Abstract

Hyperspectral imaging systems can benefit from compressed sensing to reduce data acquisition demands. We present a new reconstruction algorithm to recover the hyperspectral datacube from limited optically compressed measurements, exploiting the inherent spatial and spectral correlations through non-local means regularization. The reconstruction process is solved with the help of split Bregman optimization techniques, including penalty functions defined according to the spatial and spectral properties of the scene and noise sources. For validation purposes, we also implemented a compressive hyperspectral imaging system that relies on a digital micromirror device and a near-infrared spectrometer, where we obtained enhanced and promising reconstruction results when using our proposed technique in contrast with traditional compressive image reconstruction.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  24. J. Zhang, S. Liu, R. Xiong, S. Ma, and D. Zhao, “Improved total variation based image compressive sensing recovery by nonlocal regularization,” IEEE International Symposium on Circuits and Systems,  2013, 2836–2839 (2013).
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    [Crossref]
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    [Crossref]
  30. M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: From theory to applications,” IEEE Transactions on Signal Processing 59, 4053–4085 (2011).
    [Crossref]
  31. S. Cuomo, P. D. Michele, and F. Piccialli, “3d data denoising via nonlocal means filter by using parallel gpu strategies,” Computational and mathematical methods in medicine 2014, 523862 (2014).
    [Crossref] [PubMed]
  32. D. S. Antony and G. Rathna, “Gpu based fast non local means algorithm,” Journal of Image and Graphics 3, 122 (2015).

2017 (2)

J. Yang, Y.J. Li, C.-W. Chan, and Q. Shen, “Image fusion for spatial enhancement of hyperspectral image via pixel group based non-local sparse representation,” Remote Sensing 9, 53 (2017).

J. V. Thompson, J. N. Bixler, B. H. Hokr, G. D. Noojin, M. O. Scully, and V. V. Yakovlev, “Single-shot chemical detection and identification with compressed hyperspectral raman imaging,” Opt. Lett. 42, 2169–2172 (2017).
[Crossref] [PubMed]

2016 (3)

Y. Li, F. Li, B. Bai, and Q. Shen, “Image fusion via nonlocal sparse k-svd dictionary learning,” Appl. Opt. 55, 1814–1823 (2016).
[Crossref] [PubMed]

P. Meza, E. Vera, and J. Martinez, “Improved reconstruction for compressive hyperspectral imaging using spatial-spectral non-local means regularization,” Proc. IS&T international Symposium on Electronic Imaging 2016, 1–5 (2016).

P. Meza, J. E. Pezoa, and S. N. Torres, “Multidimensional striping noise compensation in hyperspectral imaging: Exploiting hypercubes’s spatial, spectral, and temporal redundancy,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 9, 4428–4441 (2016).
[Crossref]

2015 (3)

W. Huang, L. Xiao, H. Liu, and Z. Wei, “Hyperspectral imagery super-resolution by compressive sensing inspired dictionary learning and spatial-spectral regularization,” Sensors 15, 2041–2058 (2015).
[Crossref] [PubMed]

D. S. Antony and G. Rathna, “Gpu based fast non local means algorithm,” Journal of Image and Graphics 3, 122 (2015).

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

2014 (2)

S. Cuomo, P. D. Michele, and F. Piccialli, “3d data denoising via nonlocal means filter by using parallel gpu strategies,” Computational and mathematical methods in medicine 2014, 523862 (2014).
[Crossref] [PubMed]

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref] [PubMed]

2013 (2)

C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented lagrangian method with applications to total variation minimization,” Computational Optimization and Applications 56, 507–530 (2013).
[Crossref]

J. Zhang, S. Liu, R. Xiong, S. Ma, and D. Zhao, “Improved total variation based image compressive sensing recovery by nonlocal regularization,” IEEE International Symposium on Circuits and Systems,  2013, 2836–2839 (2013).

2011 (2)

S. Becker, J. Bobin, and E. J. Candés, “Nesta: A fast and accurate first-order method for sparse recovery,” SIAM Journal on Imaging Sciences 4, 1–39 (2011).
[Crossref]

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: From theory to applications,” IEEE Transactions on Signal Processing 59, 4053–4085 (2011).
[Crossref]

2009 (3)

R. Ward, “Compressed sensing with cross validation,” IEEE Transactions on Information Theory 55, 5773–5782 (2009).
[Crossref]

D. Needell and J. Tropp, “Cosamp: Iterative signal recovery from incomplete and inaccurate samples,” Applied and Computational Harmonic Analysis 26, 301–321 (2009).
[Crossref]

T. Goldstein and S. Osher, “The split bregman method for l1-regularized problems,” SIAM Journal on Imaging Sciences 2, 323–343 (2009).
[Crossref]

2008 (2)

2007 (4)

M. E. Gehm, R. John, D. J. Brady, R. M. Willett, and T. J. Schulz, “Single-shot compressive spectral imaging with a dual-disperser architecture,” Opt. Express 15, 14013–14027 (2007).
[Crossref] [PubMed]

J. Tropp and A. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Transactions on Information Theory 53, 4655–4666 (2007).
[Crossref]

E. Candes and T. Tao, “The dantzig selector: Statistical estimation when p is much larger than n,” The Annals of Statistics 35, 2313–2351 (2007).
[Crossref]

J. Bioucas-Dias and M. Figueiredo, “A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Transactions on Image Processing 16, 2992–3004 (2007).
[Crossref] [PubMed]

2006 (3)

D. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory 52, 1289–1306 (2006).
[Crossref]

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory 52, 489–509 (2006).
[Crossref]

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606501 (2006).

2005 (1)

A. Buades, B. Coll, and J.-M. Morel, “A non-local algorithm for image denoising,” Proc. IEEE Conference on Computer Vision and Pattern Recognition 2, 60–65 (2005).

2001 (1)

H. Tian, B. Fowler, and A. Gamal, “Analysis of temporal noise in cmos photodiode active pixel sensor,” IEEE Journal of Solid-State Circuits 36, 92–101 (2001).
[Crossref]

1998 (2)

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Journal on Scientific Computing 20, 33–61 (1998).
[Crossref]

A. E. Gamal, B. A. Fowler, H. Min, and X. Liu, “Modeling and estimation of fpn components in cmos image sensors,” Proc. SPIE 3301, 330101 (1998).

Alonso, L.

Antony, D. S.

D. S. Antony and G. Rathna, “Gpu based fast non local means algorithm,” Journal of Image and Graphics 3, 122 (2015).

Bai, B.

Baraniuk, and R. G.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606501 (2006).

Baron, D.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606501 (2006).

Becker, S.

S. Becker, J. Bobin, and E. J. Candés, “Nesta: A fast and accurate first-order method for sparse recovery,” SIAM Journal on Imaging Sciences 4, 1–39 (2011).
[Crossref]

Bioucas-Dias, J.

J. Bioucas-Dias and M. Figueiredo, “A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Transactions on Image Processing 16, 2992–3004 (2007).
[Crossref] [PubMed]

Bixler, J. N.

Bobin, J.

S. Becker, J. Bobin, and E. J. Candés, “Nesta: A fast and accurate first-order method for sparse recovery,” SIAM Journal on Imaging Sciences 4, 1–39 (2011).
[Crossref]

Borengasser, M.

M. Borengasser, W. S. Hungate, and R. L. Watkins, Hyperspectral Remote Sensing: Principles and Applications (CRC, 2008).

Brady, D.

Brady, D. J.

Buades, A.

A. Buades, B. Coll, and J.-M. Morel, “A non-local algorithm for image denoising,” Proc. IEEE Conference on Computer Vision and Pattern Recognition 2, 60–65 (2005).

Calpe, J.

Camps-Valls, G.

Candes, E.

E. Candes and T. Tao, “The dantzig selector: Statistical estimation when p is much larger than n,” The Annals of Statistics 35, 2313–2351 (2007).
[Crossref]

Candes, E. J.

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory 52, 489–509 (2006).
[Crossref]

Candés, E. J.

S. Becker, J. Bobin, and E. J. Candés, “Nesta: A fast and accurate first-order method for sparse recovery,” SIAM Journal on Imaging Sciences 4, 1–39 (2011).
[Crossref]

Chan, C.-W.

J. Yang, Y.J. Li, C.-W. Chan, and Q. Shen, “Image fusion for spatial enhancement of hyperspectral image via pixel group based non-local sparse representation,” Remote Sensing 9, 53 (2017).

Chen, S. S.

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Journal on Scientific Computing 20, 33–61 (1998).
[Crossref]

Coll, B.

A. Buades, B. Coll, and J.-M. Morel, “A non-local algorithm for image denoising,” Proc. IEEE Conference on Computer Vision and Pattern Recognition 2, 60–65 (2005).

Cuomo, S.

S. Cuomo, P. D. Michele, and F. Piccialli, “3d data denoising via nonlocal means filter by using parallel gpu strategies,” Computational and mathematical methods in medicine 2014, 523862 (2014).
[Crossref] [PubMed]

Donoho, D.

D. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory 52, 1289–1306 (2006).
[Crossref]

Donoho, D. L.

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Journal on Scientific Computing 20, 33–61 (1998).
[Crossref]

Duarte, M. F.

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: From theory to applications,” IEEE Transactions on Signal Processing 59, 4053–4085 (2011).
[Crossref]

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606501 (2006).

Eldar, Y. C.

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: From theory to applications,” IEEE Transactions on Signal Processing 59, 4053–4085 (2011).
[Crossref]

Figueiredo, M.

J. Bioucas-Dias and M. Figueiredo, “A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Transactions on Image Processing 16, 2992–3004 (2007).
[Crossref] [PubMed]

Fowler, B.

H. Tian, B. Fowler, and A. Gamal, “Analysis of temporal noise in cmos photodiode active pixel sensor,” IEEE Journal of Solid-State Circuits 36, 92–101 (2001).
[Crossref]

Fowler, B. A.

A. E. Gamal, B. A. Fowler, H. Min, and X. Liu, “Modeling and estimation of fpn components in cmos image sensors,” Proc. SPIE 3301, 330101 (1998).

Gamal, A.

H. Tian, B. Fowler, and A. Gamal, “Analysis of temporal noise in cmos photodiode active pixel sensor,” IEEE Journal of Solid-State Circuits 36, 92–101 (2001).
[Crossref]

Gamal, A. E.

A. E. Gamal, B. A. Fowler, H. Min, and X. Liu, “Modeling and estimation of fpn components in cmos image sensors,” Proc. SPIE 3301, 330101 (1998).

Gao, L.

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref] [PubMed]

Gehm, M. E.

Gilbert, A.

J. Tropp and A. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Transactions on Information Theory 53, 4655–4666 (2007).
[Crossref]

Goldstein, T.

T. Goldstein and S. Osher, “The split bregman method for l1-regularized problems,” SIAM Journal on Imaging Sciences 2, 323–343 (2009).
[Crossref]

Gómez-Chova, L.

Guanter, L.

Hokr, B. H.

Huang, W.

W. Huang, L. Xiao, H. Liu, and Z. Wei, “Hyperspectral imagery super-resolution by compressive sensing inspired dictionary learning and spatial-spectral regularization,” Sensors 15, 2041–2058 (2015).
[Crossref] [PubMed]

Hungate, W. S.

M. Borengasser, W. S. Hungate, and R. L. Watkins, Hyperspectral Remote Sensing: Principles and Applications (CRC, 2008).

Jiang, H.

C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented lagrangian method with applications to total variation minimization,” Computational Optimization and Applications 56, 507–530 (2013).
[Crossref]

John, R.

Kelly, K.

T. Sun and K. Kelly, “Compressive sensing hyperspectral imager,” Frontiers in Optics 2009/Laser Science XXV/Fall 2009 OSA Optics & Photonics Technical Digest p, CTuA5 (2009).

Kelly, K. F.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606501 (2006).

Laska, J. N.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606501 (2006).

Li, C.

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref] [PubMed]

C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented lagrangian method with applications to total variation minimization,” Computational Optimization and Applications 56, 507–530 (2013).
[Crossref]

Li, F.

Li, Y.

Li, Y.J.

J. Yang, Y.J. Li, C.-W. Chan, and Q. Shen, “Image fusion for spatial enhancement of hyperspectral image via pixel group based non-local sparse representation,” Remote Sensing 9, 53 (2017).

Liang, J.

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref] [PubMed]

Liu, H.

W. Huang, L. Xiao, H. Liu, and Z. Wei, “Hyperspectral imagery super-resolution by compressive sensing inspired dictionary learning and spatial-spectral regularization,” Sensors 15, 2041–2058 (2015).
[Crossref] [PubMed]

Liu, S.

J. Zhang, S. Liu, R. Xiong, S. Ma, and D. Zhao, “Improved total variation based image compressive sensing recovery by nonlocal regularization,” IEEE International Symposium on Circuits and Systems,  2013, 2836–2839 (2013).

Liu, X.

A. E. Gamal, B. A. Fowler, H. Min, and X. Liu, “Modeling and estimation of fpn components in cmos image sensors,” Proc. SPIE 3301, 330101 (1998).

Ma, S.

J. Zhang, S. Liu, R. Xiong, S. Ma, and D. Zhao, “Improved total variation based image compressive sensing recovery by nonlocal regularization,” IEEE International Symposium on Circuits and Systems,  2013, 2836–2839 (2013).

Martinez, J.

P. Meza, E. Vera, and J. Martinez, “Improved reconstruction for compressive hyperspectral imaging using spatial-spectral non-local means regularization,” Proc. IS&T international Symposium on Electronic Imaging 2016, 1–5 (2016).

Meza, P.

P. Meza, E. Vera, and J. Martinez, “Improved reconstruction for compressive hyperspectral imaging using spatial-spectral non-local means regularization,” Proc. IS&T international Symposium on Electronic Imaging 2016, 1–5 (2016).

P. Meza, J. E. Pezoa, and S. N. Torres, “Multidimensional striping noise compensation in hyperspectral imaging: Exploiting hypercubes’s spatial, spectral, and temporal redundancy,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 9, 4428–4441 (2016).
[Crossref]

Michele, P. D.

S. Cuomo, P. D. Michele, and F. Piccialli, “3d data denoising via nonlocal means filter by using parallel gpu strategies,” Computational and mathematical methods in medicine 2014, 523862 (2014).
[Crossref] [PubMed]

Min, H.

A. E. Gamal, B. A. Fowler, H. Min, and X. Liu, “Modeling and estimation of fpn components in cmos image sensors,” Proc. SPIE 3301, 330101 (1998).

Morel, J.-M.

A. Buades, B. Coll, and J.-M. Morel, “A non-local algorithm for image denoising,” Proc. IEEE Conference on Computer Vision and Pattern Recognition 2, 60–65 (2005).

Moreno, J.

Needell, D.

D. Needell and J. Tropp, “Cosamp: Iterative signal recovery from incomplete and inaccurate samples,” Applied and Computational Harmonic Analysis 26, 301–321 (2009).
[Crossref]

Noojin, G. D.

Osher, S.

T. Goldstein and S. Osher, “The split bregman method for l1-regularized problems,” SIAM Journal on Imaging Sciences 2, 323–343 (2009).
[Crossref]

Pezoa, J. E.

P. Meza, J. E. Pezoa, and S. N. Torres, “Multidimensional striping noise compensation in hyperspectral imaging: Exploiting hypercubes’s spatial, spectral, and temporal redundancy,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 9, 4428–4441 (2016).
[Crossref]

Piccialli, F.

S. Cuomo, P. D. Michele, and F. Piccialli, “3d data denoising via nonlocal means filter by using parallel gpu strategies,” Computational and mathematical methods in medicine 2014, 523862 (2014).
[Crossref] [PubMed]

Rathna, G.

D. S. Antony and G. Rathna, “Gpu based fast non local means algorithm,” Journal of Image and Graphics 3, 122 (2015).

Romberg, J.

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory 52, 489–509 (2006).
[Crossref]

Sarvotham, S.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606501 (2006).

Saunders, M. A.

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Journal on Scientific Computing 20, 33–61 (1998).
[Crossref]

Schulz, T. J.

Scully, M. O.

Shen, Q.

J. Yang, Y.J. Li, C.-W. Chan, and Q. Shen, “Image fusion for spatial enhancement of hyperspectral image via pixel group based non-local sparse representation,” Remote Sensing 9, 53 (2017).

Y. Li, F. Li, B. Bai, and Q. Shen, “Image fusion via nonlocal sparse k-svd dictionary learning,” Appl. Opt. 55, 1814–1823 (2016).
[Crossref] [PubMed]

Sun, T.

T. Sun and K. Kelly, “Compressive sensing hyperspectral imager,” Frontiers in Optics 2009/Laser Science XXV/Fall 2009 OSA Optics & Photonics Technical Digest p, CTuA5 (2009).

Takhar, D.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606501 (2006).

Tao, T.

E. Candes and T. Tao, “The dantzig selector: Statistical estimation when p is much larger than n,” The Annals of Statistics 35, 2313–2351 (2007).
[Crossref]

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory 52, 489–509 (2006).
[Crossref]

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H. Tian, B. Fowler, and A. Gamal, “Analysis of temporal noise in cmos photodiode active pixel sensor,” IEEE Journal of Solid-State Circuits 36, 92–101 (2001).
[Crossref]

Torres, S. N.

P. Meza, J. E. Pezoa, and S. N. Torres, “Multidimensional striping noise compensation in hyperspectral imaging: Exploiting hypercubes’s spatial, spectral, and temporal redundancy,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 9, 4428–4441 (2016).
[Crossref]

Tropp, J.

D. Needell and J. Tropp, “Cosamp: Iterative signal recovery from incomplete and inaccurate samples,” Applied and Computational Harmonic Analysis 26, 301–321 (2009).
[Crossref]

J. Tropp and A. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Transactions on Information Theory 53, 4655–4666 (2007).
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P. Meza, E. Vera, and J. Martinez, “Improved reconstruction for compressive hyperspectral imaging using spatial-spectral non-local means regularization,” Proc. IS&T international Symposium on Electronic Imaging 2016, 1–5 (2016).

Wagadarikar, A.

Wakin, M. B.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606501 (2006).

Wang, L. V.

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
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R. Ward, “Compressed sensing with cross validation,” IEEE Transactions on Information Theory 55, 5773–5782 (2009).
[Crossref]

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M. Borengasser, W. S. Hungate, and R. L. Watkins, Hyperspectral Remote Sensing: Principles and Applications (CRC, 2008).

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W. Huang, L. Xiao, H. Liu, and Z. Wei, “Hyperspectral imagery super-resolution by compressive sensing inspired dictionary learning and spatial-spectral regularization,” Sensors 15, 2041–2058 (2015).
[Crossref] [PubMed]

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Willett, R. M.

Xiao, L.

W. Huang, L. Xiao, H. Liu, and Z. Wei, “Hyperspectral imagery super-resolution by compressive sensing inspired dictionary learning and spatial-spectral regularization,” Sensors 15, 2041–2058 (2015).
[Crossref] [PubMed]

Xiong, R.

J. Zhang, S. Liu, R. Xiong, S. Ma, and D. Zhao, “Improved total variation based image compressive sensing recovery by nonlocal regularization,” IEEE International Symposium on Circuits and Systems,  2013, 2836–2839 (2013).

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Yang, J.

J. Yang, Y.J. Li, C.-W. Chan, and Q. Shen, “Image fusion for spatial enhancement of hyperspectral image via pixel group based non-local sparse representation,” Remote Sensing 9, 53 (2017).

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C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented lagrangian method with applications to total variation minimization,” Computational Optimization and Applications 56, 507–530 (2013).
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J. Zhang, S. Liu, R. Xiong, S. Ma, and D. Zhao, “Improved total variation based image compressive sensing recovery by nonlocal regularization,” IEEE International Symposium on Circuits and Systems,  2013, 2836–2839 (2013).

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J. Zhang, S. Liu, R. Xiong, S. Ma, and D. Zhao, “Improved total variation based image compressive sensing recovery by nonlocal regularization,” IEEE International Symposium on Circuits and Systems,  2013, 2836–2839 (2013).

Appl. Opt. (4)

Applied and Computational Harmonic Analysis (1)

D. Needell and J. Tropp, “Cosamp: Iterative signal recovery from incomplete and inaccurate samples,” Applied and Computational Harmonic Analysis 26, 301–321 (2009).
[Crossref]

Computational and mathematical methods in medicine (1)

S. Cuomo, P. D. Michele, and F. Piccialli, “3d data denoising via nonlocal means filter by using parallel gpu strategies,” Computational and mathematical methods in medicine 2014, 523862 (2014).
[Crossref] [PubMed]

Computational Optimization and Applications (1)

C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented lagrangian method with applications to total variation minimization,” Computational Optimization and Applications 56, 507–530 (2013).
[Crossref]

IEEE International Symposium on Circuits and Systems (1)

J. Zhang, S. Liu, R. Xiong, S. Ma, and D. Zhao, “Improved total variation based image compressive sensing recovery by nonlocal regularization,” IEEE International Symposium on Circuits and Systems,  2013, 2836–2839 (2013).

IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing (1)

P. Meza, J. E. Pezoa, and S. N. Torres, “Multidimensional striping noise compensation in hyperspectral imaging: Exploiting hypercubes’s spatial, spectral, and temporal redundancy,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 9, 4428–4441 (2016).
[Crossref]

IEEE Journal of Solid-State Circuits (1)

H. Tian, B. Fowler, and A. Gamal, “Analysis of temporal noise in cmos photodiode active pixel sensor,” IEEE Journal of Solid-State Circuits 36, 92–101 (2001).
[Crossref]

IEEE Transactions on Image Processing (1)

J. Bioucas-Dias and M. Figueiredo, “A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Transactions on Image Processing 16, 2992–3004 (2007).
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IEEE Transactions on Information Theory (4)

R. Ward, “Compressed sensing with cross validation,” IEEE Transactions on Information Theory 55, 5773–5782 (2009).
[Crossref]

D. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory 52, 1289–1306 (2006).
[Crossref]

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory 52, 489–509 (2006).
[Crossref]

J. Tropp and A. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Transactions on Information Theory 53, 4655–4666 (2007).
[Crossref]

IEEE Transactions on Signal Processing (1)

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: From theory to applications,” IEEE Transactions on Signal Processing 59, 4053–4085 (2011).
[Crossref]

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D. S. Antony and G. Rathna, “Gpu based fast non local means algorithm,” Journal of Image and Graphics 3, 122 (2015).

Nature (1)

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
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Opt. Express (1)

Opt. Lett. (1)

Proc. IEEE Conference on Computer Vision and Pattern Recognition (1)

A. Buades, B. Coll, and J.-M. Morel, “A non-local algorithm for image denoising,” Proc. IEEE Conference on Computer Vision and Pattern Recognition 2, 60–65 (2005).

Proc. IS&T international Symposium on Electronic Imaging (1)

P. Meza, E. Vera, and J. Martinez, “Improved reconstruction for compressive hyperspectral imaging using spatial-spectral non-local means regularization,” Proc. IS&T international Symposium on Electronic Imaging 2016, 1–5 (2016).

Proc. SPIE (2)

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606501 (2006).

A. E. Gamal, B. A. Fowler, H. Min, and X. Liu, “Modeling and estimation of fpn components in cmos image sensors,” Proc. SPIE 3301, 330101 (1998).

Remote Sensing (1)

J. Yang, Y.J. Li, C.-W. Chan, and Q. Shen, “Image fusion for spatial enhancement of hyperspectral image via pixel group based non-local sparse representation,” Remote Sensing 9, 53 (2017).

Sensors (1)

W. Huang, L. Xiao, H. Liu, and Z. Wei, “Hyperspectral imagery super-resolution by compressive sensing inspired dictionary learning and spatial-spectral regularization,” Sensors 15, 2041–2058 (2015).
[Crossref] [PubMed]

SIAM Journal on Imaging Sciences (2)

T. Goldstein and S. Osher, “The split bregman method for l1-regularized problems,” SIAM Journal on Imaging Sciences 2, 323–343 (2009).
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S. Becker, J. Bobin, and E. J. Candés, “Nesta: A fast and accurate first-order method for sparse recovery,” SIAM Journal on Imaging Sciences 4, 1–39 (2011).
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E. Candes and T. Tao, “The dantzig selector: Statistical estimation when p is much larger than n,” The Annals of Statistics 35, 2313–2351 (2007).
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Other (2)

T. Sun and K. Kelly, “Compressive sensing hyperspectral imager,” Frontiers in Optics 2009/Laser Science XXV/Fall 2009 OSA Optics & Photonics Technical Digest p, CTuA5 (2009).

M. Borengasser, W. S. Hungate, and R. L. Watkins, Hyperspectral Remote Sensing: Principles and Applications (CRC, 2008).

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Figures (7)

Fig. 1
Fig. 1 Experimental setups based on the a) Photonfocus Hurricane 40 V10E PBHC and the b) CHI laboratory prototype.
Fig. 2
Fig. 2 Sample images taken at 790 [nm] from the acquired hypercubes a) I and b) II. The two squares, red and blue, depict the cropped hypercubes used to simulate the CS measurements.
Fig. 3
Fig. 3 Sample images taken at 661 [nm], where (a–d) correspond to the four references images from hypercubes I and II (H.I and H.II). Images from (e–h) and (i–l) correspond to the rendered results using the TVAL3 and the proposed algorithm, respectively.
Fig. 4
Fig. 4 Sample images taken at 790 [nm], where (a–d) correspond to the four references images from hypercubes I and II (H.I and H.II). Images from (e–h) and (i–l) correspond to the rendered results using the TVAL3 and the proposed algorithm, respectively.
Fig. 5
Fig. 5 Sample images at 533 [nm] with a spatial resolution of 100 × 100 pixels using the TVAL3 algorithm (a–c) and the proposed algorithm (d–f), considering a 10%, 15%, and 20% compression ratio.
Fig. 6
Fig. 6 Sample images at 533 [nm] with a spatial resolution of 200 × 200 pixels using the TVAL3 algorithm (a–c) and the proposed algorithm (d–f), considering a 10%, 15%, and 20% compression ratio.
Fig. 7
Fig. 7 Reconstructed spectral images of 4 band-pass optical filters using the proposed algorithm, considering 5 neighboring spectral band,, tuned at a) 850, b) 900, c) 1000, and d) 1100 [nm]. The curves presented in (e) and (f) correspond to the spectral signature measured with the spectrometer and the estimated signature produced by the proposed algorithm.

Tables (3)

Tables Icon

Table 1 RMSE metrics for the estimated cropped spectral images (blue and red) from hypercubes I and II (H.I and H.II) affected by 0%, 10% and 20% noise, using the TVAL3 and the proposed algorithm.

Tables Icon

Table 2 Performance metrics for the estimated cropped spectral images (blue and red) from hypercubes I and II (H.I and H.II) using the TVAL3 and the proposed algorithm.

Tables Icon

Table 3 Roughness metric for the rendered images taken at 533 [nm], with a spatial resolution of 100 × 100 and 200 × 200, using the TVAL3 and the proposed algorithm.

Equations (13)

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f k = Φ u k + η k = Φ Ψ θ k + η k ,
min θ k N × 1 Ψ θ k 1 + β 2 f k Φ Ψ θ k 2 2 .
Ψ θ k 1 = u k 1 = | x u k | + | y u k | .
min u k N × 1 u k T V + α 2 u k l = 1 L W k l u l 2 2 + β 2 f k Φ Ψ θ k 2 2 ,
W k l = { w k l ( i , j ) : j O i 0 : otherwise ,
w k l ( i , j ) = 1 Z k ( i ) exp ( u k ( O i ) u l ( O j ) 2 , g 2 h 2 ) ,
Z k l ( i , j ) = l j exp ( u k ( O i ) u l ( O j ) 2 , g 2 h 2 ) .
( u k p + 1 , d x , k p + 1 , d y , k p + 1 ) = min u k , d x , k , d y , k | d x , k | + | d y , k | + α 2 u k l = 1 L W k l u l 2 2 + β 2 Φ u k f k + c k p 2 2 + γ 2 x u k d x , k p + e x , k p 2 2 + γ 2 y u k d y , k p + e y , k p 2 2
c k p + 1 = c k p + ( Φ u k p + 1 f k )
e x , k p + 1 = c x , k p + ( x u k p + 1 d x , k p + 1 )
e y , k p + 1 = c y , k p + ( y u k p + 1 d y , k p + 1 )
R M S E ( u ^ , u ) = [ 1 N n = 1 N ( u ^ ( n ) u ( u ) ) 2 ] 1 2 .
ρ ( u ^ ) = h * u ^ + h T * u ^ u ^ ,

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