Abstract

We present a single disperser spectral imager that exploits recent theoretical work in the area of compressed sensing to achieve snapshot spectral imaging. An experimental prototype is used to capture the spatiospectral information of a scene that consists of two balls illuminated by different light sources. An iterative algorithm is used to reconstruct the data cube. The average spectral resolution is 3.6nm per spectral channel. The accuracy of the instrument is demonstrated by comparison of the spectra acquired with the proposed system with the spectra acquired by a nonimaging reference spectrometer.

© 2008 Optical Society of America

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  1. W. L. Smith, D. K. Zhou, F. W. Harrison, H. E. Revercomb, A. M. Larar, H.-L. Huang, and B. Huang, "Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft," Proc. SPIE 4151, 94-102 (2001).
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    [CrossRef]
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  20. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems," IEEE J. Sel. Top. Signal Process. 1, 586-597 (2007).
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2007 (3)

2006 (5)

J. M. Lerner, "Imaging spectrometer fundamentals for researchers in the biosciences--a tutorial," Cytometry Part A 69(8), 712-734 (2006).
[CrossRef]

E. J. 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]

M. E. Gehm, S. T. McCain, N. P. Pitsianis, D. J. Brady, P. Potuluri, and M. E. Sullivan, "Static two-dimensional aperture coding for multimodal multiplex spectroscopy," Appl. Opt. 45, 2965-2974 (2006).
[CrossRef] [PubMed]

D. J. Brady and M. E. Gehm, "Compressive imaging spectrometers using coded apertures," Proc. SPIE 6246, 62460A (2006).
[CrossRef]

W. R. Johnson, D. W. Wilson, and G. Bearman, "Spatial-spectral modulating snapshot hyperspectral imager," Appl. Opt. 45, 1898-1908 (2006).
[CrossRef] [PubMed]

2005 (1)

Y.-H. Dai and R. Fletcher, "Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming," Numer. Math. 100, 21-47 (2005).
[CrossRef]

2001 (2)

W. L. Smith, D. K. Zhou, F. W. Harrison, H. E. Revercomb, A. M. Larar, H.-L. Huang, and B. Huang, "Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft," Proc. SPIE 4151, 94-102 (2001).
[CrossRef]

C. M. Stellman, F. M. Olchowski, and J. V. Michalowicz, "WAR HORSE (wide-area reconnaissance: hyperspectral overhead real-time surveillance experiment)," Proc. SPIE 4379, 339-346 (2001).
[CrossRef]

2000 (2)

1999 (1)

S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput. 20, 33-61 (1999).
[CrossRef]

1998 (1)

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, "Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

1997 (2)

J. M. Mooney, V. E. Vickers, M. An, and A. K. Brodzik, "High-throughput hyperspectral infrared camera," J. Opt. Soc. Am. A 14, 2951-2961 (1997).
[CrossRef]

M. R. Descour, C. E. Volin, E. L. Dereniak, K. J. Thorne, A. B. Schumacher, D. W. Wilson, and P. D. Maker, "Demonstration of a high-speed nonscanning imaging spectrometer," Opt. Lett. 22, 1271-1273 (1997).
[CrossRef] [PubMed]

1996 (1)

R. Tibshirani, "Regression shrinkage and selection via the lasso," J. R. Stat. Soc. Ser. B 58, 267-288 (1996).

1994 (2)

E. Herrala, J. T. Okkonen, T. S. Hyvarinen, M. Aikio, and J. Lammasniemi, "Imaging spectrometer for process industry applications," Proc. SPIE 2248, 33-40 (1994).
[CrossRef]

H. Morris, C. Hoyt, and P. Treado, "Imaging spectrometers for fluorescence and Raman microscopy: acousto-optic and liquid crystal tunable filters," Appl. Spectrosc. 48, 857-866 (1994).
[CrossRef]

1993 (1)

C. L. Bennett, M. R. Carter, D. J. Fields, and J. A. M. Hernandez, "Imaging Fourier transform spectrometer," Proc. SPIE 1937, 191-200 (1993).
[CrossRef]

Aikio, M.

E. Herrala, J. T. Okkonen, T. S. Hyvarinen, M. Aikio, and J. Lammasniemi, "Imaging spectrometer for process industry applications," Proc. SPIE 2248, 33-40 (1994).
[CrossRef]

An, M.

J. M. Mooney, V. E. Vickers, M. An, and A. K. Brodzik, "High-throughput hyperspectral infrared camera," J. Opt. Soc. Am. A 14, 2951-2961 (1997).
[CrossRef]

Andersson-Engels, S.

Arndt-Jovin, D.

Q. Hanley, P. Verveer, D. Arndt-Jovin, and T. Jovin, "Three dimensional spectral imaging by Hadamard transform spectroscopy in a programmable array microscope," J. Microsc. 197, 5-14 (2000).
[CrossRef] [PubMed]

Aronsson, M.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, "Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Bearman, G.

W. R. Johnson, D. W. Wilson, and G. Bearman, "Spatial-spectral modulating snapshot hyperspectral imager," Appl. Opt. 45, 1898-1908 (2006).
[CrossRef] [PubMed]

Bennett, C. L.

C. L. Bennett, M. R. Carter, D. J. Fields, and J. A. M. Hernandez, "Imaging Fourier transform spectrometer," Proc. SPIE 1937, 191-200 (1993).
[CrossRef]

Benz, A. O.

R. P. Lin, B. R. Dennis, and A. O. Benz, eds., The Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI)--Mission Description and Early Results (Kluwer Academic, 2003).
[PubMed]

Bevilacqua, F.

Brady, D.

Brady, D. J.

Brodzik, A. K.

J. M. Mooney, V. E. Vickers, M. An, and A. K. Brodzik, "High-throughput hyperspectral infrared camera," J. Opt. Soc. Am. A 14, 2951-2961 (1997).
[CrossRef]

Candes, E. J.

E. J. 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]

Carter, M. R.

C. L. Bennett, M. R. Carter, D. J. Fields, and J. A. M. Hernandez, "Imaging Fourier transform spectrometer," Proc. SPIE 1937, 191-200 (1993).
[CrossRef]

Chen, S. S.

S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput. 20, 33-61 (1999).
[CrossRef]

Chippendale, B. J.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, "Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Chovit, C. J.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, "Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Chrien, T. G.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, "Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Dai, Y.-H.

Y.-H. Dai and R. Fletcher, "Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming," Numer. Math. 100, 21-47 (2005).
[CrossRef]

Dam, J. S.

Dennis, B. R.

R. P. Lin, B. R. Dennis, and A. O. Benz, eds., The Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI)--Mission Description and Early Results (Kluwer Academic, 2003).
[PubMed]

Dereniak, E. L.

M. R. Descour, C. E. Volin, E. L. Dereniak, K. J. Thorne, A. B. Schumacher, D. W. Wilson, and P. D. Maker, "Demonstration of a high-speed nonscanning imaging spectrometer," Opt. Lett. 22, 1271-1273 (1997).
[CrossRef] [PubMed]

Descour, M. R.

M. R. Descour, C. E. Volin, E. L. Dereniak, K. J. Thorne, A. B. Schumacher, D. W. Wilson, and P. D. Maker, "Demonstration of a high-speed nonscanning imaging spectrometer," Opt. Lett. 22, 1271-1273 (1997).
[CrossRef] [PubMed]

Donoho, D. L.

S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput. 20, 33-61 (1999).
[CrossRef]

Eastwood, M. L.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, "Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Faust, J. A.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, "Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Fields, D. J.

C. L. Bennett, M. R. Carter, D. J. Fields, and J. A. M. Hernandez, "Imaging Fourier transform spectrometer," Proc. SPIE 1937, 191-200 (1993).
[CrossRef]

Figueiredo, M. A.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems," IEEE J. Sel. Top. Signal Process. 1, 586-597 (2007).
[CrossRef]

Fletcher, R.

Y.-H. Dai and R. Fletcher, "Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming," Numer. Math. 100, 21-47 (2005).
[CrossRef]

Gehm, M. E.

Green, R. O.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, "Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Hanley, Q.

Q. Hanley, P. Verveer, D. Arndt-Jovin, and T. Jovin, "Three dimensional spectral imaging by Hadamard transform spectroscopy in a programmable array microscope," J. Microsc. 197, 5-14 (2000).
[CrossRef] [PubMed]

Harrison, F. W.

W. L. Smith, D. K. Zhou, F. W. Harrison, H. E. Revercomb, A. M. Larar, H.-L. Huang, and B. Huang, "Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft," Proc. SPIE 4151, 94-102 (2001).
[CrossRef]

Harwit, M.

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

Hernandez, J. A.

C. L. Bennett, M. R. Carter, D. J. Fields, and J. A. M. Hernandez, "Imaging Fourier transform spectrometer," Proc. SPIE 1937, 191-200 (1993).
[CrossRef]

Herrala, E.

E. Herrala, J. T. Okkonen, T. S. Hyvarinen, M. Aikio, and J. Lammasniemi, "Imaging spectrometer for process industry applications," Proc. SPIE 2248, 33-40 (1994).
[CrossRef]

Hoyt, C.

Huang, B.

W. L. Smith, D. K. Zhou, F. W. Harrison, H. E. Revercomb, A. M. Larar, H.-L. Huang, and B. Huang, "Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft," Proc. SPIE 4151, 94-102 (2001).
[CrossRef]

Huang, H. L.

W. L. Smith, D. K. Zhou, F. W. Harrison, H. E. Revercomb, A. M. Larar, H.-L. Huang, and B. Huang, "Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft," Proc. SPIE 4151, 94-102 (2001).
[CrossRef]

Hyvarinen, T. S.

E. Herrala, J. T. Okkonen, T. S. Hyvarinen, M. Aikio, and J. Lammasniemi, "Imaging spectrometer for process industry applications," Proc. SPIE 2248, 33-40 (1994).
[CrossRef]

John, R.

Johnson, W. R.

W. R. Johnson, D. W. Wilson, and G. Bearman, "Spatial-spectral modulating snapshot hyperspectral imager," Appl. Opt. 45, 1898-1908 (2006).
[CrossRef] [PubMed]

Jovin, T.

Q. Hanley, P. Verveer, D. Arndt-Jovin, and T. Jovin, "Three dimensional spectral imaging by Hadamard transform spectroscopy in a programmable array microscope," J. Microsc. 197, 5-14 (2000).
[CrossRef] [PubMed]

Lammasniemi, J.

E. Herrala, J. T. Okkonen, T. S. Hyvarinen, M. Aikio, and J. Lammasniemi, "Imaging spectrometer for process industry applications," Proc. SPIE 2248, 33-40 (1994).
[CrossRef]

Larar, A. M.

W. L. Smith, D. K. Zhou, F. W. Harrison, H. E. Revercomb, A. M. Larar, H.-L. Huang, and B. Huang, "Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft," Proc. SPIE 4151, 94-102 (2001).
[CrossRef]

Lerner, J. M.

J. M. Lerner, "Imaging spectrometer fundamentals for researchers in the biosciences--a tutorial," Cytometry Part A 69(8), 712-734 (2006).
[CrossRef]

Lin, R. P.

R. P. Lin, B. R. Dennis, and A. O. Benz, eds., The Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI)--Mission Description and Early Results (Kluwer Academic, 2003).
[PubMed]

Maker, P. D.

M. R. Descour, C. E. Volin, E. L. Dereniak, K. J. Thorne, A. B. Schumacher, D. W. Wilson, and P. D. Maker, "Demonstration of a high-speed nonscanning imaging spectrometer," Opt. Lett. 22, 1271-1273 (1997).
[CrossRef] [PubMed]

McCain, S. T.

Michalowicz, J. V.

C. M. Stellman, F. M. Olchowski, and J. V. Michalowicz, "WAR HORSE (wide-area reconnaissance: hyperspectral overhead real-time surveillance experiment)," Proc. SPIE 4379, 339-346 (2001).
[CrossRef]

Mooney, J. M.

J. M. Mooney, V. E. Vickers, M. An, and A. K. Brodzik, "High-throughput hyperspectral infrared camera," J. Opt. Soc. Am. A 14, 2951-2961 (1997).
[CrossRef]

Morris, H.

Nowak, R. D.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems," IEEE J. Sel. Top. Signal Process. 1, 586-597 (2007).
[CrossRef]

Okkonen, J. T.

E. Herrala, J. T. Okkonen, T. S. Hyvarinen, M. Aikio, and J. Lammasniemi, "Imaging spectrometer for process industry applications," Proc. SPIE 2248, 33-40 (1994).
[CrossRef]

Olah, M. R.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, "Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Olchowski, F. M.

C. M. Stellman, F. M. Olchowski, and J. V. Michalowicz, "WAR HORSE (wide-area reconnaissance: hyperspectral overhead real-time surveillance experiment)," Proc. SPIE 4379, 339-346 (2001).
[CrossRef]

Pavri, B. E.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, "Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Pham, T. H.

Pitsianis, N. P.

Potuluri, P.

Revercomb, H. E.

W. L. Smith, D. K. Zhou, F. W. Harrison, H. E. Revercomb, A. M. Larar, H.-L. Huang, and B. Huang, "Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft," Proc. SPIE 4151, 94-102 (2001).
[CrossRef]

Romberg, J.

E. J. 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]

Sarture, C. M.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, "Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Saunders, M. A.

S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput. 20, 33-61 (1999).
[CrossRef]

Schroeder, D. J.

D. J. Schroeder, Astronomical Optics (Academic, 1987).

Schultz, T.

Schumacher, A. B.

M. R. Descour, C. E. Volin, E. L. Dereniak, K. J. Thorne, A. B. Schumacher, D. W. Wilson, and P. D. Maker, "Demonstration of a high-speed nonscanning imaging spectrometer," Opt. Lett. 22, 1271-1273 (1997).
[CrossRef] [PubMed]

Sloane, N. J.

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

Smith, W. L.

W. L. Smith, D. K. Zhou, F. W. Harrison, H. E. Revercomb, A. M. Larar, H.-L. Huang, and B. Huang, "Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft," Proc. SPIE 4151, 94-102 (2001).
[CrossRef]

Solis, M.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, "Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Spott, T.

Stellman, C. M.

C. M. Stellman, F. M. Olchowski, and J. V. Michalowicz, "WAR HORSE (wide-area reconnaissance: hyperspectral overhead real-time surveillance experiment)," Proc. SPIE 4379, 339-346 (2001).
[CrossRef]

Sullivan, M. E.

Tao, T.

E. J. 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]

Thorne, K. J.

M. R. Descour, C. E. Volin, E. L. Dereniak, K. J. Thorne, A. B. Schumacher, D. W. Wilson, and P. D. Maker, "Demonstration of a high-speed nonscanning imaging spectrometer," Opt. Lett. 22, 1271-1273 (1997).
[CrossRef] [PubMed]

Tibshirani, R.

R. Tibshirani, "Regression shrinkage and selection via the lasso," J. R. Stat. Soc. Ser. B 58, 267-288 (1996).

Treado, P.

Tromberg, B. J.

Verveer, P.

Q. Hanley, P. Verveer, D. Arndt-Jovin, and T. Jovin, "Three dimensional spectral imaging by Hadamard transform spectroscopy in a programmable array microscope," J. Microsc. 197, 5-14 (2000).
[CrossRef] [PubMed]

Vickers, V. E.

J. M. Mooney, V. E. Vickers, M. An, and A. K. Brodzik, "High-throughput hyperspectral infrared camera," J. Opt. Soc. Am. A 14, 2951-2961 (1997).
[CrossRef]

Volin, C. E.

M. R. Descour, C. E. Volin, E. L. Dereniak, K. J. Thorne, A. B. Schumacher, D. W. Wilson, and P. D. Maker, "Demonstration of a high-speed nonscanning imaging spectrometer," Opt. Lett. 22, 1271-1273 (1997).
[CrossRef] [PubMed]

Wagadarikar, A. A.

Willett, R.

Williams, O.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, "Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Wilson, D. W.

W. R. Johnson, D. W. Wilson, and G. Bearman, "Spatial-spectral modulating snapshot hyperspectral imager," Appl. Opt. 45, 1898-1908 (2006).
[CrossRef] [PubMed]

M. R. Descour, C. E. Volin, E. L. Dereniak, K. J. Thorne, A. B. Schumacher, D. W. Wilson, and P. D. Maker, "Demonstration of a high-speed nonscanning imaging spectrometer," Opt. Lett. 22, 1271-1273 (1997).
[CrossRef] [PubMed]

Wright, S. J.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems," IEEE J. Sel. Top. Signal Process. 1, 586-597 (2007).
[CrossRef]

Zhou, D. K.

W. L. Smith, D. K. Zhou, F. W. Harrison, H. E. Revercomb, A. M. Larar, H.-L. Huang, and B. Huang, "Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft," Proc. SPIE 4151, 94-102 (2001).
[CrossRef]

Proc. SPIE (1)

C. M. Stellman, F. M. Olchowski, and J. V. Michalowicz, "WAR HORSE (wide-area reconnaissance: hyperspectral overhead real-time surveillance experiment)," Proc. SPIE 4379, 339-346 (2001).
[CrossRef]

Appl. Opt. (1)

W. R. Johnson, D. W. Wilson, and G. Bearman, "Spatial-spectral modulating snapshot hyperspectral imager," Appl. Opt. 45, 1898-1908 (2006).
[CrossRef] [PubMed]

Appl. Opt. (3)

Appl. Spectrosc. (1)

Cytometry Part A (1)

J. M. Lerner, "Imaging spectrometer fundamentals for researchers in the biosciences--a tutorial," Cytometry Part A 69(8), 712-734 (2006).
[CrossRef]

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

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems," IEEE J. Sel. Top. Signal Process. 1, 586-597 (2007).
[CrossRef]

IEEE Trans. Inf. Theory (1)

E. J. 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]

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

J. M. Mooney, V. E. Vickers, M. An, and A. K. Brodzik, "High-throughput hyperspectral infrared camera," J. Opt. Soc. Am. A 14, 2951-2961 (1997).
[CrossRef]

J. R. Stat. Soc. Ser. B (1)

R. Tibshirani, "Regression shrinkage and selection via the lasso," J. R. Stat. Soc. Ser. B 58, 267-288 (1996).

J. Microsc. (1)

Q. Hanley, P. Verveer, D. Arndt-Jovin, and T. Jovin, "Three dimensional spectral imaging by Hadamard transform spectroscopy in a programmable array microscope," J. Microsc. 197, 5-14 (2000).
[CrossRef] [PubMed]

Numer. Math. (1)

Y.-H. Dai and R. Fletcher, "Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming," Numer. Math. 100, 21-47 (2005).
[CrossRef]

Opt. Lett. (1)

M. R. Descour, C. E. Volin, E. L. Dereniak, K. J. Thorne, A. B. Schumacher, D. W. Wilson, and P. D. Maker, "Demonstration of a high-speed nonscanning imaging spectrometer," Opt. Lett. 22, 1271-1273 (1997).
[CrossRef] [PubMed]

Opt. Express (1)

Proc. SPIE (4)

D. J. Brady and M. E. Gehm, "Compressive imaging spectrometers using coded apertures," Proc. SPIE 6246, 62460A (2006).
[CrossRef]

C. L. Bennett, M. R. Carter, D. J. Fields, and J. A. M. Hernandez, "Imaging Fourier transform spectrometer," Proc. SPIE 1937, 191-200 (1993).
[CrossRef]

W. L. Smith, D. K. Zhou, F. W. Harrison, H. E. Revercomb, A. M. Larar, H.-L. Huang, and B. Huang, "Hyperspectral remote sensing of atmospheric profiles from satellites and aircraft," Proc. SPIE 4151, 94-102 (2001).
[CrossRef]

E. Herrala, J. T. Okkonen, T. S. Hyvarinen, M. Aikio, and J. Lammasniemi, "Imaging spectrometer for process industry applications," Proc. SPIE 2248, 33-40 (1994).
[CrossRef]

Remote Sens. Environ. (1)

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, "Imaging spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

SIAM J. Sci. Comput. (1)

S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput. 20, 33-61 (1999).
[CrossRef]

Other (4)

D. J. Schroeder, Astronomical Optics (Academic, 1987).

R. P. Lin, B. R. Dennis, and A. O. Benz, eds., The Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI)--Mission Description and Early Results (Kluwer Academic, 2003).
[PubMed]

http://www.lx.it.pt/~mtf/GPSR/.

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

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Figures (8)

Fig. 1
Fig. 1

Schematic of a SD CASSI. The imaging optics image the scene onto the coded aperture. The relay optics relay the image from the plane of the coded aperture to the detector through the dispersive element.

Fig. 2
Fig. 2

(Color online) Experimental prototype of the SD CASSI.

Fig. 3
Fig. 3

(Color online) Aperture code pattern used by the reconstruction algorithm to generate an estimate of the data cube.

Fig. 4
Fig. 4

(Color online) Scene consisting of a Ping-Pong ball illuminated by a 543 nm green laser and a white light source filtered by a 560 nm narrowband filter (left), and a red Ping-Pong ball illuminated by a white light source (right).

Fig. 5
Fig. 5

(Color online) Detector measurement of the scene consisting of the two Ping-Pong balls. Given the low linear dispersion of the prism, there is spatiospectral overlap of the aperture code-modulated images of each ball.

Fig. 6
Fig. 6

(Color online) Spatial content of the scene in each of 28 spectral channels between 540 and 640 nm . The green ball can be seen in channels 3, 4, 5, 6, 7, and 8; the red ball can be seen in channels 23, 24, and 25.

Fig. 7
Fig. 7

(Color online) (a) Spectral intensity through a point on the Ping-Pong ball illuminated by a 543 nm green laser and a white light source filtered by a 560 nm narrowband filter. (b) Spectral intensity through a point on the red Ping-Pong ball illuminated by a white light source. Spectra from an Ocean Optics nonimaging reference spectrometer are shown for comparison.

Fig. 8
Fig. 8

Description of the major differences between the DD CASSI and the SD CASSI instruments.

Equations (14)

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f 1 ( x , y ; λ ) = f 0 ( x , y ; λ ) T ( x , y ) .
f 2 ( x , y ; λ ) = δ ( x [ x + α ( λ λ c ) ] ) δ ( y y ) × f 1 ( x , y ; λ ) d x d y
= δ ( x [ x + α ( λ λ c ) ] ) δ ( y y ) × f 0 ( x , y ; λ ) T ( x , y ) d x d y
= f 0 ( x + α ( λ λ c ) , y ; λ ) T ( x + α ( λ λ c ) , y ) ,
g ( x , y ) = f 0 ( x + α ( λ λ c ) , y ; λ ) T ( x + α ( λ λ c ) , y ) d λ .
g n m = g ( x , y ) rect ( x Δ m , y Δ n ) d x d y + w n m
= f 0 ( x + α ( λ λ c ) , y ; λ ) T ( x + α ( λ λ c ) , y ) × rect ( x Δ m , y Δ n ) d x d y d λ + w n m .
T ( x , y ) = m , n t n m rect ( x q Δ m , y q Δ n ) .
g n m = m , n t n m rect ( x + α ( λ λ c ) q Δ m , y q Δ n ) × rect ( x Δ m , y Δ n ) × f 0 ( x + α ( λ λ c ) , y ; λ ) d x d y d λ + w n m .
g n m = k f ( m + k ) n k t ( m + k ) n + w n m
= ( H f ) n m + w n m ,
f = W θ ,
g n m = ( H W θ ) n m + w n m ,
f ^ = W [ arg min θ { g H W θ 2 2 + τ θ 1 } ] .

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