Abstract

The compressive sensing (CS) framework states that a signal that has a sparse representation in a known basis may be reconstructed from samples obtained at a sub-Nyquist sampling rate. The Fourier domain is widely used in CS applications due to its inherent properties. Sparse signal recovery applications using a small number of Fourier transform coefficients have made solutions to large-scale data recovery problems, including image recovery problems, more practical. The sparse reconstruction of 2D images is performed using the sampling patterns generated by taking the general frequency characteristics of the images into account. In this work, instead of forming a general sampling pattern for infrared (IR) images, a special sampling pattern is obtained by gathering a database to extract the frequency characteristics of IR sea-surveillance images. Experimental results show that the proposed sampling pattern provides better sparse recovery results compared to the widely used patterns proposed in the literature. It is also shown that, together with a certain image dataset, the sampling pattern generated by the proposed scheme can be generalized for various image sparse recovery applications.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
    [CrossRef]
  2. E. Candes, 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]
  3. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
    [CrossRef]
  4. M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
    [CrossRef]
  5. W. L. Chan, M. L. Moravec, R. G. Baraniuk, and D. M. Mittleman, “Terahertz imaging with compressed sensing and phase retrieval,” Opt. Lett. 33, 974–976 (2008).
    [CrossRef]
  6. W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. Baraniuk, and D. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
    [CrossRef]
  7. M. Akcakaya and V. Tarokh, “A frame construction and a universal distortion bound for sparse representations,” IEEE Trans. Signal Process. 56, 2443–2450 (2008).
    [CrossRef]
  8. E. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005).
    [CrossRef]
  9. T. Wan and Z. Qin, “An application of compressive sensing for image fusion,” Int. J. Comput. Math. 88, 3915–3930 (2011).
    [CrossRef]
  10. X. Li and S.-Y. Qin, “Efficient fusion for infrared and visible images based on compressive sensing principle,” IET Image Process. 5, 141–147 (2011).
    [CrossRef]
  11. J. Ma, “A single-pixel imaging system for remote sensing by two-step iterative curvelet thresholding,” IEEE Geosci. Remote Sens. Lett. 6, 676–680 (2009).
    [CrossRef]
  12. J. Ma, “Single-pixel remote sensing,” IEEE Geosci. Remote Sens. Lett. 6, 199–203 (2009).
    [CrossRef]
  13. J. Bobin, J.-L. Starck, and R. Ottensamer, “Compressed sensing in astronomy,” IEEE J. Sel. Top. Signal Process. 2, 718–726 (2008).
    [CrossRef]
  14. V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, and R. G. Baraniuk, “Compressive sensing for background subtraction,” in Proceedings of the European Conference on Computer Vision (Springer, 2008), pp. 155–168.
  15. Y. Kashter, O. Levi, and A. Stern, “Optical compressive change and motion detection,” Appl. Opt. 51, 2491–2496 (2012).
    [CrossRef]
  16. H. Li, C. Shen, and Q. Shi, “Real-time visual tracking using compressive sensing,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 1305–1312.
  17. D. Reddy, A. Sankaranarayanan, V. Cevher, and R. Chellappa, “Compressed sensing for multi-view tracking and 3-d voxel reconstruction,” in Proceedings of the IEEE International Conference on Image Processing (IEEE, 2008), pp. 221–224.
  18. V. M. Patel, N. M. Nasrabadi, and R. Chellappa, “Sparsity-motivated automatic target recognition,” Appl. Opt. 50, 1425–1433 (2011).
    [CrossRef]
  19. J. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
    [CrossRef]
  20. J. Mairal, G. Sapiro, and M. Elad, “Learning multiscale sparse representations for image and video restoration,” Multiscale Model. Simul. 7, 214–241 (2008).
    [CrossRef]
  21. S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process. 56, 2346–2356 (2008).
    [CrossRef]
  22. M. Elad, “Optimized projections for compressed sensing,” IEEE Trans. Signal Process. 55, 5695–5702 (2007).
    [CrossRef]
  23. I. Ramirez and G. Sapiro, “Universal regularizers for robust sparse coding and modeling,” IEEE Trans. Image Process. 21, 3850–3864 (2012).
    [CrossRef]
  24. D. Wipf, J. Palmer, and B. Rao, “Perspectives on sparse Bayesian learning,” in Proceedings of the Advances in Neural Information Processing Systems (MIT, 2004), Vol. 16.
  25. E. Candes and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969 (2007).
    [CrossRef]
  26. M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing, October 2006 (IEEE, 2006), pp. 1273–1276.
  27. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60, 259–268, 1992.
    [CrossRef]
  28. M. P. Friedlander, “SPGL1,” UBC Computer Science, Scientific Computing Laboratory, July2009, http://www.cs.ubc.ca/~mpf/spgl1 .
  29. D. L. Donoho, V. Stodden, and Y. Tsaig, “About SparseLab,” Stanford University, Version 2.0, March2007, http://sparselab.stanford.edu .
  30. E. Candes and J. Romberg, “ℓ1-magic: recovery of sparse signals via convex programming,” 2005, www.acm.caltech.edu/l1magic/downloads/l1magic.pdf .
  31. H. Mohimani, M. Babaie-Zadeh, and C. Jutten, “A fast approach for overcomplete sparse decomposition based on smoothed ℓ0 norm,” IEEE Trans. Signal Process. 57, 289–301 (2009).
    [CrossRef]
  32. Y. Le Montagner, E. Angelini, and J.-C. Olivo-Marin, “Comparison of reconstruction algorithms in compressed sensing applied to biological imaging,” in Proceedings of the IEEE International Symposium on Biomedical Imaging: From Nano to Macro (IEEE, 2011), pp. 105–108.
  33. Z. Wang, New Sampling and Detection Approaches for Compressed Sensing and Their Application to Ultra Wideband Communications (Proquest, 2011).
  34. Y.-C. Kim, S. S. Narayanan, and K. S. Nayak, “Accelerated three-dimensional upper airway MRI using compressed sensing,” Magn. Reson. Med. 61, 1434–1440 (2009).
    [CrossRef]
  35. S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University, 2004).
  36. Z. Wang and A. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
    [CrossRef]

2012

I. Ramirez and G. Sapiro, “Universal regularizers for robust sparse coding and modeling,” IEEE Trans. Image Process. 21, 3850–3864 (2012).
[CrossRef]

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

2011

V. M. Patel, N. M. Nasrabadi, and R. Chellappa, “Sparsity-motivated automatic target recognition,” Appl. Opt. 50, 1425–1433 (2011).
[CrossRef]

T. Wan and Z. Qin, “An application of compressive sensing for image fusion,” Int. J. Comput. Math. 88, 3915–3930 (2011).
[CrossRef]

X. Li and S.-Y. Qin, “Efficient fusion for infrared and visible images based on compressive sensing principle,” IET Image Process. 5, 141–147 (2011).
[CrossRef]

2009

J. Ma, “A single-pixel imaging system for remote sensing by two-step iterative curvelet thresholding,” IEEE Geosci. Remote Sens. Lett. 6, 676–680 (2009).
[CrossRef]

J. Ma, “Single-pixel remote sensing,” IEEE Geosci. Remote Sens. Lett. 6, 199–203 (2009).
[CrossRef]

J. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
[CrossRef]

H. Mohimani, M. Babaie-Zadeh, and C. Jutten, “A fast approach for overcomplete sparse decomposition based on smoothed ℓ0 norm,” IEEE Trans. Signal Process. 57, 289–301 (2009).
[CrossRef]

Y.-C. Kim, S. S. Narayanan, and K. S. Nayak, “Accelerated three-dimensional upper airway MRI using compressed sensing,” Magn. Reson. Med. 61, 1434–1440 (2009).
[CrossRef]

2008

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. Baraniuk, and D. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

M. Akcakaya and V. Tarokh, “A frame construction and a universal distortion bound for sparse representations,” IEEE Trans. Signal Process. 56, 2443–2450 (2008).
[CrossRef]

J. Mairal, G. Sapiro, and M. Elad, “Learning multiscale sparse representations for image and video restoration,” Multiscale Model. Simul. 7, 214–241 (2008).
[CrossRef]

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

J. Bobin, J.-L. Starck, and R. Ottensamer, “Compressed sensing in astronomy,” IEEE J. Sel. Top. Signal Process. 2, 718–726 (2008).
[CrossRef]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

W. L. Chan, M. L. Moravec, R. G. Baraniuk, and D. M. Mittleman, “Terahertz imaging with compressed sensing and phase retrieval,” Opt. Lett. 33, 974–976 (2008).
[CrossRef]

2007

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

E. Candes and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969 (2007).
[CrossRef]

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

2006

E. Candes, 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]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

2005

E. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005).
[CrossRef]

2002

Z. Wang and A. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

1992

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60, 259–268, 1992.
[CrossRef]

Akcakaya, M.

M. Akcakaya and V. Tarokh, “A frame construction and a universal distortion bound for sparse representations,” IEEE Trans. Signal Process. 56, 2443–2450 (2008).
[CrossRef]

Angelini, E.

Y. Le Montagner, E. Angelini, and J.-C. Olivo-Marin, “Comparison of reconstruction algorithms in compressed sensing applied to biological imaging,” in Proceedings of the IEEE International Symposium on Biomedical Imaging: From Nano to Macro (IEEE, 2011), pp. 105–108.

Babaie-Zadeh, M.

H. Mohimani, M. Babaie-Zadeh, and C. Jutten, “A fast approach for overcomplete sparse decomposition based on smoothed ℓ0 norm,” IEEE Trans. Signal Process. 57, 289–301 (2009).
[CrossRef]

Baraniuk, R.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. Baraniuk, and D. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

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

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing, October 2006 (IEEE, 2006), pp. 1273–1276.

Baraniuk, R. G.

W. L. Chan, M. L. Moravec, R. G. Baraniuk, and D. M. Mittleman, “Terahertz imaging with compressed sensing and phase retrieval,” Opt. Lett. 33, 974–976 (2008).
[CrossRef]

V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, and R. G. Baraniuk, “Compressive sensing for background subtraction,” in Proceedings of the European Conference on Computer Vision (Springer, 2008), pp. 155–168.

Baron, D.

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing, October 2006 (IEEE, 2006), pp. 1273–1276.

Bobin, J.

J. Bobin, J.-L. Starck, and R. Ottensamer, “Compressed sensing in astronomy,” IEEE J. Sel. Top. Signal Process. 2, 718–726 (2008).
[CrossRef]

Bovik, A.

Z. Wang and A. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

Boyd, S.

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University, 2004).

Candes, E.

E. Candes and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969 (2007).
[CrossRef]

E. Candes, 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]

E. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005).
[CrossRef]

Carin, L.

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

Cevher, V.

V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, and R. G. Baraniuk, “Compressive sensing for background subtraction,” in Proceedings of the European Conference on Computer Vision (Springer, 2008), pp. 155–168.

D. Reddy, A. Sankaranarayanan, V. Cevher, and R. Chellappa, “Compressed sensing for multi-view tracking and 3-d voxel reconstruction,” in Proceedings of the IEEE International Conference on Image Processing (IEEE, 2008), pp. 221–224.

Chan, W. L.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. Baraniuk, and D. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

W. L. Chan, M. L. Moravec, R. G. Baraniuk, and D. M. Mittleman, “Terahertz imaging with compressed sensing and phase retrieval,” Opt. Lett. 33, 974–976 (2008).
[CrossRef]

Charan, K.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. Baraniuk, and D. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Chellappa, R.

V. M. Patel, N. M. Nasrabadi, and R. Chellappa, “Sparsity-motivated automatic target recognition,” Appl. Opt. 50, 1425–1433 (2011).
[CrossRef]

D. Reddy, A. Sankaranarayanan, V. Cevher, and R. Chellappa, “Compressed sensing for multi-view tracking and 3-d voxel reconstruction,” in Proceedings of the IEEE International Conference on Image Processing (IEEE, 2008), pp. 221–224.

Davenport, M.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

Duarte, M.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing, October 2006 (IEEE, 2006), pp. 1273–1276.

Duarte, M. F.

V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, and R. G. Baraniuk, “Compressive sensing for background subtraction,” in Proceedings of the European Conference on Computer Vision (Springer, 2008), pp. 155–168.

Duarte-Carvajalino, J.

J. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
[CrossRef]

Elad, M.

J. Mairal, G. Sapiro, and M. Elad, “Learning multiscale sparse representations for image and video restoration,” Multiscale Model. Simul. 7, 214–241 (2008).
[CrossRef]

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

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60, 259–268, 1992.
[CrossRef]

Ji, S.

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

Jutten, C.

H. Mohimani, M. Babaie-Zadeh, and C. Jutten, “A fast approach for overcomplete sparse decomposition based on smoothed ℓ0 norm,” IEEE Trans. Signal Process. 57, 289–301 (2009).
[CrossRef]

Kashter, Y.

Kelly, K.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing, October 2006 (IEEE, 2006), pp. 1273–1276.

Kelly, K. F.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. Baraniuk, and D. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Kim, Y.-C.

Y.-C. Kim, S. S. Narayanan, and K. S. Nayak, “Accelerated three-dimensional upper airway MRI using compressed sensing,” Magn. Reson. Med. 61, 1434–1440 (2009).
[CrossRef]

Laska, J.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing, October 2006 (IEEE, 2006), pp. 1273–1276.

Le Montagner, Y.

Y. Le Montagner, E. Angelini, and J.-C. Olivo-Marin, “Comparison of reconstruction algorithms in compressed sensing applied to biological imaging,” in Proceedings of the IEEE International Symposium on Biomedical Imaging: From Nano to Macro (IEEE, 2011), pp. 105–108.

Levi, O.

Li, H.

H. Li, C. Shen, and Q. Shi, “Real-time visual tracking using compressive sensing,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 1305–1312.

Li, X.

X. Li and S.-Y. Qin, “Efficient fusion for infrared and visible images based on compressive sensing principle,” IET Image Process. 5, 141–147 (2011).
[CrossRef]

Ma, J.

J. Ma, “A single-pixel imaging system for remote sensing by two-step iterative curvelet thresholding,” IEEE Geosci. Remote Sens. Lett. 6, 676–680 (2009).
[CrossRef]

J. Ma, “Single-pixel remote sensing,” IEEE Geosci. Remote Sens. Lett. 6, 199–203 (2009).
[CrossRef]

Mairal, J.

J. Mairal, G. Sapiro, and M. Elad, “Learning multiscale sparse representations for image and video restoration,” Multiscale Model. Simul. 7, 214–241 (2008).
[CrossRef]

Mittleman, D.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. Baraniuk, and D. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Mittleman, D. M.

Mohimani, H.

H. Mohimani, M. Babaie-Zadeh, and C. Jutten, “A fast approach for overcomplete sparse decomposition based on smoothed ℓ0 norm,” IEEE Trans. Signal Process. 57, 289–301 (2009).
[CrossRef]

Moravec, M. L.

Narayanan, S. S.

Y.-C. Kim, S. S. Narayanan, and K. S. Nayak, “Accelerated three-dimensional upper airway MRI using compressed sensing,” Magn. Reson. Med. 61, 1434–1440 (2009).
[CrossRef]

Nasrabadi, N. M.

Nayak, K. S.

Y.-C. Kim, S. S. Narayanan, and K. S. Nayak, “Accelerated three-dimensional upper airway MRI using compressed sensing,” Magn. Reson. Med. 61, 1434–1440 (2009).
[CrossRef]

Olivo-Marin, J.-C.

Y. Le Montagner, E. Angelini, and J.-C. Olivo-Marin, “Comparison of reconstruction algorithms in compressed sensing applied to biological imaging,” in Proceedings of the IEEE International Symposium on Biomedical Imaging: From Nano to Macro (IEEE, 2011), pp. 105–108.

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60, 259–268, 1992.
[CrossRef]

Ottensamer, R.

J. Bobin, J.-L. Starck, and R. Ottensamer, “Compressed sensing in astronomy,” IEEE J. Sel. Top. Signal Process. 2, 718–726 (2008).
[CrossRef]

Palmer, J.

D. Wipf, J. Palmer, and B. Rao, “Perspectives on sparse Bayesian learning,” in Proceedings of the Advances in Neural Information Processing Systems (MIT, 2004), Vol. 16.

Patel, V. M.

Qin, S.-Y.

X. Li and S.-Y. Qin, “Efficient fusion for infrared and visible images based on compressive sensing principle,” IET Image Process. 5, 141–147 (2011).
[CrossRef]

Qin, Z.

T. Wan and Z. Qin, “An application of compressive sensing for image fusion,” Int. J. Comput. Math. 88, 3915–3930 (2011).
[CrossRef]

Ramirez, I.

I. Ramirez and G. Sapiro, “Universal regularizers for robust sparse coding and modeling,” IEEE Trans. Image Process. 21, 3850–3864 (2012).
[CrossRef]

Rao, B.

D. Wipf, J. Palmer, and B. Rao, “Perspectives on sparse Bayesian learning,” in Proceedings of the Advances in Neural Information Processing Systems (MIT, 2004), Vol. 16.

Reddy, D.

V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, and R. G. Baraniuk, “Compressive sensing for background subtraction,” in Proceedings of the European Conference on Computer Vision (Springer, 2008), pp. 155–168.

D. Reddy, A. Sankaranarayanan, V. Cevher, and R. Chellappa, “Compressed sensing for multi-view tracking and 3-d voxel reconstruction,” in Proceedings of the IEEE International Conference on Image Processing (IEEE, 2008), pp. 221–224.

Romberg, J.

E. Candes and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969 (2007).
[CrossRef]

E. Candes, 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]

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60, 259–268, 1992.
[CrossRef]

Sankaranarayanan, A.

D. Reddy, A. Sankaranarayanan, V. Cevher, and R. Chellappa, “Compressed sensing for multi-view tracking and 3-d voxel reconstruction,” in Proceedings of the IEEE International Conference on Image Processing (IEEE, 2008), pp. 221–224.

V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, and R. G. Baraniuk, “Compressive sensing for background subtraction,” in Proceedings of the European Conference on Computer Vision (Springer, 2008), pp. 155–168.

Sapiro, G.

I. Ramirez and G. Sapiro, “Universal regularizers for robust sparse coding and modeling,” IEEE Trans. Image Process. 21, 3850–3864 (2012).
[CrossRef]

J. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
[CrossRef]

J. Mairal, G. Sapiro, and M. Elad, “Learning multiscale sparse representations for image and video restoration,” Multiscale Model. Simul. 7, 214–241 (2008).
[CrossRef]

Sarvotham, S.

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing, October 2006 (IEEE, 2006), pp. 1273–1276.

Shen, C.

H. Li, C. Shen, and Q. Shi, “Real-time visual tracking using compressive sensing,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 1305–1312.

Shi, Q.

H. Li, C. Shen, and Q. Shi, “Real-time visual tracking using compressive sensing,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 1305–1312.

Starck, J.-L.

J. Bobin, J.-L. Starck, and R. Ottensamer, “Compressed sensing in astronomy,” IEEE J. Sel. Top. Signal Process. 2, 718–726 (2008).
[CrossRef]

Stern, A.

Sun, T.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Takhar, D.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. Baraniuk, and D. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing, October 2006 (IEEE, 2006), pp. 1273–1276.

Tao, T.

E. Candes, 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]

E. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005).
[CrossRef]

Tarokh, V.

M. Akcakaya and V. Tarokh, “A frame construction and a universal distortion bound for sparse representations,” IEEE Trans. Signal Process. 56, 2443–2450 (2008).
[CrossRef]

Vandenberghe, L.

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University, 2004).

Wakin, M.

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing, October 2006 (IEEE, 2006), pp. 1273–1276.

Wan, T.

T. Wan and Z. Qin, “An application of compressive sensing for image fusion,” Int. J. Comput. Math. 88, 3915–3930 (2011).
[CrossRef]

Wang, Z.

Z. Wang and A. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

Z. Wang, New Sampling and Detection Approaches for Compressed Sensing and Their Application to Ultra Wideband Communications (Proquest, 2011).

Wipf, D.

D. Wipf, J. Palmer, and B. Rao, “Perspectives on sparse Bayesian learning,” in Proceedings of the Advances in Neural Information Processing Systems (MIT, 2004), Vol. 16.

Xue, Y.

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

Appl. Opt.

Appl. Phys. Lett.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. Baraniuk, and D. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

IEEE Geosci. Remote Sens. Lett.

J. Ma, “A single-pixel imaging system for remote sensing by two-step iterative curvelet thresholding,” IEEE Geosci. Remote Sens. Lett. 6, 676–680 (2009).
[CrossRef]

J. Ma, “Single-pixel remote sensing,” IEEE Geosci. Remote Sens. Lett. 6, 199–203 (2009).
[CrossRef]

IEEE J. Sel. Top. Signal Process.

J. Bobin, J.-L. Starck, and R. Ottensamer, “Compressed sensing in astronomy,” IEEE J. Sel. Top. Signal Process. 2, 718–726 (2008).
[CrossRef]

IEEE Signal Process. Lett.

Z. Wang and A. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

IEEE Signal Process. Mag.

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

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

IEEE Trans. Image Process.

J. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
[CrossRef]

I. Ramirez and G. Sapiro, “Universal regularizers for robust sparse coding and modeling,” IEEE Trans. Image Process. 21, 3850–3864 (2012).
[CrossRef]

IEEE Trans. Inf. Theory

E. Candes, 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]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[CrossRef]

E. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005).
[CrossRef]

IEEE Trans. Signal Process.

M. Akcakaya and V. Tarokh, “A frame construction and a universal distortion bound for sparse representations,” IEEE Trans. Signal Process. 56, 2443–2450 (2008).
[CrossRef]

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

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

H. Mohimani, M. Babaie-Zadeh, and C. Jutten, “A fast approach for overcomplete sparse decomposition based on smoothed ℓ0 norm,” IEEE Trans. Signal Process. 57, 289–301 (2009).
[CrossRef]

IET Image Process.

X. Li and S.-Y. Qin, “Efficient fusion for infrared and visible images based on compressive sensing principle,” IET Image Process. 5, 141–147 (2011).
[CrossRef]

Int. J. Comput. Math.

T. Wan and Z. Qin, “An application of compressive sensing for image fusion,” Int. J. Comput. Math. 88, 3915–3930 (2011).
[CrossRef]

Inverse Probl.

E. Candes and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969 (2007).
[CrossRef]

Magn. Reson. Med.

Y.-C. Kim, S. S. Narayanan, and K. S. Nayak, “Accelerated three-dimensional upper airway MRI using compressed sensing,” Magn. Reson. Med. 61, 1434–1440 (2009).
[CrossRef]

Multiscale Model. Simul.

J. Mairal, G. Sapiro, and M. Elad, “Learning multiscale sparse representations for image and video restoration,” Multiscale Model. Simul. 7, 214–241 (2008).
[CrossRef]

Opt. Lett.

Physica D

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60, 259–268, 1992.
[CrossRef]

Other

M. P. Friedlander, “SPGL1,” UBC Computer Science, Scientific Computing Laboratory, July2009, http://www.cs.ubc.ca/~mpf/spgl1 .

D. L. Donoho, V. Stodden, and Y. Tsaig, “About SparseLab,” Stanford University, Version 2.0, March2007, http://sparselab.stanford.edu .

E. Candes and J. Romberg, “ℓ1-magic: recovery of sparse signals via convex programming,” 2005, www.acm.caltech.edu/l1magic/downloads/l1magic.pdf .

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University, 2004).

Y. Le Montagner, E. Angelini, and J.-C. Olivo-Marin, “Comparison of reconstruction algorithms in compressed sensing applied to biological imaging,” in Proceedings of the IEEE International Symposium on Biomedical Imaging: From Nano to Macro (IEEE, 2011), pp. 105–108.

Z. Wang, New Sampling and Detection Approaches for Compressed Sensing and Their Application to Ultra Wideband Communications (Proquest, 2011).

M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, “An architecture for compressive imaging,” in 2006 IEEE International Conference on Image Processing, October 2006 (IEEE, 2006), pp. 1273–1276.

D. Wipf, J. Palmer, and B. Rao, “Perspectives on sparse Bayesian learning,” in Proceedings of the Advances in Neural Information Processing Systems (MIT, 2004), Vol. 16.

V. Cevher, A. Sankaranarayanan, M. F. Duarte, D. Reddy, and R. G. Baraniuk, “Compressive sensing for background subtraction,” in Proceedings of the European Conference on Computer Vision (Springer, 2008), pp. 155–168.

H. Li, C. Shen, and Q. Shi, “Real-time visual tracking using compressive sensing,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 1305–1312.

D. Reddy, A. Sankaranarayanan, V. Cevher, and R. Chellappa, “Compressed sensing for multi-view tracking and 3-d voxel reconstruction,” in Proceedings of the IEEE International Conference on Image Processing (IEEE, 2008), pp. 221–224.

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 (11)

Fig. 1.
Fig. 1.

Uniform and nonuniform sampling patterns.

Fig. 2.
Fig. 2.

Flow diagram of the sun-shaped sampling pattern generation technique.

Fig. 3.
Fig. 3.

Illustration of the sun-shaped pattern at each iteration (PSuni) of the algorithm for i=1, 2, 3, 4, 5, 6.

Fig. 4.
Fig. 4.

Sample IR images from the image dataset.

Fig. 5.
Fig. 5.

PSNR ratios of the reconstructed images using different sampling patterns for experiment 1.

Fig. 6.
Fig. 6.

Examples of reconstructed images using different sampling patterns for experiment 1.

Fig. 7.
Fig. 7.

Examples of zoomed reconstruction results obtained using different sampling patterns for experiment 1.

Fig. 8.
Fig. 8.

Error images calculated for radial sampling patterns.

Fig. 9.
Fig. 9.

Examples of reconstructed images using different sampling patterns for experiment 2.

Fig. 10.
Fig. 10.

PSNR ratios of the reconstructed images using different sampling patterns for experiment 2.

Fig. 11.
Fig. 11.

Relation between the average PSNR values and the sample size of the Psun.

Tables (2)

Tables Icon

Algorithm 1 PSun generation algorithm

Tables Icon

Table 1. Sample Sizes of Each Sampling Pattern and the Corresponding Average PSNR and UIQI Values for Experiments 1 and 2

Equations (9)

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

x=Ψs.
y=Φx=ΦΨs.
s^=argmins1such thaty=ΦΨs.
Dh(i,j)={x^(i,j+1)x^(i,j)i<W0i=WDv(i,j)={x^(i+1,j)x^(i,j)j<W0j=Wx^TV=i=1Wj=1WDh(i,j)2+Dh(i,j)2.
minx^TVsubject toX^(u,v)=X(u,v).
Xt(u,v)=1WHm=0H1n=0W1xt(m,n)ej2π(umH+vnW).
X˜ave(u,v)=1βt=1β|Xt(u,v)|.
τseg=μ+κσ.
Q=(σxxreconsσxσxrecons)(2x¯x¯reconsx¯2+(x¯recons)2)(2σxσxreconsσx2+σxrecons2).

Metrics