Abstract

Coded aperture snapshot spectral imaging systems (CASSI) sense the three-dimensional spatio-spectral information of a scene using a single two-dimensional focal plane array snapshot. The compressive CASSI measurements are often modeled as the summation of coded and shifted versions of the spectral voxels of the underlying scene. This coarse approximation of the analog CASSI sensing phenomena is then compensated by calibration preprocessing prior to signal reconstruction. This paper develops a higher-order precision model for the optical sensing in CASSI that includes a more accurate discretization of the underlying signals, leading to image reconstructions less dependent on calibration. Further, the higher-order model results in improved image quality reconstruction of the underlying scene than that achieved by the traditional model. The proposed higher precision computational model is also more suitable for reconfigurable multiframe CASSI systems where multiple coded apertures are used sequentially to capture the hyperspectral scene. Several simulations and experimental measurements demonstrate the benefits of the discretization model.

© 2013 Optical Society of America

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References

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  1. A. A. Wagadarikar, R. John, R. Willett, and D. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008).
    [CrossRef]
  2. H. Arguello, P. Ye, and G. R. 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).
  3. H. Arguello and G. R. Arce, “Code aperture design for compressive spectral imaging,” in European Signal Processing Conference, EUSIPCO (European Association for Signal Processing, 2010).
  4. H. Arguello and G. R. Arce, “Rank minimization code aperture design for spectrally selective compressive imaging,” IEEE Trans. Image Process. 22, 941–954 (2013).
    [CrossRef]
  5. H. Arguello and G. R. Arce, “Code aperture optimization for spectrally agile compressive imaging,” J. Opt. Soc. Am. 28, 2400–2413 (2011).
    [CrossRef]
  6. H. Arguello and G. R. Arce, “Code aperture agile spectral imaging (CAASI),” Imaging Systems Applications, OSA Technical Digest (CD) (Optical Society of America, 2011).
  7. D. Kittle, K. Choi, A. A. Wagadarikar, and D. J. Brady, “Multiframe image estimation for coded aperture snapshot spectral imagers,” Appl. Opt. 49, 6824–6833 (2010).
    [CrossRef]
  8. 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).
    [CrossRef]
  9. 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]
  10. 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]
  11. A. A. Wagadarikar, “Compressive spectral and coherence imaging,” Ph.D. thesis (Duke University, 2010).
  12. 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]
  13. H. Arguello, C. V. Correa, and G. R. Arce, “Fast lapped block reconstructions in compressive spectral imaging,” Submitted to Appl. Opt. (November2012).
  14. A. Ramirez, H. Arguello, G. R. Arce, and B. M. Sadler, “Spectral image classification from optimal coded-aperture compressive measurements,” Submitted to IEEE Trans. Geosci. Remote Sens. (November2012).
  15. A. Ramirez, G. R. Arce, and B. M. Sadler, “Coded-aperture compressive spectral image classification,” in Comput. Opt. Sens. Imag. (Optical Society of America, 2012).

2013

H. Arguello and G. R. Arce, “Rank minimization code aperture design for spectrally selective compressive imaging,” IEEE Trans. Image Process. 22, 941–954 (2013).
[CrossRef]

2011

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

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).
[CrossRef]

2010

2009

2008

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

2007

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]

Arce, G. R.

H. Arguello and G. R. Arce, “Rank minimization code aperture design for spectrally selective compressive imaging,” IEEE Trans. Image Process. 22, 941–954 (2013).
[CrossRef]

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

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).
[CrossRef]

A. Ramirez, G. R. Arce, and B. M. Sadler, “Coded-aperture compressive spectral image classification,” in Comput. Opt. Sens. Imag. (Optical Society of America, 2012).

A. Ramirez, H. Arguello, G. R. Arce, and B. M. Sadler, “Spectral image classification from optimal coded-aperture compressive measurements,” Submitted to IEEE Trans. Geosci. Remote Sens. (November2012).

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

H. Arguello and G. R. Arce, “Code aperture design for compressive spectral imaging,” in European Signal Processing Conference, EUSIPCO (European Association for Signal Processing, 2010).

H. Arguello, P. Ye, and G. R. 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).

H. Arguello, C. V. Correa, and G. R. Arce, “Fast lapped block reconstructions in compressive spectral imaging,” Submitted to Appl. Opt. (November2012).

Arguello, H.

H. Arguello and G. R. Arce, “Rank minimization code aperture design for spectrally selective compressive imaging,” IEEE Trans. Image Process. 22, 941–954 (2013).
[CrossRef]

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

A. Ramirez, H. Arguello, G. R. Arce, and B. M. Sadler, “Spectral image classification from optimal coded-aperture compressive measurements,” Submitted to IEEE Trans. Geosci. Remote Sens. (November2012).

H. Arguello, C. V. Correa, and G. R. Arce, “Fast lapped block reconstructions in compressive spectral imaging,” Submitted to Appl. Opt. (November2012).

H. Arguello and G. R. Arce, “Code aperture design for compressive spectral imaging,” in European Signal Processing Conference, EUSIPCO (European Association for Signal Processing, 2010).

H. Arguello, P. Ye, and G. R. 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).

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

Brady, D.

Brady, D. J.

Choi, K.

Correa, C. V.

H. Arguello, C. V. Correa, and G. R. Arce, “Fast lapped block reconstructions in compressive spectral imaging,” Submitted to Appl. Opt. (November2012).

Figueiredo, M.

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]

John, R.

Kittle, D.

Mirza, I. O.

Nowak, R.

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]

Pitsianis, N. P.

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]

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]

Prather, D. W.

Ramirez, A.

A. Ramirez, G. R. Arce, and B. M. Sadler, “Coded-aperture compressive spectral image classification,” in Comput. Opt. Sens. Imag. (Optical Society of America, 2012).

A. Ramirez, H. Arguello, G. R. Arce, and B. M. Sadler, “Spectral image classification from optimal coded-aperture compressive measurements,” Submitted to IEEE Trans. Geosci. Remote Sens. (November2012).

Sadler, B. M.

A. Ramirez, H. Arguello, G. R. Arce, and B. M. Sadler, “Spectral image classification from optimal coded-aperture compressive measurements,” Submitted to IEEE Trans. Geosci. Remote Sens. (November2012).

A. Ramirez, G. R. Arce, and B. M. Sadler, “Coded-aperture compressive spectral image classification,” in Comput. Opt. Sens. Imag. (Optical Society of America, 2012).

Sun, X.

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]

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]

Wagadarikar, A. A.

Willett, R.

Wright, S.

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]

Wu, Y.

Ye, P.

H. Arguello, P. Ye, and G. R. 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).

Appl. Opt.

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.

H. Arguello and G. R. Arce, “Rank minimization code aperture design for spectrally selective compressive imaging,” IEEE Trans. Image Process. 22, 941–954 (2013).
[CrossRef]

J. Opt. Soc. Am.

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

Opt. Express

Opt. Lett.

Proc. SPIE

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]

Other

A. A. Wagadarikar, “Compressive spectral and coherence imaging,” Ph.D. thesis (Duke University, 2010).

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

H. Arguello, P. Ye, and G. R. 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).

H. Arguello and G. R. Arce, “Code aperture design for compressive spectral imaging,” in European Signal Processing Conference, EUSIPCO (European Association for Signal Processing, 2010).

H. Arguello, C. V. Correa, and G. R. Arce, “Fast lapped block reconstructions in compressive spectral imaging,” Submitted to Appl. Opt. (November2012).

A. Ramirez, H. Arguello, G. R. Arce, and B. M. Sadler, “Spectral image classification from optimal coded-aperture compressive measurements,” Submitted to IEEE Trans. Geosci. Remote Sens. (November2012).

A. Ramirez, G. R. Arce, and B. M. Sadler, “Coded-aperture compressive spectral image classification,” in Comput. Opt. Sens. Imag. (Optical Society of America, 2012).

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Figures (14)

Fig. 1.
Fig. 1.

Optical elements present in CASSI.

Fig. 2.
Fig. 2.

CASSI integration model. A voxel of the data cube is coded by the aperture code, sheared by the dispersive element with dispersion S(λk), and projected onto several pixels of the detector.

Fig. 3.
Fig. 3.

(a) First-order discretization model. A voxel impinges onto a single FPA pixel detector. (b) Higher-order discretization model. A voxel impinges onto three FPA pixels. Notice that the light dispersion path is on the (λ,x) axis (top view).

Fig. 4.
Fig. 4.

Voxel dispersed into the regions R0, R1, and R2 in each interval [λk,λk+1]. These regions determine the voxel fractions involved in the formation of the gm1,n, gm,n, and gm+1,n detector pixels.

Fig. 5.
Fig. 5.

Structure of the matrix H˜ for a N=M=6, L=5 data cube, when K=3 for (a) CASSI traditional model (H˜R180×180) and (b) higher-order CASSI model (H˜R180×180). Extra diagonal terms account for the intervoxel interference. Notice that entries in (a) are either 0 or 1, while in (b) they vary in the interval [0, 1].

Fig. 6.
Fig. 6.

Spectral bands used in the simulations and their central wavelength.

Fig. 7.
Fig. 7.

Reconstruction using the traditional CASSI model and the corresponding attained PSNR. The average PSNR across the eight bands is 22.3 dB.

Fig. 8.
Fig. 8.

Reconstruction using the higher-order CASSI model and the corresponding attained PSNR. The average PSNR across the eight bands is 26.85 dB.

Fig. 9.
Fig. 9.

Averaged PSNR of the reconstructed data cubes as function of the number of FPA shots. The traditional and the higher-order precision models are compared.

Fig. 10.
Fig. 10.

(a) CASSI testbed setup and its six optical elements: objective lens, DMD, imaging lenses, bandpass filter, prism, and CCD. (b) Nonlinear dispersion response of the Amici prism between 450 and 620 nm.

Fig. 11.
Fig. 11.

FPA measurement at 502 nm. The coded aperture (upper left) is used in order to isolate the effect of a single voxel impinging onto the FPA (upper right). A zoomed version of a single FPA pixel shows the measured intensity taken into account for each of the discretization models. The energy classified as noise and blur by the first-order and the higher-order models, is shown.

Fig. 12.
Fig. 12.

Objects in scene used in the experimental comparison.

Fig. 13.
Fig. 13.

Reconstruction of the eight spectral bands using (a) the traditional CASSI model and (b) the proposed higher-order CASSI model.

Fig. 14.
Fig. 14.

Spectral signatures comparison from given points in Fig. 12.

Tables (1)

Tables Icon

Table 1. Weights Ri and their Distribution across Spectral Bands

Equations (15)

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

gmn=k=0L1f(mk)jkT(mk)j,
f2(x,y,λ)=T(x,y)f0(x,y,λ)δ(x(xS(λ)))δ(yy)dxdy,
g(x,y)=ΛT(xS(λ),y)f0(xS(λ),y,λ)dλ.
gmn=nΔ(n+1)ΔmΔ(m+1)ΔΛT(xS(λ),y)f0(xS(λ),y,λ)dλdxdy,
fijk=λkλk+1jΔ(j+1)ΔiΔ(i+1)Δf0(x,y,λ)dxdydλ=Ωijkf0(x,y,λ)dxdydλ=cijk·f0(xi,yj,λk),
S(λk)S(λ0)=kΔ,k=0,,L1,
gmn=nΔ(n+1)ΔmΔ(m+1)Δ[k=0L1λkλk+1T(xS(λ),y)f0(xS(λ),y,λ)dλ]dxdy.
nΔ,mΔ,λk(n+1)Δ,(m+1)Δ,λk+1T(xS(λ),y)f0(xS(λ),y,λ)dλdxdy=u=0dλkλk+1{xS(λ),y}RuT(xS(λ),y)f0(xS(λ),y,λ)dxdydλ,
λkλk+1{xS(λ),y}RuT(xS(λ),y)f0(xS(λ),y,λ)dxdydλ=wmnkut(mku)nf(mku)nk,
wmnku=(Rudxdydλ)(Ω(mku)nkdxdydλ)1,
gmn=k=0L1u=0dwmnkut(mku)nf(mku)nk.
gi=Hif.
Hi=PTi,
Ti=[diag(ti)0N20N20N2diag(ti)0N20N20N2diag(ti)],
Pu=[0Nu×N2Ldiag(W0u)0N×N20N×N20N×N2diag(W1u)0N×N20N×N20N×N2diag(WL1u)0N(du)×N2L].

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