and Photonics, 2006), p. 606509.

D. Baron, M. F. Duarte, S. Sarvotham, M. B. Wakin, and R. G. Baraniuk, “An information-theoretic approach to distributed compressed sensing,” in Proceedings of 45rd Annual Allerton Conference on Communication, Control, and Computing, Allerton, Illinois,2005.

Bolcskei, H.

Y. C. Eldar, P. Kuppinger, and H. Bolcskei, “Block-sparse signals: uncertainty relations and efficient recovery,” IEEE Trans. Signal Process. 58, 3042–3054 (2010).
[CrossRef]

Bottisti, D.

D. Bottisti and R. Muise, “Tree-based adaptive measurement design for compressive imaging under device constraints,” Proc. SPIE 8748, 874802 (2013).
[CrossRef]

Boufounos, P. T.

M. A. Davenport, J. N. Laska, P. T. Boufounos, and R. G. Baraniuk, “A simple proof that random matrices are democratic,” arXiv:0911.0736 (2009).

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. Theory 52, 489–509 (2006).
[CrossRef]

Cevher, V.

R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56, 1982–2001 (2010).
[CrossRef]

V. Cevher, P. Indyk, C. Hegde, and R. G. Baraniuk, “Recovery of clustered sparse signals from compressive measurements,” (2009).

Davenport, M. A.

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).
[CrossRef]

M. A. Davenport, J. N. Laska, P. T. Boufounos, and R. G. Baraniuk, “A simple proof that random matrices are democratic,” arXiv:0911.0736 (2009).

Donoho, D. L.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).
[CrossRef]

Duarte, M. F.

R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56, 1982–2001 (2010).
[CrossRef]

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).
[CrossRef]

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Electronic Imaging 2006 (International Society for Optics and Photonics, 2006), p. 606509.

D. Baron, M. F. Duarte, S. Sarvotham, M. B. Wakin, and R. G. Baraniuk, “An information-theoretic approach to distributed compressed sensing,” in Proceedings of 45rd Annual Allerton Conference on Communication, Control, and Computing, Allerton, Illinois,2005.

Eldar, Y. C.

Y. C. Eldar, P. Kuppinger, and H. Bolcskei, “Block-sparse signals: uncertainty relations and efficient recovery,” IEEE Trans. Signal Process. 58, 3042–3054 (2010).
[CrossRef]

Goldstein, T.

T. Goldstein and S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).
[CrossRef]

T. Goldstein, L. Xu, K. F. Kelly, and R. G. Baraniuk, “The STONE transform: multi-resolution image enhancement and real-time compressive video,” arXiv:1311.34056 (2013).

Hansen, A. C.

B. Adcock, A. C. Hansen, C. Poon, and B. Roman, “Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing,” arXiv:1302.0561 (2013).

Hegde, C.

R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56, 1982–2001 (2010).
[CrossRef]

V. Cevher, P. Indyk, C. Hegde, and R. G. Baraniuk, “Recovery of clustered sparse signals from compressive measurements,” (2009).

Huang, J.

J. Huang and T. Zhang, “The benefit of group sparsity,” Annals Stat. 38, 1978–2004 (2010).

Huang, L.

Indyk, P.

V. Cevher, P. Indyk, C. Hegde, and R. G. Baraniuk, “Recovery of clustered sparse signals from compressive measurements,” (2009).

Kelly, K. F.

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).
[CrossRef]

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Electronic Imaging 2006 (International Society for Optics and Photonics, 2006), p. 606509.

T. Goldstein, L. Xu, K. F. Kelly, and R. G. Baraniuk, “The STONE transform: multi-resolution image enhancement and real-time compressive video,” arXiv:1311.34056 (2013).

L. Xu, A. C. Sankaranarayanan, C. Studer, Y. Li, R. G. Baraniuk, and K. F. Kelly, “Multi-scale compressive video acquisition,” in Computational Optical Sensing and Imaging (Optical Society of America, 2013), paper CW2C.4.

Kuppinger, P.

Y. C. Eldar, P. Kuppinger, and H. Bolcskei, “Block-sparse signals: uncertainty relations and efficient recovery,” IEEE Trans. Signal Process. 58, 3042–3054 (2010).
[CrossRef]

Laska, J. N.

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).
[CrossRef]

M. A. Davenport, J. N. Laska, P. T. Boufounos, and R. G. Baraniuk, “A simple proof that random matrices are democratic,” arXiv:0911.0736 (2009).

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Electronic Imaging 2006 (International Society for Optics and Photonics, 2006), p. 606509.

Li, Y.

L. Xu, A. C. Sankaranarayanan, C. Studer, Y. Li, R. G. Baraniuk, and K. F. Kelly, “Multi-scale compressive video acquisition,” in Computational Optical Sensing and Imaging (Optical Society of America, 2013), paper CW2C.4.

Liang, J.

J. Liang and T. D. Tran, “Fast multiplierless approximations of the DCT with the lifting scheme,” IEEE Trans. Signal Process. 49, 3032–3044 (2001).
[CrossRef]

Lustig, M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).
[CrossRef]

Muise, R.

D. Bottisti and R. Muise, “Tree-based adaptive measurement design for compressive imaging under device constraints,” Proc. SPIE 8748, 874802 (2013).
[CrossRef]

Neifeld, M. A.

Nishimura, D. G.

C. Tsai and D. G. Nishimura, “Reduced aliasing artifacts using variable-density k-space sampling trajectories,” Magn. Reson. Med. 43, 452–458 (2000).
[CrossRef]

Osher, S.

T. Goldstein and S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).
[CrossRef]

Pauly, J. M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).
[CrossRef]

Poon, C.

B. Adcock, A. C. Hansen, C. Poon, and B. Roman, “Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing,” arXiv:1302.0561 (2013).

Roman, B.

B. Adcock, A. C. Hansen, C. Poon, and B. Roman, “Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing,” arXiv:1302.0561 (2013).

Romberg, J.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Sankaranarayanan, A. C.

A. C. Sankaranarayanan, C. Studer, and R. G. Baraniuk, “CS-MUVI: video compressive sensing for spatial-multiplexing cameras,” in IEEE International Conference on Computational Photography (ICCP) (2012), pp. 1–10.

L. Xu, A. C. Sankaranarayanan, C. Studer, Y. Li, R. G. Baraniuk, and K. F. Kelly, “Multi-scale compressive video acquisition,” in Computational Optical Sensing and Imaging (Optical Society of America, 2013), paper CW2C.4.

A. E. Waters, A. C. Sankaranarayanan, and R. G. Baraniuk, “SpaRCS: recovering low-rank and sparse matrices from compressive measurements,” in Advances in Neural Information Processing Systems (2011), pp. 1089–1097.

Santos, J. M.

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).
[CrossRef]

Sarvotham, S.

D. Baron, M. F. Duarte, S. Sarvotham, M. B. Wakin, and R. G. Baraniuk, “An information-theoretic approach to distributed compressed sensing,” in Proceedings of 45rd Annual Allerton Conference on Communication, Control, and Computing, Allerton, Illinois,2005.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Electronic Imaging 2006 (International Society for Optics and Photonics, 2006), p. 606509.

Studer, C.

L. Xu, A. C. Sankaranarayanan, C. Studer, Y. Li, R. G. Baraniuk, and K. F. Kelly, “Multi-scale compressive video acquisition,” in Computational Optical Sensing and Imaging (Optical Society of America, 2013), paper CW2C.4.

A. C. Sankaranarayanan, C. Studer, and R. G. Baraniuk, “CS-MUVI: video compressive sensing for spatial-multiplexing cameras,” in IEEE International Conference on Computational Photography (ICCP) (2012), pp. 1–10.

Sun, T.

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).
[CrossRef]

Takhar, D.

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).
[CrossRef]

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Electronic Imaging 2006 (International Society for Optics and Photonics, 2006), p. 606509.

Tao, T.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Tran, T. D.

J. Liang and T. D. Tran, “Fast multiplierless approximations of the DCT with the lifting scheme,” IEEE Trans. Signal Process. 49, 3032–3044 (2001).
[CrossRef]

Tsai, C.

C. Tsai and D. G. Nishimura, “Reduced aliasing artifacts using variable-density k-space sampling trajectories,” Magn. Reson. Med. 43, 452–458 (2000).
[CrossRef]

Wakin, M. B.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Electronic Imaging 2006 (International Society for Optics and Photonics, 2006), p. 606509.

D. Baron, M. F. Duarte, S. Sarvotham, M. B. Wakin, and R. G. Baraniuk, “An information-theoretic approach to distributed compressed sensing,” in Proceedings of 45rd Annual Allerton Conference on Communication, Control, and Computing, Allerton, Illinois,2005.

Waters, A. E.

A. E. Waters, A. C. Sankaranarayanan, and R. G. Baraniuk, “SpaRCS: recovering low-rank and sparse matrices from compressive measurements,” in Advances in Neural Information Processing Systems (2011), pp. 1089–1097.

Xu, L.

L. Xu, A. C. Sankaranarayanan, C. Studer, Y. Li, R. G. Baraniuk, and K. F. Kelly, “Multi-scale compressive video acquisition,” in Computational Optical Sensing and Imaging (Optical Society of America, 2013), paper CW2C.4.

T. Goldstein, L. Xu, K. F. Kelly, and R. G. Baraniuk, “The STONE transform: multi-resolution image enhancement and real-time compressive video,” arXiv:1311.34056 (2013).

Zhang, T.

J. Huang and T. Zhang, “The benefit of group sparsity,” Annals Stat. 38, 1978–2004 (2010).

Annals Stat.

J. Huang and T. Zhang, “The benefit of group sparsity,” Annals Stat. 38, 1978–2004 (2010).

IEEE Signal Process. Mag.

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).
[CrossRef]

R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
[CrossRef]

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).
[CrossRef]

IEEE Trans. Inf. Theory

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, “Model-based compressive sensing,” IEEE Trans. Inf. Theory 56, 1982–2001 (2010).
[CrossRef]

IEEE Trans. Signal Process.

Y. C. Eldar, P. Kuppinger, and H. Bolcskei, “Block-sparse signals: uncertainty relations and efficient recovery,” IEEE Trans. Signal Process. 58, 3042–3054 (2010).
[CrossRef]

J. Liang and T. D. Tran, “Fast multiplierless approximations of the DCT with the lifting scheme,” IEEE Trans. Signal Process. 49, 3032–3044 (2001).
[CrossRef]

J. Opt. Soc. Am. A

Magn. Reson. Med.

C. Tsai and D. G. Nishimura, “Reduced aliasing artifacts using variable-density k-space sampling trajectories,” Magn. Reson. Med. 43, 452–458 (2000).
[CrossRef]

Proc. SPIE

D. Bottisti and R. Muise, “Tree-based adaptive measurement design for compressive imaging under device constraints,” Proc. SPIE 8748, 874802 (2013).
[CrossRef]

SIAM J. Imaging Sci.

T. Goldstein and S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).
[CrossRef]

Other

B. Adcock, A. C. Hansen, C. Poon, and B. Roman, “Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing,” arXiv:1302.0561 (2013).

E. Van Den Berg and M. P. Friedlander, “SPGL1: a solver for large-scale sparse reconstruction,” http://www.cs.ubc.ca/labs/scl/spgl1 , 2007.

V. Cevher, P. Indyk, C. Hegde, and R. G. Baraniuk, “Recovery of clustered sparse signals from compressive measurements,” (2009).

M. A. Davenport, J. N. Laska, P. T. Boufounos, and R. G. Baraniuk, “A simple proof that random matrices are democratic,” arXiv:0911.0736 (2009).

D. Baron, M. F. Duarte, S. Sarvotham, M. B. Wakin, and R. G. Baraniuk, “An information-theoretic approach to distributed compressed sensing,” in Proceedings of 45rd Annual Allerton Conference on Communication, Control, and Computing, Allerton, Illinois,2005.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in Electronic Imaging 2006 (International Society for Optics and Photonics, 2006), p. 606509.

A. C. Sankaranarayanan, C. Studer, and R. G. Baraniuk, “CS-MUVI: video compressive sensing for spatial-multiplexing cameras,” in IEEE International Conference on Computational Photography (ICCP) (2012), pp. 1–10.

L. Xu, A. C. Sankaranarayanan, C. Studer, Y. Li, R. G. Baraniuk, and K. F. Kelly, “Multi-scale compressive video acquisition,” in Computational Optical Sensing and Imaging (Optical Society of America, 2013), paper CW2C.4.

T. Goldstein, L. Xu, K. F. Kelly, and R. G. Baraniuk, “The STONE transform: multi-resolution image enhancement and real-time compressive video,” arXiv:1311.34056 (2013).

A. E. Waters, A. C. Sankaranarayanan, and R. G. Baraniuk, “SpaRCS: recovering low-rank and sparse matrices from compressive measurements,” in Advances in Neural Information Processing Systems (2011), pp. 1089–1097.

“Columbus large image format (CLIF) 2007 dataset,” https://www.sdms.afrl.af.mil/index.php?collection=clif2007 .

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1.
Fig. 1.

Discrete cosine transform spectrum in the zig–zag ordering for 64×64 cameraman image. Inset: (a) Cameraman image. (b) Its discrete cosine transform in the logarithm domain.

Fig. 2.
Fig. 2.

Illustration of hybrid image recovery. (a) Low-frequency components/structure sensed by subspace patterns. (b) High-frequency residual after e1 minimization. (c) Final recovered image by adding structure components and the high-frequency residual.

Fig. 3.
Fig. 3.

(a) DCT patterns with 8×8 resolution. (b) Patterns learned by PCA from a library of natural image [19] with 64×64 resolution.

Fig. 4.
Fig. 4.

Simulation results. (a) SNR comparison between DCT hybrid patterns and random patterns. (b) SNR comparison between PCA hybrid patterns and random patterns. (c) SNR comparison between PCA hybrid patterns and DCT hybrid patterns. (d) Example MSE plot for three specific patterns.

Fig. 5.
Fig. 5.

Experimental results on Texas icon and checkerboard through DCT hybrid patterns (top row), PCA hybrid patterns (middle row), and random patterns (bottom row) at different numbers of compression ratios. The numbers at the top of each column are the corresponding compression ratios. For both experiments, hybrid schemes work better than purely random CI at high compression rate.

Fig. 6.
Fig. 6.

Plots of MSE versus number of measurements. (a) Texas icon test. (b) Checkerboard test.

Fig. 7.
Fig. 7.

Plot of SNR over four different levels of illumination (100%, 50%, 1.5%, and 0.3%) given the compression ratio of 20 for the checkerboard test image. Inset: visual reconstructions for the checkerboard with the Texas icon at corresponding light levels.

Fig. 8.
Fig. 8.

Optimal number of low-frequency patterns for Texas icon test image in the case of (a) DCT hybrid patterns and (b) PCA hybrid patterns.

Fig. 9.
Fig. 9.

SNR versus numbers of bits used to approximate DCT hybrid and PCA patterns. As we can see, when using gray-scale patterns with at least 2 bits for the DCT patterns or 3 bits for PCA patterns, the SNR would remain at the same levels. Thus, in real experiments, gray-scale patterns with a corresponding number of depths are the optimal patterns, which balance the speed of acquisition and precision.

Equations (5)

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

[ΦsΦr]x=[bsbr].
x^s=minxsΦsxsbs2.
bh=brΦrx^s.
s^=minss1:bh=ΦrΨs.
x^=x^s+Ψs^.

Metrics