Abstract

Based on compressed sensing, snapshot compressive imaging aims to optically compress high resolution images using low resolution detectors. The challenge is the generation of the simultaneous optical projections that can fulfill compressed sensing reconstruction requirements. We propose the use of aberrations to produce point spread functions that can simultaneously code and multiplex partial parts the scene. We explore different Zernike modes and analyze the corresponding coherence parameter. Simulation and experimental reconstruction results from 16X compressed measurements of natively sparse and natural scenes demonstrate the feasibility of using aberrations, in particular primary and secondary astigmatism, for simple, effective single-shot compressive imaging.

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

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References

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2017 (1)

W. Li, X. Yin, Y. Liu, and M. Zhang, “Computational imaging through chromatic aberration corrected simple lenses,” J. Mod. Opt. 64, 2211–2220 (2017).
[Crossref]

2016 (2)

2015 (1)

2014 (2)

A. Ashok, J. Huang, Y. Lin, and R. Kerviche, “Information optimal compressive imaging: design and implementation,” Proc. SPIE 9186, 91860K (2014).
[Crossref]

H. Fang, S. Vorobyov, H. Jiang, and O. Taheri, “Permutation meets parallel compressed sensing: How to relax restricted isometry property for 2d sparse signals,” IEEE Transactions on Signal Processing 62, 196–210 (2014).
[Crossref]

2012 (1)

2011 (2)

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

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

2010 (1)

2009 (2)

D. Donoho and J. Tanner, “Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing,” Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 367, 4273–4293 (2009).
[Crossref] [PubMed]

D. Robinson, G. Feng, and D. G. Stork, “Spherical coded imagers: improving lens speed, depth-of-field, and manufacturing yield through enhanced spherical aberration and compensating image processing,” Proc. SPIE 7429, 1–12 (2009).

2008 (3)

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine 25, 21–30 (2008).
[Crossref]

J. Romberg, “Imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 14–20 (2008).
[Crossref]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[Crossref]

2007 (2)

M. Elad, “Optimized projections for compressed sensing,” IEEE Transactions on Signal Processing 55, 5695–5702 (2007).
[Crossref]

M. A. Neifeld and J. Ke, “Optical architectures for compressive imaging,” Appl. Opt. 46, 5293–5303 (2007).
[Crossref] [PubMed]

Ashok, A.

A. Ashok, J. Huang, Y. Lin, and R. Kerviche, “Information optimal compressive imaging: design and implementation,” Proc. SPIE 9186, 91860K (2014).
[Crossref]

Bajwa, W. U.

Baraniuk, R.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[Crossref]

Becker, S.

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

Bobin, J.

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

Bourquard, A.

Brady, D.

D. Brady, Optical Imaging and Spectroscopy (Wiley, 2009).
[Crossref]

Brady, D. J.

Candes, E.

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine 25, 21–30 (2008).
[Crossref]

Candes, E. J.

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

Davenport, M.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[Crossref]

Donoho, D.

D. Donoho and J. Tanner, “Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing,” Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 367, 4273–4293 (2009).
[Crossref] [PubMed]

Duarte, M.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[Crossref]

Dumas, J. P.

Elad, M.

M. Elad, “Optimized projections for compressed sensing,” IEEE Transactions on Signal Processing 55, 5695–5702 (2007).
[Crossref]

Fang, H.

H. Fang, S. Vorobyov, H. Jiang, and O. Taheri, “Permutation meets parallel compressed sensing: How to relax restricted isometry property for 2d sparse signals,” IEEE Transactions on Signal Processing 62, 196–210 (2014).
[Crossref]

Feng, G.

D. Robinson, G. Feng, and D. G. Stork, “Spherical coded imagers: improving lens speed, depth-of-field, and manufacturing yield through enhanced spherical aberration and compensating image processing,” Proc. SPIE 7429, 1–12 (2009).

Gehm, M. E.

Huang, J.

A. Ashok, J. Huang, Y. Lin, and R. Kerviche, “Information optimal compressive imaging: design and implementation,” Proc. SPIE 9186, 91860K (2014).
[Crossref]

Javidi, B.

Jiang, H.

H. Fang, S. Vorobyov, H. Jiang, and O. Taheri, “Permutation meets parallel compressed sensing: How to relax restricted isometry property for 2d sparse signals,” IEEE Transactions on Signal Processing 62, 196–210 (2014).
[Crossref]

Ke, J.

Kelly, K.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[Crossref]

Kerviche, R.

A. Ashok, J. Huang, Y. Lin, and R. Kerviche, “Information optimal compressive imaging: design and implementation,” Proc. SPIE 9186, 91860K (2014).
[Crossref]

Laska, J.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[Crossref]

Lasser, T.

Li, W.

W. Li, X. Yin, Y. Liu, and M. Zhang, “Computational imaging through chromatic aberration corrected simple lenses,” J. Mod. Opt. 64, 2211–2220 (2017).
[Crossref]

Lin, Y.

A. Ashok, J. Huang, Y. Lin, and R. Kerviche, “Information optimal compressive imaging: design and implementation,” Proc. SPIE 9186, 91860K (2014).
[Crossref]

Liu, Y.

W. Li, X. Yin, Y. Liu, and M. Zhang, “Computational imaging through chromatic aberration corrected simple lenses,” J. Mod. Opt. 64, 2211–2220 (2017).
[Crossref]

Lodhi, M. A.

López, A.

Marcia, R. F.

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

Marcos, D.

Mariano, A. V.

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,” Optical Engineering 50, 072601 (2011).
[Crossref]

Osman, T.

Pierce, M. C.

Poon, P. K.

Rivenson, Y.

Robinson, D.

D. Robinson, G. Feng, and D. G. Stork, “Spherical coded imagers: improving lens speed, depth-of-field, and manufacturing yield through enhanced spherical aberration and compensating image processing,” Proc. SPIE 7429, 1–12 (2009).

Romberg, J.

J. Romberg, “Imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 14–20 (2008).
[Crossref]

Stenner, M. D.

Stern, A.

Stork, D. G.

D. Robinson, G. Feng, and D. G. Stork, “Spherical coded imagers: improving lens speed, depth-of-field, and manufacturing yield through enhanced spherical aberration and compensating image processing,” Proc. SPIE 7429, 1–12 (2009).

Sun, T.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[Crossref]

Taheri, O.

H. Fang, S. Vorobyov, H. Jiang, and O. Taheri, “Permutation meets parallel compressed sensing: How to relax restricted isometry property for 2d sparse signals,” IEEE Transactions on Signal Processing 62, 196–210 (2014).
[Crossref]

Takhar, D.

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[Crossref]

Tanner, J.

D. Donoho and J. Tanner, “Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing,” Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 367, 4273–4293 (2009).
[Crossref] [PubMed]

Townsend, D. J.

Vera, E. M.

Vorobyov, S.

H. Fang, S. Vorobyov, H. Jiang, and O. Taheri, “Permutation meets parallel compressed sensing: How to relax restricted isometry property for 2d sparse signals,” IEEE Transactions on Signal Processing 62, 196–210 (2014).
[Crossref]

Wakin, M.

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine 25, 21–30 (2008).
[Crossref]

Wehrwein, S.

Willett, R. M.

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

Yin, X.

W. Li, X. Yin, Y. Liu, and M. Zhang, “Computational imaging through chromatic aberration corrected simple lenses,” J. Mod. Opt. 64, 2211–2220 (2017).
[Crossref]

Zhang, M.

W. Li, X. Yin, Y. Liu, and M. Zhang, “Computational imaging through chromatic aberration corrected simple lenses,” J. Mod. Opt. 64, 2211–2220 (2017).
[Crossref]

Appl. Opt. (2)

IEEE Signal Processing Magazine (3)

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine 25, 21–30 (2008).
[Crossref]

J. Romberg, “Imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 14–20 (2008).
[Crossref]

M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine 25, 83–91 (2008).
[Crossref]

IEEE Transactions on Signal Processing (2)

H. Fang, S. Vorobyov, H. Jiang, and O. Taheri, “Permutation meets parallel compressed sensing: How to relax restricted isometry property for 2d sparse signals,” IEEE Transactions on Signal Processing 62, 196–210 (2014).
[Crossref]

M. Elad, “Optimized projections for compressed sensing,” IEEE Transactions on Signal Processing 55, 5695–5702 (2007).
[Crossref]

J. Mod. Opt. (1)

W. Li, X. Yin, Y. Liu, and M. Zhang, “Computational imaging through chromatic aberration corrected simple lenses,” J. Mod. Opt. 64, 2211–2220 (2017).
[Crossref]

Opt. Express (4)

Optical Engineering (1)

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

Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (1)

D. Donoho and J. Tanner, “Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing,” Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 367, 4273–4293 (2009).
[Crossref] [PubMed]

Proc. SPIE (2)

A. Ashok, J. Huang, Y. Lin, and R. Kerviche, “Information optimal compressive imaging: design and implementation,” Proc. SPIE 9186, 91860K (2014).
[Crossref]

D. Robinson, G. Feng, and D. G. Stork, “Spherical coded imagers: improving lens speed, depth-of-field, and manufacturing yield through enhanced spherical aberration and compensating image processing,” Proc. SPIE 7429, 1–12 (2009).

SIAM Journal on Imaging Sciences (1)

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

Other (2)

A. Stern, Optical Compressive Imaging (CRC Press, 2016).
[Crossref]

D. Brady, Optical Imaging and Spectroscopy (Wiley, 2009).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Example of aberrations, its associated PSF and system matrix for the unaberrated system Ab×0 and the aberrated systems Ab×1, Ab×2 and Ab×3 with different degrees of secondary astigmatism z13. (a) phase profile; (b) PSF; (c) 16× compressive system matrix.
Fig. 2
Fig. 2 Compressive acquisition and reconstruction examples. (a) 128 × 128 original image; (b) 32 × 32 downsampled version; (c) 32 × 32 compressed version with the Ab×0 system matrix; (d) 32 × 32 compressed version with the z13 Ab×3 system matrix; (e) 128 × 128 bicubic interpolation of (b); (f) 128 × 128 sparse reconstruction (TV) of (f); (g) 128 × 128 sparse reconstruction (TV) of (g).
Fig. 3
Fig. 3 Average performance in PSNR of the reconstructed images from compressive measurements using the unaberrated system Ab×0 and aberrated systems with Zernike modes from z4 to z15 at different strength levels Ab×1, Ab×2 and Ab×3.
Fig. 4
Fig. 4 Reconstruction samples for the 16× simulated snapshot compressive imaging systems using the secondary astigmatism z13 aberration at different strengths Ab×0, Ab×1, Ab×2 and Ab×3.
Fig. 5
Fig. 5 Average mutual coherence of the unaberrated system Ab×0 and aberrated systems with Zernike modes from z4 to z15 at different strength levels Ab×1, Ab×2 and Ab×3.
Fig. 6
Fig. 6 Schematic of the proposed snapshot compressive imaging system. (Inset) Picture of the experimental setup.
Fig. 7
Fig. 7 Comparison of reconstruction results from 16× experimental compressive imaging measurements from the Lena, Peppers, House, Man and Stars images. (Left to right) the original high resolution image is compared with reconstructions from systems with no aberrations, primary astigmatism z6 and secondary astigmatism z13.
Fig. 8
Fig. 8 Zoomed-in versions of the highlighted patches of the reconstructed House and Stars images in Fig. 7: (Left to Right) original, unaberrated, primary astigmatism z6, and secondary astigmatism z13.

Tables (2)

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Table 1 Average reconstruction PSNR for 16× simulated compressive imaging systems. The average is performed over all images and Zernike modes for a particular strength.

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Table 2 Average mutual coherence for simulated 16× compressive imaging systems.

Equations (6)

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H = H D H O
y = Hx ,
min x x T V subject to y = Hx ,
min x x l 1 subject to y = Hx ,
P S N R = 20 log 10 ( 255 R M S E ) ,
μ ( H ) = max i j | h i T h j | ,

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