Abstract

An efficient method and system for compressive sensing of hyperspectral data is presented. Compression efficiency is achieved by randomly encoding both the spatial and the spectral domains of the hyperspectral datacube. Separable sensing architecture is used to reduce the computational complexity associated with the compressive sensing of a large volume of data, which is typical of hyperspectral imaging. The system enables optimizing the ratio between the spatial and the spectral compression sensing ratios. The method is demonstrated by simulations performed on real hyperspectral data.

© 2013 Optical Society of America

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2012 (8)

L. McMackin, M. A. Herman, B. Chatterjee, and M. Weldon, “A high-resolution SWIR camera via compressed sensing,” Proc. SPIE 8353, 835303 (2012).
[CrossRef]

S. Evladov, O. Levi, and A. Stern, “Progressive compressive imaging from radon projections,” Opt. Express 20, 4260–4271 (2012).
[CrossRef]

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

D. J. Townsend, P. K. Poon, S. Wehrwein, T. Osman, A. V. Mariano, E. M. Vera, M. D. Stenner, and M. E. Gehm, “Static compressive tracking,” Opt. Express 20, 21160–21172 (2012).
[CrossRef]

S. Schwartz, A. Wong, and D. A. Clausi, “Compressive fluorescence microscopy using saliency-guided sparse reconstruction ensemble fusion,” Opt. Express 20, 17281–17296 (2012).
[CrossRef]

V. Studer, “PNAS plus: Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. USA 109, E1679–E1687 (2012).
[CrossRef]

C. Li, T. Sun, K. F. Kelly, and Y. Zhang, “A compressive sensing and unmixing scheme for hyperspectral data processing,” IEEE Trans. Image Process. 21, 1200–1210 (2012).
[CrossRef]

M. F. Duarte and R. G. Baraniuk, “Kronecker compressive sensing,” IEEE Trans. Image Process. 21, 494–504 (2012).
[CrossRef]

2011 (5)

2010 (2)

J. Lv, Y. Li, B. Huang, and C. Wu, “Hyperspectral compressive sensing,” Proc. SPIE 7810, 781003 (2010).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6, 506–509 (2010).
[CrossRef]

2009 (5)

A. A. Wagadarikar, N. P. Pitsianis, X. Sun, and D. J. Brady, “Video rate spectral imaging using a coded aperture snapshot spectral imager,” Opt. Express 17, 6368–6388 (2009).
[CrossRef]

Y. Rivenson and A. Stern, “Compressed imaging with a separable sensing operator,” IEEE Signal Process. Lett. 16, 449–452 (2009).
[CrossRef]

M. de Moraes Marim, E. D. Angelini, and J. Olivo-Marin, “Compressed sensing in biological microscopy,” Proc. SPIE 7446, 744605 (2009).
[CrossRef]

J. Ma, “Single-pixel remote sensing,” IEEE Geosci. Remote Sens. Lett. 2, 199–203 (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]

2008 (6)

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, Ting Sun, K. F. Kelly, and R. G. 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. G. Baraniuk, and D. M. 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,” in Opt. Lett. 33, 974–976 (2008).

A. Ashok, P. K. Baheti, and M. A. Neifeld, “Compressive imaging system design using task-specific information,” Appl. Opt. 47, 4457–4471 (2008).
[CrossRef]

A. Stern, Y. Rivenson, and B. Javidi, “Optically compressed image sensing using random aperture coding,” Proc. SPIE 6975, 69750D (2008).
[CrossRef]

2007 (3)

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]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).
[CrossRef]

A. Stern, and B. Javidi, “Random projections imaging with extended space-bandwidth product,” J. Disp. Technol. 3, 315–320 (2007).
[CrossRef]

2006 (1)

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

2003 (1)

G. A. Shaw, and H.-H. K. Burke, “Spectral imaging for remote sensing,” Lincoln Lab. J. 14, 3–28(2003).

2002 (1)

N. Keshava, and J. F. Mustard, “Spectral unmixing,” IEEE Signal Process. Mag. 19(1), 44–57 (2002).
[CrossRef]

2001 (1)

S.-E. Qian, A. B. Hollinger, M. Dutkiewicz, H. A. Z. Tsang, and J. R. Freemantle, “Effect of lossy vector quantization hyperspectral data compression on retrieval of red-edge indices,” IEEE Trans. Geosci. Remote Sens. 39, 1459–1470 (2001).
[CrossRef]

1997 (1)

M. J. Ryan and J. F. Arnold, “Lossy compression of hyperspectral data using vector quantization,” Remote Sens. Environ. 61, 419–436 (1997).
[CrossRef]

Angelini, E. D.

M. de Moraes Marim, E. D. Angelini, and J. Olivo-Marin, “Compressed sensing in biological microscopy,” Proc. SPIE 7446, 744605 (2009).
[CrossRef]

Arce, G.

Y. Wu, and G. Arce, “Snapshot spectral imaging via compressive random convolution,” in 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2011), pp. 1465–1468.

H. Arguello, and G. Arce, “Code aperture agile spectral imaging (CAASI),” in Imaging Systems Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper ITuA4.

Arce, G. R.

Arguello, H.

H. Arguello, and G. R. Arce, “Code aperture optimization for spectrally agile compressive imaging,” J. Opt. Soc. Am. A 28, 2400–2413 (2011).
[CrossRef]

H. Arguello, and G. Arce, “Code aperture agile spectral imaging (CAASI),” in Imaging Systems Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper ITuA4.

Arnold, J. F.

M. J. Ryan and J. F. Arnold, “Lossy compression of hyperspectral data using vector quantization,” Remote Sens. Environ. 61, 419–436 (1997).
[CrossRef]

Ashok, A.

Baheti, P. K.

Baraniuk, R. G.

M. F. Duarte and R. G. Baraniuk, “Kronecker compressive sensing,” IEEE Trans. Image Process. 21, 494–504 (2012).
[CrossRef]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, Ting Sun, K. F. Kelly, and R. G. 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. G. Baraniuk, and D. M. 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,” in Opt. Lett. 33, 974–976 (2008).

Bioucas-Dias, J. M.

M. Iordache, J. M. Bioucas-Dias, and A. Plaza, “Sparse unmixing of hyperspectral data,” IEEE Trans. Geosci. Remote Sens. 49, 2014–2039 (2011).
[CrossRef]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).
[CrossRef]

Brady, D.

Q. Zhang, R. Plemmons, D. Kittle, D. Brady, and S. Prasad, “Reconstructing and segmenting hyperspectral images from compressed measurements,” in 3rd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS) (IEEE, 2011).

Brady, D. J.

Burke, H.-H. K.

G. A. Shaw, and H.-H. K. Burke, “Spectral imaging for remote sensing,” Lincoln Lab. J. 14, 3–28(2003).

Candes, E. J.

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

Chan, W. L.

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

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

Charan, K.

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

Chatterjee, B.

L. McMackin, M. A. Herman, B. Chatterjee, and M. Weldon, “A high-resolution SWIR camera via compressed sensing,” Proc. SPIE 8353, 835303 (2012).
[CrossRef]

Clausi, D. A.

Davenport, M. A.

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

de Moraes Marim, M.

M. de Moraes Marim, E. D. Angelini, and J. Olivo-Marin, “Compressed sensing in biological microscopy,” Proc. SPIE 7446, 744605 (2009).
[CrossRef]

Dinakarababu, D.

Donoho, D. L.

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

Driggers, R. G.

J. S. Sanders, R. E. Williams, R. G. Driggers, and C. E. Halford, “A novel concept for hyperspectral remote sensing,” in Proceedings, IEEE Southeastcon (IEEE, 1992), vol. 1, pp. 363–367.

Duarte, M. F.

M. F. Duarte and R. G. Baraniuk, “Kronecker compressive sensing,” IEEE Trans. Image Process. 21, 494–504 (2012).
[CrossRef]

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

Dutkiewicz, M.

S.-E. Qian, A. B. Hollinger, M. Dutkiewicz, H. A. Z. Tsang, and J. R. Freemantle, “Effect of lossy vector quantization hyperspectral data compression on retrieval of red-edge indices,” IEEE Trans. Geosci. Remote Sens. 39, 1459–1470 (2001).
[CrossRef]

Evladov, S.

Felt, R.

T. Wilson and R. Felt, “Hyperspectral remote sensing technology (HRST) program,” in Proceedings IEEE Aerospace Conference (IEEE, 1998), vol. 5, pp. 193–200.

Figueiredo, M. A. T.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).
[CrossRef]

Freemantle, J. R.

S.-E. Qian, A. B. Hollinger, M. Dutkiewicz, H. A. Z. Tsang, and J. R. Freemantle, “Effect of lossy vector quantization hyperspectral data compression on retrieval of red-edge indices,” IEEE Trans. Geosci. Remote Sens. 39, 1459–1470 (2001).
[CrossRef]

Gehm, M.

Gehm, M. E.

Golish, D.

Halford, C. E.

J. S. Sanders, R. E. Williams, R. G. Driggers, and C. E. Halford, “A novel concept for hyperspectral remote sensing,” in Proceedings, IEEE Southeastcon (IEEE, 1992), vol. 1, pp. 363–367.

Hassibi, B.

M. Stojnic, W. Xu, and B. Hassibi, “Compressed sensing of approximately sparse signals,” in IEEE International Symposium on Information Theory (IEEE, 2008), pp. 2182–2186.

Herman, M. A.

L. McMackin, M. A. Herman, B. Chatterjee, and M. Weldon, “A high-resolution SWIR camera via compressed sensing,” Proc. SPIE 8353, 835303 (2012).
[CrossRef]

Hollinger, A. B.

S.-E. Qian, A. B. Hollinger, M. Dutkiewicz, H. A. Z. Tsang, and J. R. Freemantle, “Effect of lossy vector quantization hyperspectral data compression on retrieval of red-edge indices,” IEEE Trans. Geosci. Remote Sens. 39, 1459–1470 (2001).
[CrossRef]

Huang, B.

J. Lv, Y. Li, B. Huang, and C. Wu, “Hyperspectral compressive sensing,” Proc. SPIE 7810, 781003 (2010).
[CrossRef]

In, J.

J. In, S. Shirani, and F. Kossentini, “JPEG compliant efficient progressive image coding,” in Proceedings of the 1998 IEEE International Conference On Acoustics, Speech and Signal Processing (IEEE, 1998), vol. 5, pp. 2633–2636.

Iordache, M.

M. Iordache, J. M. Bioucas-Dias, and A. Plaza, “Sparse unmixing of hyperspectral data,” IEEE Trans. Geosci. Remote Sens. 49, 2014–2039 (2011).
[CrossRef]

Javidi, B.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6, 506–509 (2010).
[CrossRef]

A. Stern, Y. Rivenson, and B. Javidi, “Optically compressed image sensing using random aperture coding,” Proc. SPIE 6975, 69750D (2008).
[CrossRef]

A. Stern, and B. Javidi, “Random projections imaging with extended space-bandwidth product,” J. Disp. Technol. 3, 315–320 (2007).
[CrossRef]

John, R.

Kashter, Y.

Kelly, K.

T. Sun, and K. Kelly, “Compressive sensing hyperspectral imager,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CTuA5.

Kelly, K. F.

C. Li, T. Sun, K. F. Kelly, and Y. Zhang, “A compressive sensing and unmixing scheme for hyperspectral data processing,” IEEE Trans. Image Process. 21, 1200–1210 (2012).
[CrossRef]

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

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

Keshava, N.

N. Keshava, and J. F. Mustard, “Spectral unmixing,” IEEE Signal Process. Mag. 19(1), 44–57 (2002).
[CrossRef]

Kittle, D.

Q. Zhang, R. Plemmons, D. Kittle, D. Brady, and S. Prasad, “Reconstructing and segmenting hyperspectral images from compressed measurements,” in 3rd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS) (IEEE, 2011).

Kossentini, F.

J. In, S. Shirani, and F. Kossentini, “JPEG compliant efficient progressive image coding,” in Proceedings of the 1998 IEEE International Conference On Acoustics, Speech and Signal Processing (IEEE, 1998), vol. 5, pp. 2633–2636.

Laska, J. N.

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

Lee, C.

S. Lim, K. H. Sohn, and C. Lee, “Principal component analysis for compression of hyperspectral images,” in IEEE 2001 International Geoscience and Remote Sensing Symposium (IEEE, 2001), vol. 1, pp. 97–99.

S. Lim, K. Sohn, and C. Lee, “Compression for hyperspectral images using three dimensional wavelet transform,” in IEEE 2001 International Geoscience and Remote Sensing Symposium (IEEE, 2001), vol. 1, pp. 109–111.

Levi, O.

Li, C.

C. Li, T. Sun, K. F. Kelly, and Y. Zhang, “A compressive sensing and unmixing scheme for hyperspectral data processing,” IEEE Trans. Image Process. 21, 1200–1210 (2012).
[CrossRef]

Li, Y.

J. Lv, Y. Li, B. Huang, and C. Wu, “Hyperspectral compressive sensing,” Proc. SPIE 7810, 781003 (2010).
[CrossRef]

Lim, S.

S. Lim, K. H. Sohn, and C. Lee, “Principal component analysis for compression of hyperspectral images,” in IEEE 2001 International Geoscience and Remote Sensing Symposium (IEEE, 2001), vol. 1, pp. 97–99.

S. Lim, K. Sohn, and C. Lee, “Compression for hyperspectral images using three dimensional wavelet transform,” in IEEE 2001 International Geoscience and Remote Sensing Symposium (IEEE, 2001), vol. 1, pp. 109–111.

Lv, J.

J. Lv, Y. Li, B. Huang, and C. Wu, “Hyperspectral compressive sensing,” Proc. SPIE 7810, 781003 (2010).
[CrossRef]

Ma, J.

J. Ma, “Single-pixel remote sensing,” IEEE Geosci. Remote Sens. Lett. 2, 199–203 (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]

Marcia, R. F.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 072601 (2011).
[CrossRef]

Mariano, A. V.

McMackin, L.

L. McMackin, M. A. Herman, B. Chatterjee, and M. Weldon, “A high-resolution SWIR camera via compressed sensing,” Proc. SPIE 8353, 835303 (2012).
[CrossRef]

Mirza, I. O.

Mittleman, D. M.

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

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

Moravec, M. L.

Mustard, J. F.

N. Keshava, and J. F. Mustard, “Spectral unmixing,” IEEE Signal Process. Mag. 19(1), 44–57 (2002).
[CrossRef]

Neifeld, M. A.

Nichols, J. M.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 072601 (2011).
[CrossRef]

Olivo-Marin, J.

M. de Moraes Marim, E. D. Angelini, and J. Olivo-Marin, “Compressed sensing in biological microscopy,” Proc. SPIE 7446, 744605 (2009).
[CrossRef]

Osman, T.

Pitsianis, N. P.

Plaza, A.

M. Iordache, J. M. Bioucas-Dias, and A. Plaza, “Sparse unmixing of hyperspectral data,” IEEE Trans. Geosci. Remote Sens. 49, 2014–2039 (2011).
[CrossRef]

Plemmons, R.

Q. Zhang, R. Plemmons, D. Kittle, D. Brady, and S. Prasad, “Reconstructing and segmenting hyperspectral images from compressed measurements,” in 3rd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS) (IEEE, 2011).

Poon, P. K.

Prasad, S.

Q. Zhang, R. Plemmons, D. Kittle, D. Brady, and S. Prasad, “Reconstructing and segmenting hyperspectral images from compressed measurements,” in 3rd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS) (IEEE, 2011).

Prather, D. W.

Qian, S.-E.

S.-E. Qian, A. B. Hollinger, M. Dutkiewicz, H. A. Z. Tsang, and J. R. Freemantle, “Effect of lossy vector quantization hyperspectral data compression on retrieval of red-edge indices,” IEEE Trans. Geosci. Remote Sens. 39, 1459–1470 (2001).
[CrossRef]

Rivenson, Y.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6, 506–509 (2010).
[CrossRef]

Y. Rivenson and A. Stern, “Compressed imaging with a separable sensing operator,” IEEE Signal Process. Lett. 16, 449–452 (2009).
[CrossRef]

A. Stern, Y. Rivenson, and B. Javidi, “Optically compressed image sensing using random aperture coding,” Proc. SPIE 6975, 69750D (2008).
[CrossRef]

Y. Rivenson, and A. Stern, “Compressive sensing techniques in holography,” in 10th Euro-American Workshop OnInformation Optics (WIO), (IEEE, 2011), pp. 1–2.

Y. Rivenson and A. Stern, “Practical compressive sensing of large images,” presented at 16th International Conference on Digital Signal Processing (IEEE, 2009), pp. 1–9.

Ryan, M. J.

M. J. Ryan and J. F. Arnold, “Lossy compression of hyperspectral data using vector quantization,” Remote Sens. Environ. 61, 419–436 (1997).
[CrossRef]

Sanders, J. S.

J. S. Sanders, R. E. Williams, R. G. Driggers, and C. E. Halford, “A novel concept for hyperspectral remote sensing,” in Proceedings, IEEE Southeastcon (IEEE, 1992), vol. 1, pp. 363–367.

Schulz, T. J.

Schwartz, S.

Shaw, G. A.

G. A. Shaw, and H.-H. K. Burke, “Spectral imaging for remote sensing,” Lincoln Lab. J. 14, 3–28(2003).

Shen, Y.

Q. Wang, and Y. Shen, “A JPEG2000 and nonlinear correlation measurement based method to enhance hyperspectral image compression,” in Proceedings IEEE Instrumentation and Measurement Technology Conference (IEEE, 2005), pp. 2009–2011.

Shirani, S.

J. In, S. Shirani, and F. Kossentini, “JPEG compliant efficient progressive image coding,” in Proceedings of the 1998 IEEE International Conference On Acoustics, Speech and Signal Processing (IEEE, 1998), vol. 5, pp. 2633–2636.

Sohn, K.

S. Lim, K. Sohn, and C. Lee, “Compression for hyperspectral images using three dimensional wavelet transform,” in IEEE 2001 International Geoscience and Remote Sensing Symposium (IEEE, 2001), vol. 1, pp. 109–111.

Sohn, K. H.

S. Lim, K. H. Sohn, and C. Lee, “Principal component analysis for compression of hyperspectral images,” in IEEE 2001 International Geoscience and Remote Sensing Symposium (IEEE, 2001), vol. 1, pp. 97–99.

Stenner, M. D.

Stern, A.

Y. Kashter, O. Levi, and A. Stern, “Optical compressive change and motion detection,” Appl. Opt. 51, 2491–2496 (2012).
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S. Evladov, O. Levi, and A. Stern, “Progressive compressive imaging from radon projections,” Opt. Express 20, 4260–4271 (2012).
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Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6, 506–509 (2010).
[CrossRef]

Y. Rivenson and A. Stern, “Compressed imaging with a separable sensing operator,” IEEE Signal Process. Lett. 16, 449–452 (2009).
[CrossRef]

A. Stern, Y. Rivenson, and B. Javidi, “Optically compressed image sensing using random aperture coding,” Proc. SPIE 6975, 69750D (2008).
[CrossRef]

A. Stern, and B. Javidi, “Random projections imaging with extended space-bandwidth product,” J. Disp. Technol. 3, 315–320 (2007).
[CrossRef]

Y. Rivenson, and A. Stern, “Compressive sensing techniques in holography,” in 10th Euro-American Workshop OnInformation Optics (WIO), (IEEE, 2011), pp. 1–2.

Y. Rivenson and A. Stern, “Practical compressive sensing of large images,” presented at 16th International Conference on Digital Signal Processing (IEEE, 2009), pp. 1–9.

Stojnic, M.

M. Stojnic, W. Xu, and B. Hassibi, “Compressed sensing of approximately sparse signals,” in IEEE International Symposium on Information Theory (IEEE, 2008), pp. 2182–2186.

Studer, V.

V. Studer, “PNAS plus: Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. USA 109, E1679–E1687 (2012).
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Sun, T.

C. Li, T. Sun, K. F. Kelly, and Y. Zhang, “A compressive sensing and unmixing scheme for hyperspectral data processing,” IEEE Trans. Image Process. 21, 1200–1210 (2012).
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T. Sun, and K. Kelly, “Compressive sensing hyperspectral imager,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CTuA5.

Sun, Ting

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

Sun, X.

Takhar, D.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008).
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M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, Ting Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[CrossRef]

Townsend, D. J.

Tsang, H. A. Z.

S.-E. Qian, A. B. Hollinger, M. Dutkiewicz, H. A. Z. Tsang, and J. R. Freemantle, “Effect of lossy vector quantization hyperspectral data compression on retrieval of red-edge indices,” IEEE Trans. Geosci. Remote Sens. 39, 1459–1470 (2001).
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Vera, E. M.

Wagadarikar, A. A.

Wakin, M. B.

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
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Wang, Q.

Q. Wang, and Y. Shen, “A JPEG2000 and nonlinear correlation measurement based method to enhance hyperspectral image compression,” in Proceedings IEEE Instrumentation and Measurement Technology Conference (IEEE, 2005), pp. 2009–2011.

Wehrwein, S.

Weldon, M.

L. McMackin, M. A. Herman, B. Chatterjee, and M. Weldon, “A high-resolution SWIR camera via compressed sensing,” Proc. SPIE 8353, 835303 (2012).
[CrossRef]

Willett, R. M.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 072601 (2011).
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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).
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Williams, R. E.

J. S. Sanders, R. E. Williams, R. G. Driggers, and C. E. Halford, “A novel concept for hyperspectral remote sensing,” in Proceedings, IEEE Southeastcon (IEEE, 1992), vol. 1, pp. 363–367.

Wilson, T.

T. Wilson and R. Felt, “Hyperspectral remote sensing technology (HRST) program,” in Proceedings IEEE Aerospace Conference (IEEE, 1998), vol. 5, pp. 193–200.

Wong, A.

Wu, C.

J. Lv, Y. Li, B. Huang, and C. Wu, “Hyperspectral compressive sensing,” Proc. SPIE 7810, 781003 (2010).
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Wu, Y.

Y. Wu, I. O. Mirza, G. R. Arce, and D. W. Prather, “Development of a digital-micromirror-device-based multishot snapshot spectral imaging system,” Opt. Lett. 36, 2692–2694 (2011).
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Y. Wu, and G. Arce, “Snapshot spectral imaging via compressive random convolution,” in 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2011), pp. 1465–1468.

Xu, W.

M. Stojnic, W. Xu, and B. Hassibi, “Compressed sensing of approximately sparse signals,” in IEEE International Symposium on Information Theory (IEEE, 2008), pp. 2182–2186.

Zhang, Q.

Q. Zhang, R. Plemmons, D. Kittle, D. Brady, and S. Prasad, “Reconstructing and segmenting hyperspectral images from compressed measurements,” in 3rd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS) (IEEE, 2011).

Zhang, Y.

C. Li, T. Sun, K. F. Kelly, and Y. Zhang, “A compressive sensing and unmixing scheme for hyperspectral data processing,” IEEE Trans. Image Process. 21, 1200–1210 (2012).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

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

IEEE Geosci. Remote Sens. Lett. (2)

J. Ma, “Single-pixel remote sensing,” IEEE Geosci. Remote Sens. Lett. 2, 199–203 (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]

IEEE Signal Process. Lett. (1)

Y. Rivenson and A. Stern, “Compressed imaging with a separable sensing operator,” IEEE Signal Process. Lett. 16, 449–452 (2009).
[CrossRef]

IEEE Signal Process. Mag. (3)

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[CrossRef]

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

N. Keshava, and J. F. Mustard, “Spectral unmixing,” IEEE Signal Process. Mag. 19(1), 44–57 (2002).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (2)

M. Iordache, J. M. Bioucas-Dias, and A. Plaza, “Sparse unmixing of hyperspectral data,” IEEE Trans. Geosci. Remote Sens. 49, 2014–2039 (2011).
[CrossRef]

S.-E. Qian, A. B. Hollinger, M. Dutkiewicz, H. A. Z. Tsang, and J. R. Freemantle, “Effect of lossy vector quantization hyperspectral data compression on retrieval of red-edge indices,” IEEE Trans. Geosci. Remote Sens. 39, 1459–1470 (2001).
[CrossRef]

IEEE Trans. Image Process. (3)

M. F. Duarte and R. G. Baraniuk, “Kronecker compressive sensing,” IEEE Trans. Image Process. 21, 494–504 (2012).
[CrossRef]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).
[CrossRef]

C. Li, T. Sun, K. F. Kelly, and Y. Zhang, “A compressive sensing and unmixing scheme for hyperspectral data processing,” IEEE Trans. Image Process. 21, 1200–1210 (2012).
[CrossRef]

IEEE Trans. Inf. Theory (1)

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

J. Disp. Technol. (2)

A. Stern, and B. Javidi, “Random projections imaging with extended space-bandwidth product,” J. Disp. Technol. 3, 315–320 (2007).
[CrossRef]

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6, 506–509 (2010).
[CrossRef]

J. Opt. Soc. Am. A (1)

Lincoln Lab. J. (1)

G. A. Shaw, and H.-H. K. Burke, “Spectral imaging for remote sensing,” Lincoln Lab. J. 14, 3–28(2003).

Opt. Eng. (1)

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50, 072601 (2011).
[CrossRef]

Opt. Express (6)

Opt. Lett. (2)

Proc. Natl. Acad. Sci. USA (1)

V. Studer, “PNAS plus: Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. USA 109, E1679–E1687 (2012).
[CrossRef]

Proc. SPIE (4)

M. de Moraes Marim, E. D. Angelini, and J. Olivo-Marin, “Compressed sensing in biological microscopy,” Proc. SPIE 7446, 744605 (2009).
[CrossRef]

L. McMackin, M. A. Herman, B. Chatterjee, and M. Weldon, “A high-resolution SWIR camera via compressed sensing,” Proc. SPIE 8353, 835303 (2012).
[CrossRef]

A. Stern, Y. Rivenson, and B. Javidi, “Optically compressed image sensing using random aperture coding,” Proc. SPIE 6975, 69750D (2008).
[CrossRef]

J. Lv, Y. Li, B. Huang, and C. Wu, “Hyperspectral compressive sensing,” Proc. SPIE 7810, 781003 (2010).
[CrossRef]

Remote Sens. Environ. (1)

M. J. Ryan and J. F. Arnold, “Lossy compression of hyperspectral data using vector quantization,” Remote Sens. Environ. 61, 419–436 (1997).
[CrossRef]

Other (13)

Q. Zhang, R. Plemmons, D. Kittle, D. Brady, and S. Prasad, “Reconstructing and segmenting hyperspectral images from compressed measurements,” in 3rd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS) (IEEE, 2011).

Y. Rivenson and A. Stern, “Practical compressive sensing of large images,” presented at 16th International Conference on Digital Signal Processing (IEEE, 2009), pp. 1–9.

S. Lim, K. Sohn, and C. Lee, “Compression for hyperspectral images using three dimensional wavelet transform,” in IEEE 2001 International Geoscience and Remote Sensing Symposium (IEEE, 2001), vol. 1, pp. 109–111.

S. Lim, K. H. Sohn, and C. Lee, “Principal component analysis for compression of hyperspectral images,” in IEEE 2001 International Geoscience and Remote Sensing Symposium (IEEE, 2001), vol. 1, pp. 97–99.

J. S. Sanders, R. E. Williams, R. G. Driggers, and C. E. Halford, “A novel concept for hyperspectral remote sensing,” in Proceedings, IEEE Southeastcon (IEEE, 1992), vol. 1, pp. 363–367.

T. Wilson and R. Felt, “Hyperspectral remote sensing technology (HRST) program,” in Proceedings IEEE Aerospace Conference (IEEE, 1998), vol. 5, pp. 193–200.

J. In, S. Shirani, and F. Kossentini, “JPEG compliant efficient progressive image coding,” in Proceedings of the 1998 IEEE International Conference On Acoustics, Speech and Signal Processing (IEEE, 1998), vol. 5, pp. 2633–2636.

Q. Wang, and Y. Shen, “A JPEG2000 and nonlinear correlation measurement based method to enhance hyperspectral image compression,” in Proceedings IEEE Instrumentation and Measurement Technology Conference (IEEE, 2005), pp. 2009–2011.

T. Sun, and K. Kelly, “Compressive sensing hyperspectral imager,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CTuA5.

Y. Wu, and G. Arce, “Snapshot spectral imaging via compressive random convolution,” in 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2011), pp. 1465–1468.

H. Arguello, and G. Arce, “Code aperture agile spectral imaging (CAASI),” in Imaging Systems Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper ITuA4.

Y. Rivenson, and A. Stern, “Compressive sensing techniques in holography,” in 10th Euro-American Workshop OnInformation Optics (WIO), (IEEE, 2011), pp. 1–2.

M. Stojnic, W. Xu, and B. Hassibi, “Compressed sensing of approximately sparse signals,” in IEEE International Symposium on Information Theory (IEEE, 2008), pp. 2182–2186.

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Figures (9)

Fig. 1.
Fig. 1.

Hyperspectral cube.

Fig. 2.
Fig. 2.

(a) Schematic diagram of single pixel CS camera and its photodiode detector. (b) Expansion to multispectral imaging using a grating and a CCD vector.

Fig. 3.
Fig. 3.

Compressive sensing block diagram [10].

Fig. 4.
Fig. 4.

Schematic diagram of the spectral separable operator.

Fig. 5.
Fig. 5.

Schematic diagram of CHSISS system for CS HS imaging.

Fig. 6.
Fig. 6.

Left: original image of “Iris painting,” and (lower image) its reconstruction from 10% samples. Right: original image of “Parking lot,” and (lower image) its reconstruction from 10% samples.

Fig. 7.
Fig. 7.

RGB projection of 256 x 256 x 256 HS cube. (a) Source, (b) reconstruction from 128 x 128(spatial) x 102(spectral) measurements=10%, (c) reconstruction from 197 x 197(spatial) x 163(spectral) measurements=38%, (d) reconstruction from 204 x 204(spatial) x 20(spectral) measurements=5%, (e) reconstruction from 204 x 204(spatial) x 51(spectral) measurements=13%.

Fig. 8.
Fig. 8.

Reconstruction PSNR calculation for “Parking lot.” HS as function of spatial and spectral compression ratios. Points with same color represent the same overall compression ratio. For visualization purposes a surfaces grid was built by bilinear interpolation.

Fig. 9.
Fig. 9.

Reconstruction PSNR contours plots the CSHSS of the “Parking lot.”

Equations (17)

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

g = Φ f ,
M C μ 2 K log ( N ) .
μ ( Φ , Ψ ) = N max 1 i j M | Φ i H Ψ j | ,
f ^ = Ψ α ^ subject to min α ^ { g Φ Ψ α 2 2 + γ α 1 } ,
Φ y x = Φ y Φ x = [ ϕ y 1 , 1 Φ x ϕ y 1 , 2 Φ x ϕ y 1 , p Φ x ϕ y 2 , 1 Φ x ϕ y 2 , 2 Φ x ϕ y 2 , p Φ x ϕ y n , 1 Φ x ϕ y n , 1 Φ x ϕ y n , p Φ x ] .
vec ( F ) = [ f 1 f 2 f n ] .
vec ( G ) = Φ y x × vec ( F ) = ( Φ y T Φ x ) × vec ( F ) ,
G = Φ y F Φ x .
F ^ = Ψ A ^ Ψ T subject to min α { vec ( G ) vec ( Φ y Ψ A Ψ T Φ x ) 2 + γ vec ( A ) 1 } α = vec ( A )
μ ( Φ y x , Ψ y x ) = μ ( Φ y Φ x , Ψ y Ψ x ) = μ ( Φ y , Ψ y ) μ ( Φ x , Ψ x ) .
μ ( Φ y Φ x , Ψ ) μ ( Φ , Ψ ) 2 log 10 ( N ) 2 log 10 ( N ) = 1 2 log 10 ( N ) ,
1 2 log 10 ( N )
M x × M y × M λ N x × N y × N λ ,
M x × M y N x × N y = ( 217 256 ) 2 71.2 % ,
M λ N λ = 38 256 14.8 % .
M x × M y N x × N y = ( 181 256 ) 2 49.9 % ,
M λ N λ = 51 256 19.9 % ,

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