Abstract

A coded aperture snapshot spectral imager (CASSI) estimates the three-dimensional spatiospectral data cube from a snapshot two-dimensional coded projection, assuming that the scene is spatially and spectrally sparse. For less spectrally sparse scenes, we show that the use of multiple nondegenerate snapshots can make data cube recovery less ill-posed, yielding improved spatial and spectral reconstruction fidelity. Additionally, data acquisition can be easily scaled to meet the time/resolution requirements of the scene with little modification or extension of the original CASSI hardware. A multiframe reconstruction of a 640×480×53 voxel datacube with 450650nm white-light illumination of a scene reveals substantial improvement in the reconstruction fidelity, with limited increase in acquisition and reconstruction time.

© 2010 Optical Society of America

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  1. D. J. Brady, Optical Imaging and Spectroscopy (Wiley-Interscience, 2008), pp. 387–390.
  2. M. E. Gehm, S. T. McCain, N. P. Pitsianis, D. J. Brady, P. Potulri, and M. E. Sullivan, “Static two-dimensional aperture coding for multimodal, multiplex spectroscopy,” Appl. Opt. 45, 2965–2974 (2006).
    [CrossRef] [PubMed]
  3. S. T. McCain, M. E. Gehm, Y. Wang, N. P. Pitsianis, and D. J. Brady, “Coded aperture Raman spectrosopy for quantitative measurements of ethanol in a tissue phantom,” Appl. Spectrosc. 60, 663–671 (2006).
    [CrossRef] [PubMed]
  4. M. E. Gehm, M. S. Kim, C. Fernandez, and D. J. Brady, “High-throughput, multiplexed pushbroom hyperspectral microscopy,” Opt. Express 16, 11032–11043 (2008).
    [CrossRef] [PubMed]
  5. A. Wagadarikar, R. J., R. Willett, and D. J. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008).
    [CrossRef] [PubMed]
  6. C. F. Cull, K. Choi, D. J. Brady, and T. Oliver, “Identification of fluorescent beads using a coded aperture snapshot spectral imager,” Appl. Opt. 49, B59–B70 (2010).
    [CrossRef] [PubMed]
  7. B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, “Computed tomography-based spectral imaging for fluorescence microscopy,” Biophys. J. 80, 986–993(2001).
    [CrossRef] [PubMed]
  8. B. Ford, M. Descour, and R. Lynch, “Large-image-format computed tomography imaging spectrometer for fluorescence microscopy,” Opt. Express 9, 444–453 (2001).
    [CrossRef] [PubMed]
  9. M. H. W. Johnson, D. W. W. Fink, and G. Bearman, “Snapshot hyperspectral imaging in ophthalmology,” J. Biomed. Opt. 12, 014036 (2007).
    [CrossRef] [PubMed]
  10. L. Gao, R. T. Kester, N. Hagen, and T. S. Tkaczyk, “Snapshot image mapping spectrometer (IMS) with high sampling density for hyperspectral microscopy,” Opt. Express 18, 14330–14344 (2010).
    [CrossRef] [PubMed]
  11. A. Gorman, D. W. Fletcher-Holmes, and A. R. Harvey, “Generalization of the Lyot filter and its application to snapshot spectral imaging,” Opt. Express 18, 5602–5608 (2010).
    [CrossRef] [PubMed]
  12. E. J. Candès, “Compressive sampling,” in Proceedings of the International Congress of Mathematicians (European Mathematical Society, 2006), pp. 1433–1452.
  13. P. Ye, H. Arguello, and G. Arce, “Spectral aperture code design for multi-shot compressive spectral imaging,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2010), paper DWA6.
  14. H. Arguello and G. R. Arce, “Code aperture design for band selectivity in spectral imaging using cassi system,” in Proceedings of the European Signal Processing Conference (EUSIPCO) (European Association for Signal Processing, 2010).
  15. M. Figueiredo, R. Nowak, and S. 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]
  16. A. A. Wagadarikar, N. P. Pitsianis, X. Sun, and D. J. Brady, “Spectral image estimation for coded aperture snapshot spectral imagers,” Proc. SPIE 7076, 707602 (2008).
    [CrossRef]
  17. X. Sun and N. P. Pitsianis, “Solving non-negative linear inverse problems with the NeAREst method,” Proc. SPIE 7074, 707402 (2008).
    [CrossRef]
  18. S. Wright, R. Nowak, and M. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Signal Process. 57, 2479–2493 (2009).
    [CrossRef]
  19. J. Bioucas-Dias and M. Figueiredo, “A new twist: two-step iterative shrinkage/thresholding for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).
    [CrossRef] [PubMed]
  20. P. A. Mitchell, “Hyperspectral digital imagery collection experiment (HYDICE),” Proc. SPIE 2587, 70–95 (1995).
    [CrossRef]

2010

2009

S. Wright, R. Nowak, and M. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Signal Process. 57, 2479–2493 (2009).
[CrossRef]

2008

A. A. Wagadarikar, N. P. Pitsianis, X. Sun, and D. J. Brady, “Spectral image estimation for coded aperture snapshot spectral imagers,” Proc. SPIE 7076, 707602 (2008).
[CrossRef]

X. Sun and N. P. Pitsianis, “Solving non-negative linear inverse problems with the NeAREst method,” Proc. SPIE 7074, 707402 (2008).
[CrossRef]

A. Wagadarikar, R. J., R. Willett, and D. J. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008).
[CrossRef] [PubMed]

M. E. Gehm, M. S. Kim, C. Fernandez, and D. J. Brady, “High-throughput, multiplexed pushbroom hyperspectral microscopy,” Opt. Express 16, 11032–11043 (2008).
[CrossRef] [PubMed]

2007

M. H. W. Johnson, D. W. W. Fink, and G. Bearman, “Snapshot hyperspectral imaging in ophthalmology,” J. Biomed. Opt. 12, 014036 (2007).
[CrossRef] [PubMed]

M. Figueiredo, R. Nowak, and S. 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]

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

2006

2001

B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, “Computed tomography-based spectral imaging for fluorescence microscopy,” Biophys. J. 80, 986–993(2001).
[CrossRef] [PubMed]

B. Ford, M. Descour, and R. Lynch, “Large-image-format computed tomography imaging spectrometer for fluorescence microscopy,” Opt. Express 9, 444–453 (2001).
[CrossRef] [PubMed]

1995

P. A. Mitchell, “Hyperspectral digital imagery collection experiment (HYDICE),” Proc. SPIE 2587, 70–95 (1995).
[CrossRef]

Arce, G.

P. Ye, H. Arguello, and G. Arce, “Spectral aperture code design for multi-shot compressive spectral imaging,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2010), paper DWA6.

Arce, G. R.

H. Arguello and G. R. Arce, “Code aperture design for band selectivity in spectral imaging using cassi system,” in Proceedings of the European Signal Processing Conference (EUSIPCO) (European Association for Signal Processing, 2010).

Arguello, H.

H. Arguello and G. R. Arce, “Code aperture design for band selectivity in spectral imaging using cassi system,” in Proceedings of the European Signal Processing Conference (EUSIPCO) (European Association for Signal Processing, 2010).

P. Ye, H. Arguello, and G. Arce, “Spectral aperture code design for multi-shot compressive spectral imaging,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2010), paper DWA6.

Bearman, G.

M. H. W. Johnson, D. W. W. Fink, and G. Bearman, “Snapshot hyperspectral imaging in ophthalmology,” J. Biomed. Opt. 12, 014036 (2007).
[CrossRef] [PubMed]

Bioucas-Dias, J.

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

Brady, D. J.

Candès, E. J.

E. J. Candès, “Compressive sampling,” in Proceedings of the International Congress of Mathematicians (European Mathematical Society, 2006), pp. 1433–1452.

Choi, K.

Cull, C. F.

Descour, M.

Descour, M. R.

B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, “Computed tomography-based spectral imaging for fluorescence microscopy,” Biophys. J. 80, 986–993(2001).
[CrossRef] [PubMed]

Fernandez, C.

Figueiredo, M.

S. Wright, R. Nowak, and M. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Signal Process. 57, 2479–2493 (2009).
[CrossRef]

M. Figueiredo, R. Nowak, and S. 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]

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

Fink, D. W. W.

M. H. W. Johnson, D. W. W. Fink, and G. Bearman, “Snapshot hyperspectral imaging in ophthalmology,” J. Biomed. Opt. 12, 014036 (2007).
[CrossRef] [PubMed]

Fletcher-Holmes, D. W.

Ford, B.

Ford, B. K.

B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, “Computed tomography-based spectral imaging for fluorescence microscopy,” Biophys. J. 80, 986–993(2001).
[CrossRef] [PubMed]

Gao, L.

Gehm, M. E.

Gorman, A.

Hagen, N.

Harvey, A. R.

J., R.

Johnson, M. H. W.

M. H. W. Johnson, D. W. W. Fink, and G. Bearman, “Snapshot hyperspectral imaging in ophthalmology,” J. Biomed. Opt. 12, 014036 (2007).
[CrossRef] [PubMed]

Kester, R. T.

Kim, M. S.

Lynch, R.

Lynch, R. M.

B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, “Computed tomography-based spectral imaging for fluorescence microscopy,” Biophys. J. 80, 986–993(2001).
[CrossRef] [PubMed]

McCain, S. T.

Mitchell, P. A.

P. A. Mitchell, “Hyperspectral digital imagery collection experiment (HYDICE),” Proc. SPIE 2587, 70–95 (1995).
[CrossRef]

Murphy, S. M.

B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, “Computed tomography-based spectral imaging for fluorescence microscopy,” Biophys. J. 80, 986–993(2001).
[CrossRef] [PubMed]

Nowak, R.

S. Wright, R. Nowak, and M. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Signal Process. 57, 2479–2493 (2009).
[CrossRef]

M. Figueiredo, R. Nowak, and S. 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]

Oliver, T.

Pitsianis, N. P.

Potulri, P.

Sullivan, M. E.

Sun, X.

A. A. Wagadarikar, N. P. Pitsianis, X. Sun, and D. J. Brady, “Spectral image estimation for coded aperture snapshot spectral imagers,” Proc. SPIE 7076, 707602 (2008).
[CrossRef]

X. Sun and N. P. Pitsianis, “Solving non-negative linear inverse problems with the NeAREst method,” Proc. SPIE 7074, 707402 (2008).
[CrossRef]

Tkaczyk, T. S.

Volin, C. E.

B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, “Computed tomography-based spectral imaging for fluorescence microscopy,” Biophys. J. 80, 986–993(2001).
[CrossRef] [PubMed]

Wagadarikar, A.

Wagadarikar, A. A.

A. A. Wagadarikar, N. P. Pitsianis, X. Sun, and D. J. Brady, “Spectral image estimation for coded aperture snapshot spectral imagers,” Proc. SPIE 7076, 707602 (2008).
[CrossRef]

Wang, Y.

Willett, R.

Wright, S.

S. Wright, R. Nowak, and M. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Signal Process. 57, 2479–2493 (2009).
[CrossRef]

M. Figueiredo, R. Nowak, and S. 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]

Ye, P.

P. Ye, H. Arguello, and G. Arce, “Spectral aperture code design for multi-shot compressive spectral imaging,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2010), paper DWA6.

Appl. Opt.

Appl. Spectrosc.

Biophys. J.

B. K. Ford, C. E. Volin, S. M. Murphy, R. M. Lynch, and M. R. Descour, “Computed tomography-based spectral imaging for fluorescence microscopy,” Biophys. J. 80, 986–993(2001).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Signal Process.

M. Figueiredo, R. Nowak, and S. 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. Image Process.

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

IEEE Trans. Signal Process.

S. Wright, R. Nowak, and M. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Signal Process. 57, 2479–2493 (2009).
[CrossRef]

J. Biomed. Opt.

M. H. W. Johnson, D. W. W. Fink, and G. Bearman, “Snapshot hyperspectral imaging in ophthalmology,” J. Biomed. Opt. 12, 014036 (2007).
[CrossRef] [PubMed]

Opt. Express

Proc. SPIE

P. A. Mitchell, “Hyperspectral digital imagery collection experiment (HYDICE),” Proc. SPIE 2587, 70–95 (1995).
[CrossRef]

A. A. Wagadarikar, N. P. Pitsianis, X. Sun, and D. J. Brady, “Spectral image estimation for coded aperture snapshot spectral imagers,” Proc. SPIE 7076, 707602 (2008).
[CrossRef]

X. Sun and N. P. Pitsianis, “Solving non-negative linear inverse problems with the NeAREst method,” Proc. SPIE 7074, 707402 (2008).
[CrossRef]

Other

D. J. Brady, Optical Imaging and Spectroscopy (Wiley-Interscience, 2008), pp. 387–390.

E. J. Candès, “Compressive sampling,” in Proceedings of the International Congress of Mathematicians (European Mathematical Society, 2006), pp. 1433–1452.

P. Ye, H. Arguello, and G. Arce, “Spectral aperture code design for multi-shot compressive spectral imaging,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2010), paper DWA6.

H. Arguello and G. R. Arce, “Code aperture design for band selectivity in spectral imaging using cassi system,” in Proceedings of the European Signal Processing Conference (EUSIPCO) (European Association for Signal Processing, 2010).

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Figures (9)

Fig. 1
Fig. 1

τ versus PSNR for a ten-channel CASSI reconstruction using six frames and 100 iterations.

Fig. 2
Fig. 2

Schematic and photo showing the entire CASSI instrument. Left to right: CCD, double Amici prism, relay lens, piezo stage, bandpass filter, aperture code, and objective lens.

Fig. 3
Fig. 3

(a) Ideal aperture code and (b) image of aperture code at detector under 550 nm monochromatic light. Notice the blur added to the aperture code relative to the ideal code.

Fig. 4
Fig. 4

Simulation using HYDICE data set for comparison of snapshot versus multiframe acquisition in a 41-channel sunlight illuminated scene. (a) Original image, (b) snapshot, (c) 12 frames, and (d) 32 frames.

Fig. 5
Fig. 5

Using the GretagMacbeth ColorChecker as a baseline, comparisons were made with white-light sunlight emulation. (a)–(d) compare snapshot versus 4, 8, and 16 frame reconstructions. Nearby colors can bleed into the spectra, as seen in the RGB image, where the blue just to the right of the orange square was dispersed into the orange. Multiple frames eliminate this problem.

Fig. 6
Fig. 6

Multiframe CASSI reconstruction of the GretagMacbeth ColorChecker, showing all the channels from 460 650 nm .

Fig. 7
Fig. 7

Comparison between a single snapshot and various multiframe reconstructions for a single channel at 605 nm .

Fig. 8
Fig. 8

All channels from 500 650 nm from a 24-frame reconstruction of the data cube.

Fig. 9
Fig. 9

RGB image of the holly leaf from a Nikon digital SLR.

Tables (3)

Tables Icon

Table 1 PSNR versus Number of CASSI Frames for a Simulated CASSI Reconstruction on HYDIC Data Set

Tables Icon

Table 2 RMSE of CASSI Spectra versus Reference Spectrometer

Tables Icon

Table 3 PSNR versus Number of CASSI Frames for Actual Data, Referenced to a 24-Frame Image in Fig. 7

Equations (12)

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

f ( x , y , λ ) = T ( x , y ) f 0 ( x , y , λ ) h ( x ϕ ( λ ) x , y y , λ ) d x d y ,
g ; n , m = Λ T ( x , y ) f 0 ( x , y , λ ) h ( x ϕ ( λ ) , x , y , y , λ ) ,
rect ( x Δ m , y Δ n ) d x d y d x d y d λ .
f i , n , m = Λ rect ( x Δ , y Δ ) Detector rect ( x Δ , y Δ ) Coded Aperture × f 0 ( x + i Δ , y + n Δ , λ + m Δ α ) h ( x x α λ , y y , λ + m Δ i Δ α ) × d x d y d x d y d λ ,
g ; n , m = i t ; i , n f i , n , m + i = k t ; k m , n f k m , n , k ,
g = Φ f .
g n , m , = i t i , n , f i , n , m , , i .
[ g 1 g 2 g N ] = [ Φ 1 Φ 2 Φ N ] f .
μ N max i , j | φ i , ψ j | ,
f ^ TwIST ( τ , Γ ) = arg min f [ 1 2 g Φ f 2 2 + τ Γ ( f ) ] .
Γ i TV ( f ) = i ( Δ i h f ) 2 + ( Δ i v f ) 2 ,
Γ TV ( f ) = k i , j ( f ( i + 1 , j , k ) f ( i , j , k ) ) 2 + ( f ( i , j + 1 , k ) f ( i , j , k ) ) 2 .

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