Abstract

We present a prototype compressive video camera that encodes scene movement using a translated binary photomask in the optical path. The encoded recording can then be used to reconstruct multiple output frames from each captured image, effectively synthesizing high speed video. The use of a printed binary mask allows reconstruction at higher spatial resolutions than has been previously demonstrated. In addition, we improve upon previous work by investigating tradeoffs in mask design and reconstruction algorithm selection. We identify a mask design that consistently provides the best performance across multiple reconstruction strategies in simulation, and verify it with our prototype hardware. Finally, we compare reconstruction algorithms and identify the best choice in terms of balancing reconstruction quality and speed.

© 2015 Optical Society of America

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References

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    [Crossref]
  33. S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
    [Crossref]
  34. X. Liao, H. Li, and L. Carin, “Generalized Alternating Projection for weighted-2,1 minimization with applications to model-based compressive sensing,” SIAM J. Imag. Sci. 7, 797–823 (2014).
    [Crossref]
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    [Crossref]
  36. E. Tsiligianni, L. Kondi, and A. Katsaggelos, “Construction of incoherent unit norm tight frames with application to compressed sensing,” IEEE Trans. Inf. Theory 60, 2319–2330 (2014).
    [Crossref]

2014 (6)

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-Shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref] [PubMed]

K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

R. Pournaghi and X. Wu, “Coded acquisition of high frame rate video,” IEEE Trans. Image Process. 23, 5670–5682 (2014).
[Crossref] [PubMed]

C. Fernandez-Cull, B. M. Tyrrell, R. D’Onofrio, A. Bolstad, J. Lin, J. W. Little, M. Blackwell, M. Renzi, and M. Kelly, “Smart pixel imaging with computational-imaging arrays,” Proc. SPIE 9070, 90703D (2014).

X. Liao, H. Li, and L. Carin, “Generalized Alternating Projection for weighted-2,1 minimization with applications to model-based compressive sensing,” SIAM J. Imag. Sci. 7, 797–823 (2014).
[Crossref]

E. Tsiligianni, L. Kondi, and A. Katsaggelos, “Construction of incoherent unit norm tight frames with application to compressed sensing,” IEEE Trans. Inf. Theory 60, 2319–2330 (2014).
[Crossref]

2013 (3)

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high speed imaging,” IEEE Trans. Pattern Anal. Mach. Intell. 99, 1 (2013).

Y. Oike and A. El Gamal, “CMOS image sensor with per-column ΣΔ; ADC and programmable compressed sensing,” IEEE J. Solid-State Circ. 48, 318–328 (2013).
[Crossref]

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
[Crossref] [PubMed]

2012 (4)

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

N. Gopalsami, S. Liao, T. W. Elmer, E. R. Koehl, A. Heifetz, A. C. Raptis, L. Spinoulas, and A. K. Katsaggelos, “Passive millimeter-wave imaging with compressive sensing,” Opt. Eng. 51, 091614 (2012).
[Crossref]

L. Spinoulas, J. Qi, A. K. Katsaggelos, T. W. Elmer, N. Gopalsami, and A. C. Raptis, “Optimized compressive sampling for passive millimeter-wave imaging,” Appl. Opt. 51, 6335–6342 (2012).
[Crossref] [PubMed]

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE Trans. Emerg. Sel. Topics Circuits Syst. 2, 604–615 (2012).
[Crossref]

2011 (1)

A. Veeraraghavan, D. Reddy, and R. Raskar, “Coded Strobing Photography: Compressive sensing of high speed periodic videos,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 671–686 (2011).
[Crossref]

2010 (2)

G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7, 209–211 (2010).
[Crossref] [PubMed]

R. Robucci, J. D. Gray, L. K. Chiu, J. Romberg, and P. Hasler, “Compressive sensing on a CMOS separable-transform image sensor,” Proc. IEEE 98, 1089–1101 (2010).
[Crossref]

2009 (1)

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imag. Sci. 2, 183–202 (2009).
[Crossref]

2008 (1)

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

2007 (2)

S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
[Crossref]

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

2005 (1)

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776 (2005).
[Crossref]

2004 (1)

M. Ben-Ezra and S. K. Nayar, “Motion-based Motion Deblurring,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 689–698 (2004).
[Crossref]

Adams, A.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776 (2005).
[Crossref]

Agrawal, A.

A. Agrawal, M. Gupta, A. Veeraraghavan, and S. G. Narasimhan, “Optimal coded sampling for temporal super-resolution,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2010), pp. 599–606.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “Flexible voxels for motion-aware videography,” in “Proceedings of European Conference on Computer Vision,” (2010), pp. 100–114.

Antunez, E.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776 (2005).
[Crossref]

Baraniuk, R. G.

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

A. C. Sankaranarayanan, C. Studer, and R. G. Baraniuk, “CS-MUVI: Video compressive sensing for spatial-multiplexing cameras,” in “Proceedings of IEEE International Conference on Computational Photography,” (2012), pp. 1–10.

A. C. Sankaranarayanan, C. Studer, and R. G. Baraniuk, “Video compressive sensing for spatial-multiplexing cameras using motion-flow models,” SIAM J. Imag. Sci. (submitted).

L. Xu, A. Sankaranarayanan, C. Studer, Y. Li, R. G. Baraniuk, and K. F. Kelly, “Multi-Scale compressive video acquisition,” in “Imaging and Appl. Opt.”, (Optical Society of America, 2013), p. CW2C.4.
[Crossref]

Barth, A.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776 (2005).
[Crossref]

Beck, A.

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imag. Sci. 2, 183–202 (2009).
[Crossref]

Ben-Ezra, M.

M. Ben-Ezra and S. K. Nayar, “Motion-based Motion Deblurring,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 689–698 (2004).
[Crossref]

Blackwell, M.

C. Fernandez-Cull, B. M. Tyrrell, R. D’Onofrio, A. Bolstad, J. Lin, J. W. Little, M. Blackwell, M. Renzi, and M. Kelly, “Smart pixel imaging with computational-imaging arrays,” Proc. SPIE 9070, 90703D (2014).

Bolstad, A.

C. Fernandez-Cull, B. M. Tyrrell, R. D’Onofrio, A. Bolstad, J. Lin, J. W. Little, M. Blackwell, M. Renzi, and M. Kelly, “Smart pixel imaging with computational-imaging arrays,” Proc. SPIE 9070, 90703D (2014).

Boyd, S.

S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
[Crossref]

Brady, D. J.

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
[Crossref] [PubMed]

X. Yuan, P. Llull, X. Liao, J. Yang, D. J. Brady, G. Sapiro, and L. Carin, “Low-Cost compressive sensing for color video and depth,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2014), pp. 3318–3325.

Bub, G.

G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7, 209–211 (2010).
[Crossref] [PubMed]

Carin, L.

X. Liao, H. Li, and L. Carin, “Generalized Alternating Projection for weighted-2,1 minimization with applications to model-based compressive sensing,” SIAM J. Imag. Sci. 7, 797–823 (2014).
[Crossref]

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
[Crossref] [PubMed]

X. Yuan, P. Llull, X. Liao, J. Yang, D. J. Brady, G. Sapiro, and L. Carin, “Low-Cost compressive sensing for color video and depth,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2014), pp. 3318–3325.

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).

Chellappa, R.

D. Reddy, A. Veeraraghavan, and R. Chellappa, “P2C2: Programmable pixel compressive camera for high speed imaging,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2011), pp. 329–336.

Chin, S.

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE Trans. Emerg. Sel. Topics Circuits Syst. 2, 604–615 (2012).
[Crossref]

Chiu, L. K.

R. Robucci, J. D. Gray, L. K. Chiu, J. Romberg, and P. Hasler, “Compressive sensing on a CMOS separable-transform image sensor,” Proc. IEEE 98, 1089–1101 (2010).
[Crossref]

D’Onofrio, R.

C. Fernandez-Cull, B. M. Tyrrell, R. D’Onofrio, A. Bolstad, J. Lin, J. W. Little, M. Blackwell, M. Renzi, and M. Kelly, “Smart pixel imaging with computational-imaging arrays,” Proc. SPIE 9070, 90703D (2014).

Dai, Q.

X. Lin, J. Suo, G. Wetzstein, Q. Dai, and R. Raskar, “Coded focal stack photography,” in “Proceedings of IEEE International Conference on Computational Photography,” (2013), pp. 1–9.

Dao, M.

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE Trans. Emerg. Sel. Topics Circuits Syst. 2, 604–615 (2012).
[Crossref]

Davenport, M. A.

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

Duarte, M. F.

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

El Gamal, A.

Y. Oike and A. El Gamal, “CMOS image sensor with per-column ΣΔ; ADC and programmable compressed sensing,” IEEE J. Solid-State Circ. 48, 318–328 (2013).
[Crossref]

Elad, M.

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

M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing, 1st ed. (Springer Publishing Company, Incorporated, 2010).
[Crossref]

Elmer, T. W.

N. Gopalsami, S. Liao, T. W. Elmer, E. R. Koehl, A. Heifetz, A. C. Raptis, L. Spinoulas, and A. K. Katsaggelos, “Passive millimeter-wave imaging with compressive sensing,” Opt. Eng. 51, 091614 (2012).
[Crossref]

L. Spinoulas, J. Qi, A. K. Katsaggelos, T. W. Elmer, N. Gopalsami, and A. C. Raptis, “Optimized compressive sampling for passive millimeter-wave imaging,” Appl. Opt. 51, 6335–6342 (2012).
[Crossref] [PubMed]

Etienne-Cummings, R.

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE Trans. Emerg. Sel. Topics Circuits Syst. 2, 604–615 (2012).
[Crossref]

Fernandez-Cull, C.

C. Fernandez-Cull, B. M. Tyrrell, R. D’Onofrio, A. Bolstad, J. Lin, J. W. Little, M. Blackwell, M. Renzi, and M. Kelly, “Smart pixel imaging with computational-imaging arrays,” Proc. SPIE 9070, 90703D (2014).

Gao, L.

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-Shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref] [PubMed]

Goda, K.

K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Gopalsami, N.

N. Gopalsami, S. Liao, T. W. Elmer, E. R. Koehl, A. Heifetz, A. C. Raptis, L. Spinoulas, and A. K. Katsaggelos, “Passive millimeter-wave imaging with compressive sensing,” Opt. Eng. 51, 091614 (2012).
[Crossref]

L. Spinoulas, J. Qi, A. K. Katsaggelos, T. W. Elmer, N. Gopalsami, and A. C. Raptis, “Optimized compressive sampling for passive millimeter-wave imaging,” Appl. Opt. 51, 6335–6342 (2012).
[Crossref] [PubMed]

Gorinevsky, D.

S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
[Crossref]

Gray, J. D.

R. Robucci, J. D. Gray, L. K. Chiu, J. Romberg, and P. Hasler, “Compressive sensing on a CMOS separable-transform image sensor,” Proc. IEEE 98, 1089–1101 (2010).
[Crossref]

Gu, J.

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high speed imaging,” IEEE Trans. Pattern Anal. Mach. Intell. 99, 1 (2013).

Y. Hitomi, J. Gu, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Video from a single coded exposure photograph using a learned over-complete dictionary,” in “Proceedings of IEEE International Conference on Computer Vision,” (2011).

Gupta, M.

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high speed imaging,” IEEE Trans. Pattern Anal. Mach. Intell. 99, 1 (2013).

A. Agrawal, M. Gupta, A. Veeraraghavan, and S. G. Narasimhan, “Optimal coded sampling for temporal super-resolution,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2010), pp. 599–606.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “Flexible voxels for motion-aware videography,” in “Proceedings of European Conference on Computer Vision,” (2010), pp. 100–114.

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K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
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Y. Hitomi, J. Gu, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Video from a single coded exposure photograph using a learned over-complete dictionary,” in “Proceedings of IEEE International Conference on Computer Vision,” (2011).

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B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776 (2005).
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C. Fernandez-Cull, B. M. Tyrrell, R. D’Onofrio, A. Bolstad, J. Lin, J. W. Little, M. Blackwell, M. Renzi, and M. Kelly, “Smart pixel imaging with computational-imaging arrays,” Proc. SPIE 9070, 90703D (2014).

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S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
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E. Tsiligianni, L. Kondi, and A. Katsaggelos, “Construction of incoherent unit norm tight frames with application to compressed sensing,” IEEE Trans. Inf. Theory 60, 2319–2330 (2014).
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M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
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N. Katic, M. H. Kamal, A. Schmid, P. Vandergheynst, and Y. Leblebici, “Compressive image acquisition in modern CMOS IC design,” Int. J. Circ. Theor. App., 190063 (2013).
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G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7, 209–211 (2010).
[Crossref] [PubMed]

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B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776 (2005).
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L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-Shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
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X. Liao, H. Li, and L. Carin, “Generalized Alternating Projection for weighted-2,1 minimization with applications to model-based compressive sensing,” SIAM J. Imag. Sci. 7, 797–823 (2014).
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L. Xu, A. Sankaranarayanan, C. Studer, Y. Li, R. G. Baraniuk, and K. F. Kelly, “Multi-Scale compressive video acquisition,” in “Imaging and Appl. Opt.”, (Optical Society of America, 2013), p. CW2C.4.
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L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-Shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
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K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
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Liao, S.

N. Gopalsami, S. Liao, T. W. Elmer, E. R. Koehl, A. Heifetz, A. C. Raptis, L. Spinoulas, and A. K. Katsaggelos, “Passive millimeter-wave imaging with compressive sensing,” Opt. Eng. 51, 091614 (2012).
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Liao, X.

X. Liao, H. Li, and L. Carin, “Generalized Alternating Projection for weighted-2,1 minimization with applications to model-based compressive sensing,” SIAM J. Imag. Sci. 7, 797–823 (2014).
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P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
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X. Yuan, P. Llull, X. Liao, J. Yang, D. J. Brady, G. Sapiro, and L. Carin, “Low-Cost compressive sensing for color video and depth,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2014), pp. 3318–3325.

Lin, J.

C. Fernandez-Cull, B. M. Tyrrell, R. D’Onofrio, A. Bolstad, J. Lin, J. W. Little, M. Blackwell, M. Renzi, and M. Kelly, “Smart pixel imaging with computational-imaging arrays,” Proc. SPIE 9070, 90703D (2014).

Lin, X.

X. Lin, J. Suo, G. Wetzstein, Q. Dai, and R. Raskar, “Coded focal stack photography,” in “Proceedings of IEEE International Conference on Computational Photography,” (2013), pp. 1–9.

Little, J. W.

C. Fernandez-Cull, B. M. Tyrrell, R. D’Onofrio, A. Bolstad, J. Lin, J. W. Little, M. Blackwell, M. Renzi, and M. Kelly, “Smart pixel imaging with computational-imaging arrays,” Proc. SPIE 9070, 90703D (2014).

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D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high speed imaging,” IEEE Trans. Pattern Anal. Mach. Intell. 99, 1 (2013).

Llull, P.

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
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X. Yuan, P. Llull, X. Liao, J. Yang, D. J. Brady, G. Sapiro, and L. Carin, “Low-Cost compressive sensing for color video and depth,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2014), pp. 3318–3325.

Lustig, M.

S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
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Z. T. Harmany, R. F. Marcia, and R. M. Willett, “Dual-Scale masks for spatio-temporal compressive imaging,” in “Proceedings of IEEE Global Conference on Signal and Information Processing,” (2013), pp. 1045–1048.

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

Mitsunaga, T.

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high speed imaging,” IEEE Trans. Pattern Anal. Mach. Intell. 99, 1 (2013).

Y. Hitomi, J. Gu, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Video from a single coded exposure photograph using a learned over-complete dictionary,” in “Proceedings of IEEE International Conference on Computer Vision,” (2011).

Nakagawa, K.

K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
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K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
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Narasimhan, S. G.

A. Agrawal, M. Gupta, A. Veeraraghavan, and S. G. Narasimhan, “Optimal coded sampling for temporal super-resolution,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2010), pp. 599–606.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “Flexible voxels for motion-aware videography,” in “Proceedings of European Conference on Computer Vision,” (2010), pp. 100–114.

Nayar, S. K.

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high speed imaging,” IEEE Trans. Pattern Anal. Mach. Intell. 99, 1 (2013).

M. Ben-Ezra and S. K. Nayar, “Motion-based Motion Deblurring,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 689–698 (2004).
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Y. Hitomi, J. Gu, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Video from a single coded exposure photograph using a learned over-complete dictionary,” in “Proceedings of IEEE International Conference on Computer Vision,” (2011).

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G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE Trans. Emerg. Sel. Topics Circuits Syst. 2, 604–615 (2012).
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G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE Trans. Emerg. Sel. Topics Circuits Syst. 2, 604–615 (2012).
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T. Portz, L. Zhang, and H. Jiang, “Random coded sampling for high-speed HDR video,” in “Proceedings of IEEE International Conference on Computational Photography,” (2013), pp. 1–8.

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G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE Trans. Emerg. Sel. Topics Circuits Syst. 2, 604–615 (2012).
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Raptis, A. C.

L. Spinoulas, J. Qi, A. K. Katsaggelos, T. W. Elmer, N. Gopalsami, and A. C. Raptis, “Optimized compressive sampling for passive millimeter-wave imaging,” Appl. Opt. 51, 6335–6342 (2012).
[Crossref] [PubMed]

N. Gopalsami, S. Liao, T. W. Elmer, E. R. Koehl, A. Heifetz, A. C. Raptis, L. Spinoulas, and A. K. Katsaggelos, “Passive millimeter-wave imaging with compressive sensing,” Opt. Eng. 51, 091614 (2012).
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X. Lin, J. Suo, G. Wetzstein, Q. Dai, and R. Raskar, “Coded focal stack photography,” in “Proceedings of IEEE International Conference on Computational Photography,” (2013), pp. 1–9.

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C. Fernandez-Cull, B. M. Tyrrell, R. D’Onofrio, A. Bolstad, J. Lin, J. W. Little, M. Blackwell, M. Renzi, and M. Kelly, “Smart pixel imaging with computational-imaging arrays,” Proc. SPIE 9070, 90703D (2014).

Robucci, R.

R. Robucci, J. D. Gray, L. K. Chiu, J. Romberg, and P. Hasler, “Compressive sensing on a CMOS separable-transform image sensor,” Proc. IEEE 98, 1089–1101 (2010).
[Crossref]

Romberg, J.

R. Robucci, J. D. Gray, L. K. Chiu, J. Romberg, and P. Hasler, “Compressive sensing on a CMOS separable-transform image sensor,” Proc. IEEE 98, 1089–1101 (2010).
[Crossref]

Sakuma, I.

K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Sankaranarayanan, A.

L. Xu, A. Sankaranarayanan, C. Studer, Y. Li, R. G. Baraniuk, and K. F. Kelly, “Multi-Scale compressive video acquisition,” in “Imaging and Appl. Opt.”, (Optical Society of America, 2013), p. CW2C.4.
[Crossref]

Sankaranarayanan, A. C.

J. Holloway, A. C. Sankaranarayanan, A. Veeraraghavan, and S. Tambe, “Flutter shutter video camera for compressive sensing of videos,” in “Proceedings of IEEE International Conference on Computational Photography,” (2012), pp. 1–9.

A. C. Sankaranarayanan, C. Studer, and R. G. Baraniuk, “Video compressive sensing for spatial-multiplexing cameras using motion-flow models,” SIAM J. Imag. Sci. (submitted).

A. C. Sankaranarayanan, C. Studer, and R. G. Baraniuk, “CS-MUVI: Video compressive sensing for spatial-multiplexing cameras,” in “Proceedings of IEEE International Conference on Computational Photography,” (2012), pp. 1–10.

Sapiro, G.

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
[Crossref] [PubMed]

X. Yuan, P. Llull, X. Liao, J. Yang, D. J. Brady, G. Sapiro, and L. Carin, “Low-Cost compressive sensing for color video and depth,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2014), pp. 3318–3325.

Schmid, A.

N. Katic, M. H. Kamal, A. Schmid, P. Vandergheynst, and Y. Leblebici, “Compressive image acquisition in modern CMOS IC design,” Int. J. Circ. Theor. App., 190063 (2013).
[Crossref]

Spinoulas, L.

N. Gopalsami, S. Liao, T. W. Elmer, E. R. Koehl, A. Heifetz, A. C. Raptis, L. Spinoulas, and A. K. Katsaggelos, “Passive millimeter-wave imaging with compressive sensing,” Opt. Eng. 51, 091614 (2012).
[Crossref]

L. Spinoulas, J. Qi, A. K. Katsaggelos, T. W. Elmer, N. Gopalsami, and A. C. Raptis, “Optimized compressive sampling for passive millimeter-wave imaging,” Appl. Opt. 51, 6335–6342 (2012).
[Crossref] [PubMed]

Studer, C.

L. Xu, A. Sankaranarayanan, C. Studer, Y. Li, R. G. Baraniuk, and K. F. Kelly, “Multi-Scale compressive video acquisition,” in “Imaging and Appl. Opt.”, (Optical Society of America, 2013), p. CW2C.4.
[Crossref]

A. C. Sankaranarayanan, C. Studer, and R. G. Baraniuk, “CS-MUVI: Video compressive sensing for spatial-multiplexing cameras,” in “Proceedings of IEEE International Conference on Computational Photography,” (2012), pp. 1–10.

A. C. Sankaranarayanan, C. Studer, and R. G. Baraniuk, “Video compressive sensing for spatial-multiplexing cameras using motion-flow models,” SIAM J. Imag. Sci. (submitted).

Sun, T.

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

Suo, J.

X. Lin, J. Suo, G. Wetzstein, Q. Dai, and R. Raskar, “Coded focal stack photography,” in “Proceedings of IEEE International Conference on Computational Photography,” (2013), pp. 1–9.

Suo, Y.

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE Trans. Emerg. Sel. Topics Circuits Syst. 2, 604–615 (2012).
[Crossref]

Takhar, D.

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

Talvala, E.-V.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776 (2005).
[Crossref]

Tambe, S.

J. Holloway, A. C. Sankaranarayanan, A. Veeraraghavan, and S. Tambe, “Flutter shutter video camera for compressive sensing of videos,” in “Proceedings of IEEE International Conference on Computational Photography,” (2012), pp. 1–9.

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A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imag. Sci. 2, 183–202 (2009).
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Tecza, M.

G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7, 209–211 (2010).
[Crossref] [PubMed]

Tran, T. D.

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE Trans. Emerg. Sel. Topics Circuits Syst. 2, 604–615 (2012).
[Crossref]

Tsiligianni, E.

E. Tsiligianni, L. Kondi, and A. Katsaggelos, “Construction of incoherent unit norm tight frames with application to compressed sensing,” IEEE Trans. Inf. Theory 60, 2319–2330 (2014).
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Tsukamoto, A.

K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Tyrrell, B. M.

C. Fernandez-Cull, B. M. Tyrrell, R. D’Onofrio, A. Bolstad, J. Lin, J. W. Little, M. Blackwell, M. Renzi, and M. Kelly, “Smart pixel imaging with computational-imaging arrays,” Proc. SPIE 9070, 90703D (2014).

Ushida, T.

K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Vaish, V.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776 (2005).
[Crossref]

Vandergheynst, P.

N. Katic, M. H. Kamal, A. Schmid, P. Vandergheynst, and Y. Leblebici, “Compressive image acquisition in modern CMOS IC design,” Int. J. Circ. Theor. App., 190063 (2013).
[Crossref]

Veeraraghavan, A.

A. Veeraraghavan, D. Reddy, and R. Raskar, “Coded Strobing Photography: Compressive sensing of high speed periodic videos,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 671–686 (2011).
[Crossref]

D. Reddy, A. Veeraraghavan, and R. Chellappa, “P2C2: Programmable pixel compressive camera for high speed imaging,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2011), pp. 329–336.

J. Holloway, A. C. Sankaranarayanan, A. Veeraraghavan, and S. Tambe, “Flutter shutter video camera for compressive sensing of videos,” in “Proceedings of IEEE International Conference on Computational Photography,” (2012), pp. 1–9.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “Flexible voxels for motion-aware videography,” in “Proceedings of European Conference on Computer Vision,” (2010), pp. 100–114.

A. Agrawal, M. Gupta, A. Veeraraghavan, and S. G. Narasimhan, “Optimal coded sampling for temporal super-resolution,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2010), pp. 599–606.

Wang, L. V.

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-Shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref] [PubMed]

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).

Wetzstein, G.

X. Lin, J. Suo, G. Wetzstein, Q. Dai, and R. Raskar, “Coded focal stack photography,” in “Proceedings of IEEE International Conference on Computational Photography,” (2013), pp. 1–9.

Wilburn, B.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776 (2005).
[Crossref]

Willett, R. M.

Z. T. Harmany, R. F. Marcia, and R. M. Willett, “Dual-Scale masks for spatio-temporal compressive imaging,” in “Proceedings of IEEE Global Conference on Signal and Information Processing,” (2013), pp. 1045–1048.

Wu, X.

R. Pournaghi and X. Wu, “Coded acquisition of high frame rate video,” IEEE Trans. Image Process. 23, 5670–5682 (2014).
[Crossref] [PubMed]

Xu, L.

L. Xu, A. Sankaranarayanan, C. Studer, Y. Li, R. G. Baraniuk, and K. F. Kelly, “Multi-Scale compressive video acquisition,” in “Imaging and Appl. Opt.”, (Optical Society of America, 2013), p. CW2C.4.
[Crossref]

Yang, J.

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
[Crossref] [PubMed]

X. Yuan, P. Llull, X. Liao, J. Yang, D. J. Brady, G. Sapiro, and L. Carin, “Low-Cost compressive sensing for color video and depth,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2014), pp. 3318–3325.

Yuan, X.

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).
[Crossref] [PubMed]

X. Yuan, P. Llull, X. Liao, J. Yang, D. J. Brady, G. Sapiro, and L. Carin, “Low-Cost compressive sensing for color video and depth,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2014), pp. 3318–3325.

Zhang, J.

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE Trans. Emerg. Sel. Topics Circuits Syst. 2, 604–615 (2012).
[Crossref]

Zhang, L.

T. Portz, L. Zhang, and H. Jiang, “Random coded sampling for high-speed HDR video,” in “Proceedings of IEEE International Conference on Computational Photography,” (2013), pp. 1–8.

ACM Trans. Graph. (1)

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776 (2005).
[Crossref]

Appl. Opt. (1)

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

S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
[Crossref]

IEEE J. Solid-State Circ. (1)

Y. Oike and A. El Gamal, “CMOS image sensor with per-column ΣΔ; ADC and programmable compressed sensing,” IEEE J. Solid-State Circ. 48, 318–328 (2013).
[Crossref]

IEEE Signal Process. Mag. (1)

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

IEEE Trans. Emerg. Sel. Topics Circuits Syst. (1)

G. Orchard, J. Zhang, Y. Suo, M. Dao, D. T. Nguyen, S. Chin, C. Posch, T. D. Tran, and R. Etienne-Cummings, “Real time compressive sensing video reconstruction in hardware,” IEEE Trans. Emerg. Sel. Topics Circuits Syst. 2, 604–615 (2012).
[Crossref]

IEEE Trans. Image Process. (1)

R. Pournaghi and X. Wu, “Coded acquisition of high frame rate video,” IEEE Trans. Image Process. 23, 5670–5682 (2014).
[Crossref] [PubMed]

IEEE Trans. Inf. Theory (1)

E. Tsiligianni, L. Kondi, and A. Katsaggelos, “Construction of incoherent unit norm tight frames with application to compressed sensing,” IEEE Trans. Inf. Theory 60, 2319–2330 (2014).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (3)

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high speed imaging,” IEEE Trans. Pattern Anal. Mach. Intell. 99, 1 (2013).

M. Ben-Ezra and S. K. Nayar, “Motion-based Motion Deblurring,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 689–698 (2004).
[Crossref]

A. Veeraraghavan, D. Reddy, and R. Raskar, “Coded Strobing Photography: Compressive sensing of high speed periodic videos,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 671–686 (2011).
[Crossref]

IEEE Trans. Signal Process. (1)

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

Nat. Methods (1)

G. Bub, M. Tecza, M. Helmes, P. Lee, and P. Kohl, “Temporal pixel multiplexing for simultaneous high-speed, high-resolution imaging,” Nat. Methods 7, 209–211 (2010).
[Crossref] [PubMed]

Nat. Photonics (1)

K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Nature (1)

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-Shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref] [PubMed]

Opt. Eng. (1)

N. Gopalsami, S. Liao, T. W. Elmer, E. R. Koehl, A. Heifetz, A. C. Raptis, L. Spinoulas, and A. K. Katsaggelos, “Passive millimeter-wave imaging with compressive sensing,” Opt. Eng. 51, 091614 (2012).
[Crossref]

Opt. Express (1)

Proc. IEEE (1)

R. Robucci, J. D. Gray, L. K. Chiu, J. Romberg, and P. Hasler, “Compressive sensing on a CMOS separable-transform image sensor,” Proc. IEEE 98, 1089–1101 (2010).
[Crossref]

Proc. SPIE (2)

C. Fernandez-Cull, B. M. Tyrrell, R. D’Onofrio, A. Bolstad, J. Lin, J. W. Little, M. Blackwell, M. Renzi, and M. Kelly, “Smart pixel imaging with computational-imaging arrays,” Proc. SPIE 9070, 90703D (2014).

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

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A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imag. Sci. 2, 183–202 (2009).
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X. Liao, H. Li, and L. Carin, “Generalized Alternating Projection for weighted-2,1 minimization with applications to model-based compressive sensing,” SIAM J. Imag. Sci. 7, 797–823 (2014).
[Crossref]

Other (14)

X. Yuan, P. Llull, X. Liao, J. Yang, D. J. Brady, G. Sapiro, and L. Carin, “Low-Cost compressive sensing for color video and depth,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2014), pp. 3318–3325.

M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing, 1st ed. (Springer Publishing Company, Incorporated, 2010).
[Crossref]

Y. Hitomi, J. Gu, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Video from a single coded exposure photograph using a learned over-complete dictionary,” in “Proceedings of IEEE International Conference on Computer Vision,” (2011).

N. Katic, M. H. Kamal, A. Schmid, P. Vandergheynst, and Y. Leblebici, “Compressive image acquisition in modern CMOS IC design,” Int. J. Circ. Theor. App., 190063 (2013).
[Crossref]

D. Reddy, A. Veeraraghavan, and R. Chellappa, “P2C2: Programmable pixel compressive camera for high speed imaging,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2011), pp. 329–336.

A. Agrawal, M. Gupta, A. Veeraraghavan, and S. G. Narasimhan, “Optimal coded sampling for temporal super-resolution,” in “Proceedings of IEEE Conference on Computer Vision and Pattern Recognition,” (2010), pp. 599–606.

J. Holloway, A. C. Sankaranarayanan, A. Veeraraghavan, and S. Tambe, “Flutter shutter video camera for compressive sensing of videos,” in “Proceedings of IEEE International Conference on Computational Photography,” (2012), pp. 1–9.

X. Lin, J. Suo, G. Wetzstein, Q. Dai, and R. Raskar, “Coded focal stack photography,” in “Proceedings of IEEE International Conference on Computational Photography,” (2013), pp. 1–9.

T. Portz, L. Zhang, and H. Jiang, “Random coded sampling for high-speed HDR video,” in “Proceedings of IEEE International Conference on Computational Photography,” (2013), pp. 1–8.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “Flexible voxels for motion-aware videography,” in “Proceedings of European Conference on Computer Vision,” (2010), pp. 100–114.

A. C. Sankaranarayanan, C. Studer, and R. G. Baraniuk, “CS-MUVI: Video compressive sensing for spatial-multiplexing cameras,” in “Proceedings of IEEE International Conference on Computational Photography,” (2012), pp. 1–10.

A. C. Sankaranarayanan, C. Studer, and R. G. Baraniuk, “Video compressive sensing for spatial-multiplexing cameras using motion-flow models,” SIAM J. Imag. Sci. (submitted).

Z. T. Harmany, R. F. Marcia, and R. M. Willett, “Dual-Scale masks for spatio-temporal compressive imaging,” in “Proceedings of IEEE Global Conference on Signal and Information Processing,” (2013), pp. 1045–1048.

L. Xu, A. Sankaranarayanan, C. Studer, Y. Li, R. G. Baraniuk, and K. F. Kelly, “Multi-Scale compressive video acquisition,” in “Imaging and Appl. Opt.”, (Optical Society of America, 2013), p. CW2C.4.
[Crossref]

Supplementary Material (4)

» Media 1: AVI (1732 KB)     
» Media 2: AVI (1901 KB)     
» Media 3: AVI (1993 KB)     
» Media 4: AVI (1336 KB)     

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Figures (9)

Fig. 1:
Fig. 1:

The forward sensing model used in this paper. A space-time volume x consisting of a set of T frames, with H × W pixels each, is multiplied by a set of mask patterns embedded within the sensing matrix Φ. The sensor integrates over time, producing a single coded captured image y consisting of H × W pixels.

Fig. 2:
Fig. 2:

The four different mask patterns considered in this paper. (a) and (b) show a set of T different masks to be displayed on an SLM; (a) shows a set of thresholded Gaussian masks; (b) shows a set of masks that, when summed across the t direction, result to the same number of samples per pixel. The forefront masks presented in (c) and (d) depict a mask pattern which will be placed on a translating stage in order to produce the datacube shown, when translated horizontally on the x direction; (c) corresponds to a thresholded Gaussian mask; (d) corresponds to the optimized mask proposed in this paper. The proposed mask, when translated, produces an average value that is identical across all pixels of the sensor.

Fig. 3:
Fig. 3:

Simulated reconstruction results: (a) The Monster and Road test scenes used for simulation; (b) Average reconstruction PSNRs for three different algorithms discussed in section 3 and the four masks discussed in section 4. The SLM-based approach performs 1–3 dB better than the translating mask approach and the Normalized masks provide an increase of 1–3 dB in reconstruction quality, compared to their Random counterparts; (c) PSNR for each of the 36 reconstructed video frames of the Monster scene using our proposed Shifted-Normalized mask. Reconstruction quality varies due to varying motion between subsequent frames in the video sequence. OMP and GAP perform best, with CLS performing slightly worse. Note that the selection of a 2 × 2 × 36 patch size for the GAP algorithm is because the code necessitated that the time dimension of the patch would be a multiple of the spatial patch size. The code was further tested with a 7 × 7 × 35 patch and resulted in performance comparable to the one of the CLS/HP algorithm (not reported here for consistency in the presented number of total reconstructed frames). FISTA and L1 LS lead to the worst reconstruction quality; (d) PSNR vs Runtime comparison using 4 algorithms for the reconstruction of the Monster scene. CLS provides the best balance between reconstruction quality and speed.

Fig. 4:
Fig. 4:

System design: (1) Moving scene; (2) Objective Lens; (3) Piezoelectric stage; (4) Coded optical mask; (5) Relay Lens; (6) Sensor; (7) Coded image. See section 5.1 for details.

Fig. 5:
Fig. 5:

Hardware prototype: Our completed camera system with its dust cover removed.

Fig. 6:
Fig. 6:

Coded mask detail: (a) Real capture of a static mask (with P = 4 and T = 10) where fiducial calibration lines are visible, as described in section 5.2; (b) Real capture while the mask moves by 10 pixels or 45μm horizontally (full duration of acquisition); (c) Microscope images of two different coded masks (upper part for P = 6 and T = 36; lower part for P = 12 and T = 36) showing imperfections of the fabrication process.

Fig. 7:
Fig. 7:

Reconstruction of the Metronome scene using the Constrained Least-Squares method with a high-pass filter. The scene consists of small amounts of translating motion. Parts (a)–(b) show the captured image; Parts (c)–(h) present 3 of the 10 reconstructed frames; Part (i) depicts closeups on the translating “Jack”. Please see the complete video in Media 1.

Fig. 8:
Fig. 8:

Reconstruction of the Ball scene using the Constrained Least-Squares method with a high-pass filter. The scene consists of large amounts of translating motion. Parts (a)–(b) show the captured image; Parts (c)–(h) present 3 of the 10 reconstructed frames; Part (i) depicts closeups of the falling soccer ball. Please see the complete video in Media 2 and the corresponding Orthogonal Matching Pursuit/Dictionary reconstruction in Media 3.

Fig. 9:
Fig. 9:

Reconstruction of the Deck of Cards scene using the Constrained Least-Squares method with a high-pass filter. The scene consists of large amounts of arbitrary motion. Parts (a)–(b) show the captured image; Parts (c)–(h) present 3 of the 10 reconstructed frames; Part (i) depicts closeups of the rotating “Jack”. Please see the complete video in Media 4.

Tables (1)

Tables Icon

Table 1: Reconstruction performance for the Monster scene using 1 minimization (FISTA/DCT) and the proposed mask (see Fig. 2(d)) for different values of P and T.

Equations (6)

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

y = Φ x
Φ = [ 𝕄 0 𝕄 1 𝕄 T ] .
a ^ = arg min a y Φ Ψ 1 a 2 2 + λ F ( a ) .
a ^ = arg min a a 0 subject to y Φ Ψ 1 a 2 2 ε ,
a ^ = arg min a y Φ Ψ 1 a 2 2 + λ a 1 .
x ^ = arg min x y Φ x 2 2 + λ Θ x 2 2 .

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