Abstract

Computational imaging based on compressed sensing (CS) has shown potential for outperforming conventional techniques in many applications, but challenges arise when translating CS theory to practical imaging systems. Here we examine such challenges in two physical architectures under coherent and incoherent illumination. We describe hardware alignment protocols that can be used to optimize system performance for each case. We found that an architecture using coded masks located at a conjugate image plane outperformed an identical architecture using masks at a Fourier plane, enabling recovery of images with up to 64 times more resolvable points than pixels in the image sensor. We demonstrate and explain the basis for the tradeoff between achievable resolution and dynamic range of reconstructed CS images. Finally, we demonstrate that these principles can be applied beyond binary test targets by reconstructing a 480 × 480 image of a human tissue section from a 120 × 120 pixel sensor. These results provide a basis to further develop compressive imaging architectures for biomedical imaging and we also anticipate that these findings may be useful to investigators focused on translating CS theory to other real-world imaging applications.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2017 (3)

R. G. Baraniuk, T. Goldstein, A. C. Sankaranarayanan, C. Studer, A. Veeraraghavan, and M. B. Wakin, “Compressive video sensing: algorithms, architectures, and applications,” IEEE Signal Process. Mag. 34(1), 52–66 (2017).

L. Liu, C. Guo, and Y. He, “Single exposure superresolution restoration for optical sparse aperture based on random convolution,” Opt. Eng. 56(7), 073102 (2017).

M. S. Asif, A. Ayremlou, A. Sankaranarayanan, A. Veeraraghavan, and R. Baraniuk, “Flatcam: thin, bare-sensor cameras using coded aperture and computation,” IEEE Trans. Comp. Imag. 3(3), 384–397 (2017).

2016 (4)

D. Marcos, T. Lasser, A. López, and A. Bourquard, “Compressed imaging by sparse random convolution,” Opt. Express 24(2), 1269–1290 (2016).
[PubMed]

Y. Sun, X. Sui, G. Gu, Y. Liu, and S. Xu, “Compressive super-resolution imaging based on scrambled block Hadamard ensemble,” IEEE Photonics J. 8(2), 1–8 (2016).

E. McLeod and A. Ozcan, “Unconventional methods of imaging: computational microscopy and compact implementations,” Rep. Prog. Phys. 79(7), 076001 (2016).
[PubMed]

J. P. Dumas, M. A. Lodhi, W. U. Bajwa, and M. C. Pierce, “Computational imaging with a highly parallel image-plane-coded architecture: challenges and solutions,” Opt. Express 24(6), 6145–6155 (2016).
[PubMed]

2015 (4)

D. Thapa, K. Raahemifar, and V. Lakshminarayanan, “Less is more: compressive sensing in optics and image science,” J. Mod. Opt. 62(6), 415–429 (2015).

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

G. Komis, M. Mistrik, O. Šamajová, M. Ovečka, J. Bartek, and J. Šamaj, “Superresolution live imaging of plant cells using structured illumination microscopy,” Nat. Protoc. 10(8), 1248–1263 (2015).
[PubMed]

M. J. DeWeert and B. P. Farm, “Lensless coded-aperture imaging with separable Doubly-Toeplitz masks,” Opt. Eng. 54(2), 023102 (2015).

2014 (6)

S. Dong, P. Nanda, R. Shiradkar, K. Guo, and G. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express 22(17), 20856–20870 (2014).
[PubMed]

L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomed. Opt. Express 5(7), 2376–2389 (2014).
[PubMed]

A. Greenbaum, Y. Zhang, A. Feizi, P. L. Chung, W. Luo, S. R. Kandukuri, and A. Ozcan, “Wide-field computational imaging of pathology slides using lens-free on-chip microscopy,” Sci. Transl. Med. 6(267), 267ra175 (2014).
[PubMed]

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).

A. F. Coskun and A. Ozcan, “Computational imaging, sensing and diagnostics for global health applications,” Curr. Opin. Biotechnol. 25, 8–16 (2014).
[PubMed]

2013 (3)

A. Stern, “Optical compressive sensing: a new field benefiting from classical optical signal processing techniques,” Proc. SPIE 8833, 88330B (2013).

O. Cossairt, M. Gupta, and S. K. Nayar, “When does computational imaging improve performance?” IEEE Trans. Image Process. 22(2), 447–458 (2013).
[PubMed]

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).

2012 (2)

J. Y. Park and M. B. Wakin, “A geometric approach to multi-view compressive imaging,” J. Adv. Sig. Proc. 37, 1–15 (2012).

H. Arguello, H. Rueda, and G. R. Arce, “Spatial super-resolution in code aperture spectral imaging,” Proc. SPIE 8365, 83650A (2012).

2011 (2)

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50(7), 072601 (2011).

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: From theory to applications,” IEEE Trans. Image Process. 59(9), 4053–4085 (2011).

2010 (2)

2009 (3)

J. Y. Zheng, R. M. Pasternack, and N. N. Boustany, “Optical scatter imaging with a digital micromirror device,” Opt. Express 17(22), 20401–20414 (2009).
[PubMed]

J. Romberg, “Compressive sensing by random convolution,” SIAM J. Imaging Sci. 2(4), 1098–1128 (2009).

J. Tang, B. E. Nett, and G. H. Chen, “Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms,” Phys. Med. Biol. 54(19), 5781–5804 (2009).
[PubMed]

2008 (1)

R. Voelkel and K. J. Weible, “Laser beam homogenizing: limitations and constraints,” Proc. SPIE 7102, 71020J (2008).

2007 (2)

J. M. Bioucas-Dias and M. A. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
[PubMed]

R. G. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24(4), 118–121 (2007).

2006 (3)

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).

2003 (1)

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14–25 (2003).

1995 (1)

Aguet, F.

Arce, G. R.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).

H. Arguello, H. Rueda, and G. R. Arce, “Spatial super-resolution in code aperture spectral imaging,” Proc. SPIE 8365, 83650A (2012).

Arguello, H.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).

H. Arguello, H. Rueda, and G. R. Arce, “Spatial super-resolution in code aperture spectral imaging,” Proc. SPIE 8365, 83650A (2012).

Asif, M. S.

M. S. Asif, A. Ayremlou, A. Sankaranarayanan, A. Veeraraghavan, and R. Baraniuk, “Flatcam: thin, bare-sensor cameras using coded aperture and computation,” IEEE Trans. Comp. Imag. 3(3), 384–397 (2017).

H. Chen, M. S. Asif, A. C. Sankaranarayanan, and A. Veeraraghavan, “FPA-CS: Focal plane array-based compressive imaging in short-wave infrared,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE 2015), pp. 2358–2366.

Ayremlou, A.

M. S. Asif, A. Ayremlou, A. Sankaranarayanan, A. Veeraraghavan, and R. Baraniuk, “Flatcam: thin, bare-sensor cameras using coded aperture and computation,” IEEE Trans. Comp. Imag. 3(3), 384–397 (2017).

Baird, M. A.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

Bajwa, W. U.

Bando, Y.

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).

Baraniuk, R.

M. S. Asif, A. Ayremlou, A. Sankaranarayanan, A. Veeraraghavan, and R. Baraniuk, “Flatcam: thin, bare-sensor cameras using coded aperture and computation,” IEEE Trans. Comp. Imag. 3(3), 384–397 (2017).

Baraniuk, R. G.

R. G. Baraniuk, T. Goldstein, A. C. Sankaranarayanan, C. Studer, A. Veeraraghavan, and M. B. Wakin, “Compressive video sensing: algorithms, architectures, and applications,” IEEE Signal Process. Mag. 34(1), 52–66 (2017).

R. G. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24(4), 118–121 (2007).

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Baron, D.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Barsi, C.

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).

Bartek, J.

G. Komis, M. Mistrik, O. Šamajová, M. Ovečka, J. Bartek, and J. Šamaj, “Superresolution live imaging of plant cells using structured illumination microscopy,” Nat. Protoc. 10(8), 1248–1263 (2015).
[PubMed]

Beach, J. R.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

Betzig, E.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
[PubMed]

Bourquard, A.

Boustany, N. N.

Brady, D. J.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).

Candès, E. J.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).

Carin, L.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).

Chen, B. C.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

Chen, G. H.

J. Tang, B. E. Nett, and G. H. Chen, “Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms,” Phys. Med. Biol. 54(19), 5781–5804 (2009).
[PubMed]

Chen, H.

H. Chen, M. S. Asif, A. C. Sankaranarayanan, and A. Veeraraghavan, “FPA-CS: Focal plane array-based compressive imaging in short-wave infrared,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE 2015), pp. 2358–2366.

Chung, P. L.

A. Greenbaum, Y. Zhang, A. Feizi, P. L. Chung, W. Luo, S. R. Kandukuri, and A. Ozcan, “Wide-field computational imaging of pathology slides using lens-free on-chip microscopy,” Sci. Transl. Med. 6(267), 267ra175 (2014).
[PubMed]

Coskun, A. F.

A. F. Coskun and A. Ozcan, “Computational imaging, sensing and diagnostics for global health applications,” Curr. Opin. Biotechnol. 25, 8–16 (2014).
[PubMed]

Cossairt, O.

O. Cossairt, M. Gupta, and S. K. Nayar, “When does computational imaging improve performance?” IEEE Trans. Image Process. 22(2), 447–458 (2013).
[PubMed]

Davidson, M. W.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

DeWeert, M. J.

M. J. DeWeert and B. P. Farm, “Lensless coded-aperture imaging with separable Doubly-Toeplitz masks,” Opt. Eng. 54(2), 023102 (2015).

Dogandžic, A.

R. Gu and A. Dogandžić, “A fast proximal gradient algorithm for reconstructing nonnegative signals with sparse transform coefficients,” in Proceedings of IEEE Asilomar Conference on Signals, Systems and Computers (IEEE, 2014), pp. 1662–1667.

Dong, S.

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).

Duarte, M. F.

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: From theory to applications,” IEEE Trans. Image Process. 59(9), 4053–4085 (2011).

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Dudley, D.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14–25 (2003).

Dumas, J. P.

Duncan, W.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14–25 (2003).

Eldar, Y. C.

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: From theory to applications,” IEEE Trans. Image Process. 59(9), 4053–4085 (2011).

Farm, B. P.

M. J. DeWeert and B. P. Farm, “Lensless coded-aperture imaging with separable Doubly-Toeplitz masks,” Opt. Eng. 54(2), 023102 (2015).

Feizi, A.

A. Greenbaum, Y. Zhang, A. Feizi, P. L. Chung, W. Luo, S. R. Kandukuri, and A. Ozcan, “Wide-field computational imaging of pathology slides using lens-free on-chip microscopy,” Sci. Transl. Med. 6(267), 267ra175 (2014).
[PubMed]

Fernandez-Cull, C.

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).

Figueiredo, M. A.

J. M. Bioucas-Dias and M. A. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
[PubMed]

Golbabaee, M.

M. Kamal, M. Golbabaee, and P. Vandergheynst, “Light field compressive sensing in camera arrays,” in Proceedings of IEEE ICASSP (IEEE, 2012), pp. 5413–5416.

Goldstein, T.

R. G. Baraniuk, T. Goldstein, A. C. Sankaranarayanan, C. Studer, A. Veeraraghavan, and M. B. Wakin, “Compressive video sensing: algorithms, architectures, and applications,” IEEE Signal Process. Mag. 34(1), 52–66 (2017).

Greenbaum, A.

A. Greenbaum, Y. Zhang, A. Feizi, P. L. Chung, W. Luo, S. R. Kandukuri, and A. Ozcan, “Wide-field computational imaging of pathology slides using lens-free on-chip microscopy,” Sci. Transl. Med. 6(267), 267ra175 (2014).
[PubMed]

Gu, G.

Y. Sun, X. Sui, G. Gu, Y. Liu, and S. Xu, “Compressive super-resolution imaging based on scrambled block Hadamard ensemble,” IEEE Photonics J. 8(2), 1–8 (2016).

Gu, R.

R. Gu and A. Dogandžić, “A fast proximal gradient algorithm for reconstructing nonnegative signals with sparse transform coefficients,” in Proceedings of IEEE Asilomar Conference on Signals, Systems and Computers (IEEE, 2014), pp. 1662–1667.

Guo, C.

L. Liu, C. Guo, and Y. He, “Single exposure superresolution restoration for optical sparse aperture based on random convolution,” Opt. Eng. 56(7), 073102 (2017).

Guo, K.

Gupta, M.

O. Cossairt, M. Gupta, and S. K. Nayar, “When does computational imaging improve performance?” IEEE Trans. Image Process. 22(2), 447–458 (2013).
[PubMed]

Hammer, J. A.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

He, Y.

L. Liu, C. Guo, and Y. He, “Single exposure superresolution restoration for optical sparse aperture based on random convolution,” Opt. Eng. 56(7), 073102 (2017).

Huang, G.

G. Huang, H. Jiang, K. Matthews, and P. Wilford, “Lensless imaging by compressive sensing,” in Proceedings of IEEE ICIP (IEEE, 2013), pp. 2101–2105.

Javidi, B.

Jiang, H.

G. Huang, H. Jiang, K. Matthews, and P. Wilford, “Lensless imaging by compressive sensing,” in Proceedings of IEEE ICIP (IEEE, 2013), pp. 2101–2105.

Kamal, M.

M. Kamal, M. Golbabaee, and P. Vandergheynst, “Light field compressive sensing in camera arrays,” in Proceedings of IEEE ICASSP (IEEE, 2012), pp. 5413–5416.

Kandukuri, S. R.

A. Greenbaum, Y. Zhang, A. Feizi, P. L. Chung, W. Luo, S. R. Kandukuri, and A. Ozcan, “Wide-field computational imaging of pathology slides using lens-free on-chip microscopy,” Sci. Transl. Med. 6(267), 267ra175 (2014).
[PubMed]

Kelly, K. F.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Kirchhausen, T.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

Kittle, D.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).

Komis, G.

G. Komis, M. Mistrik, O. Šamajová, M. Ovečka, J. Bartek, and J. Šamaj, “Superresolution live imaging of plant cells using structured illumination microscopy,” Nat. Protoc. 10(8), 1248–1263 (2015).
[PubMed]

Lakshminarayanan, V.

D. Thapa, K. Raahemifar, and V. Lakshminarayanan, “Less is more: compressive sensing in optics and image science,” J. Mod. Opt. 62(6), 415–429 (2015).

Laska, J. N.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Lasser, T.

Li, D.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

Li, X.

Liu, L.

L. Liu, C. Guo, and Y. He, “Single exposure superresolution restoration for optical sparse aperture based on random convolution,” Opt. Eng. 56(7), 073102 (2017).

Liu, Y.

Y. Sun, X. Sui, G. Gu, Y. Liu, and S. Xu, “Compressive super-resolution imaging based on scrambled block Hadamard ensemble,” IEEE Photonics J. 8(2), 1–8 (2016).

Lodhi, M. A.

López, A.

Luo, W.

A. Greenbaum, Y. Zhang, A. Feizi, P. L. Chung, W. Luo, S. R. Kandukuri, and A. Ozcan, “Wide-field computational imaging of pathology slides using lens-free on-chip microscopy,” Sci. Transl. Med. 6(267), 267ra175 (2014).
[PubMed]

Marcia, R. F.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50(7), 072601 (2011).

Marcos, D.

Marwah, K.

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).

Matthews, K.

G. Huang, H. Jiang, K. Matthews, and P. Wilford, “Lensless imaging by compressive sensing,” in Proceedings of IEEE ICIP (IEEE, 2013), pp. 2101–2105.

McLeod, E.

E. McLeod and A. Ozcan, “Unconventional methods of imaging: computational microscopy and compact implementations,” Rep. Prog. Phys. 79(7), 076001 (2016).
[PubMed]

Milkie, D. E.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

Mistrik, M.

G. Komis, M. Mistrik, O. Šamajová, M. Ovečka, J. Bartek, and J. Šamaj, “Superresolution live imaging of plant cells using structured illumination microscopy,” Nat. Protoc. 10(8), 1248–1263 (2015).
[PubMed]

Moses, B.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

Nanda, P.

Nayar, S. K.

O. Cossairt, M. Gupta, and S. K. Nayar, “When does computational imaging improve performance?” IEEE Trans. Image Process. 22(2), 447–458 (2013).
[PubMed]

Nett, B. E.

J. Tang, B. E. Nett, and G. H. Chen, “Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms,” Phys. Med. Biol. 54(19), 5781–5804 (2009).
[PubMed]

Nichols, J. M.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50(7), 072601 (2011).

Ovecka, M.

G. Komis, M. Mistrik, O. Šamajová, M. Ovečka, J. Bartek, and J. Šamaj, “Superresolution live imaging of plant cells using structured illumination microscopy,” Nat. Protoc. 10(8), 1248–1263 (2015).
[PubMed]

Ozcan, A.

E. McLeod and A. Ozcan, “Unconventional methods of imaging: computational microscopy and compact implementations,” Rep. Prog. Phys. 79(7), 076001 (2016).
[PubMed]

A. Greenbaum, Y. Zhang, A. Feizi, P. L. Chung, W. Luo, S. R. Kandukuri, and A. Ozcan, “Wide-field computational imaging of pathology slides using lens-free on-chip microscopy,” Sci. Transl. Med. 6(267), 267ra175 (2014).
[PubMed]

A. F. Coskun and A. Ozcan, “Computational imaging, sensing and diagnostics for global health applications,” Curr. Opin. Biotechnol. 25, 8–16 (2014).
[PubMed]

Park, J. Y.

J. Y. Park and M. B. Wakin, “A geometric approach to multi-view compressive imaging,” J. Adv. Sig. Proc. 37, 1–15 (2012).

Pasham, M.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

Pasternack, R. M.

Pierce, M. C.

Raahemifar, K.

D. Thapa, K. Raahemifar, and V. Lakshminarayanan, “Less is more: compressive sensing in optics and image science,” J. Mod. Opt. 62(6), 415–429 (2015).

Ramchandran, K.

Raskar, R.

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).

Refregier, P.

Rivenson, Y.

Romberg, J.

J. Romberg, “Compressive sensing by random convolution,” SIAM J. Imaging Sci. 2(4), 1098–1128 (2009).

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).

Rueda, H.

H. Arguello, H. Rueda, and G. R. Arce, “Spatial super-resolution in code aperture spectral imaging,” Proc. SPIE 8365, 83650A (2012).

Šamaj, J.

G. Komis, M. Mistrik, O. Šamajová, M. Ovečka, J. Bartek, and J. Šamaj, “Superresolution live imaging of plant cells using structured illumination microscopy,” Nat. Protoc. 10(8), 1248–1263 (2015).
[PubMed]

Šamajová, O.

G. Komis, M. Mistrik, O. Šamajová, M. Ovečka, J. Bartek, and J. Šamaj, “Superresolution live imaging of plant cells using structured illumination microscopy,” Nat. Protoc. 10(8), 1248–1263 (2015).
[PubMed]

Sankaranarayanan, A.

M. S. Asif, A. Ayremlou, A. Sankaranarayanan, A. Veeraraghavan, and R. Baraniuk, “Flatcam: thin, bare-sensor cameras using coded aperture and computation,” IEEE Trans. Comp. Imag. 3(3), 384–397 (2017).

Sankaranarayanan, A. C.

R. G. Baraniuk, T. Goldstein, A. C. Sankaranarayanan, C. Studer, A. Veeraraghavan, and M. B. Wakin, “Compressive video sensing: algorithms, architectures, and applications,” IEEE Signal Process. Mag. 34(1), 52–66 (2017).

H. Chen, M. S. Asif, A. C. Sankaranarayanan, and A. Veeraraghavan, “FPA-CS: Focal plane array-based compressive imaging in short-wave infrared,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE 2015), pp. 2358–2366.

Sarvotham, S.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Shao, L.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

Shepard, R. H.

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).

Shi, B.

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).

Shiradkar, R.

Slaughter, J.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14–25 (2003).

Stern, A.

A. Stern, “Optical compressive sensing: a new field benefiting from classical optical signal processing techniques,” Proc. SPIE 8833, 88330B (2013).

Y. Rivenson, A. Stern, and B. Javidi, “Single exposure super-resolution compressive imaging by double phase encoding,” Opt. Express 18(14), 15094–15103 (2010).
[PubMed]

Studer, C.

R. G. Baraniuk, T. Goldstein, A. C. Sankaranarayanan, C. Studer, A. Veeraraghavan, and M. B. Wakin, “Compressive video sensing: algorithms, architectures, and applications,” IEEE Signal Process. Mag. 34(1), 52–66 (2017).

Sui, X.

Y. Sun, X. Sui, G. Gu, Y. Liu, and S. Xu, “Compressive super-resolution imaging based on scrambled block Hadamard ensemble,” IEEE Photonics J. 8(2), 1–8 (2016).

Sun, Y.

Y. Sun, X. Sui, G. Gu, Y. Liu, and S. Xu, “Compressive super-resolution imaging based on scrambled block Hadamard ensemble,” IEEE Photonics J. 8(2), 1–8 (2016).

Takhar, D.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Tang, J.

J. Tang, B. E. Nett, and G. H. Chen, “Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms,” Phys. Med. Biol. 54(19), 5781–5804 (2009).
[PubMed]

Tao, T.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).

Thapa, D.

D. Thapa, K. Raahemifar, and V. Lakshminarayanan, “Less is more: compressive sensing in optics and image science,” J. Mod. Opt. 62(6), 415–429 (2015).

Tian, L.

Unser, M.

Vandergheynst, P.

M. Kamal, M. Golbabaee, and P. Vandergheynst, “Light field compressive sensing in camera arrays,” in Proceedings of IEEE ICASSP (IEEE, 2012), pp. 5413–5416.

Veeraraghavan, A.

R. G. Baraniuk, T. Goldstein, A. C. Sankaranarayanan, C. Studer, A. Veeraraghavan, and M. B. Wakin, “Compressive video sensing: algorithms, architectures, and applications,” IEEE Signal Process. Mag. 34(1), 52–66 (2017).

M. S. Asif, A. Ayremlou, A. Sankaranarayanan, A. Veeraraghavan, and R. Baraniuk, “Flatcam: thin, bare-sensor cameras using coded aperture and computation,” IEEE Trans. Comp. Imag. 3(3), 384–397 (2017).

H. Chen, M. S. Asif, A. C. Sankaranarayanan, and A. Veeraraghavan, “FPA-CS: Focal plane array-based compressive imaging in short-wave infrared,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE 2015), pp. 2358–2366.

Voelkel, R.

R. Voelkel and K. J. Weible, “Laser beam homogenizing: limitations and constraints,” Proc. SPIE 7102, 71020J (2008).

Wakin, M. B.

R. G. Baraniuk, T. Goldstein, A. C. Sankaranarayanan, C. Studer, A. Veeraraghavan, and M. B. Wakin, “Compressive video sensing: algorithms, architectures, and applications,” IEEE Signal Process. Mag. 34(1), 52–66 (2017).

J. Y. Park and M. B. Wakin, “A geometric approach to multi-view compressive imaging,” J. Adv. Sig. Proc. 37, 1–15 (2012).

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 606509 (2006).

Waller, L.

Weible, K. J.

R. Voelkel and K. J. Weible, “Laser beam homogenizing: limitations and constraints,” Proc. SPIE 7102, 71020J (2008).

Wetzstein, G.

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).

Wilford, P.

G. Huang, H. Jiang, K. Matthews, and P. Wilford, “Lensless imaging by compressive sensing,” in Proceedings of IEEE ICIP (IEEE, 2013), pp. 2101–2105.

Willett, R. M.

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50(7), 072601 (2011).

Xu, P.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

Xu, S.

Y. Sun, X. Sui, G. Gu, Y. Liu, and S. Xu, “Compressive super-resolution imaging based on scrambled block Hadamard ensemble,” IEEE Photonics J. 8(2), 1–8 (2016).

Zhang, M.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

Zhang, X.

D. Li, L. Shao, B. C. Chen, X. Zhang, M. Zhang, B. Moses, D. E. Milkie, J. R. Beach, J. A. Hammer, M. Pasham, T. Kirchhausen, M. A. Baird, M. W. Davidson, P. Xu, and E. Betzig, “Extended-resolution structured illumination imaging of endocytic and cytoskeletal dynamics,” Science 349(6251), aab3500 (2015).
[PubMed]

Zhang, Y.

A. Greenbaum, Y. Zhang, A. Feizi, P. L. Chung, W. Luo, S. R. Kandukuri, and A. Ozcan, “Wide-field computational imaging of pathology slides using lens-free on-chip microscopy,” Sci. Transl. Med. 6(267), 267ra175 (2014).
[PubMed]

Zhao, H.

R. H. Shepard, C. Fernandez-Cull, R. Raskar, B. Shi, C. Barsi, and H. Zhao, “Optical design and characterization of an advanced computational imaging system,” Proc. SPIE 9216, 92160A (2014).

Zheng, G.

Zheng, J. Y.

ACM Trans. Graph. (1)

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).

Biomed. Opt. Express (1)

Curr. Opin. Biotechnol. (1)

A. F. Coskun and A. Ozcan, “Computational imaging, sensing and diagnostics for global health applications,” Curr. Opin. Biotechnol. 25, 8–16 (2014).
[PubMed]

IEEE Photonics J. (1)

Y. Sun, X. Sui, G. Gu, Y. Liu, and S. Xu, “Compressive super-resolution imaging based on scrambled block Hadamard ensemble,” IEEE Photonics J. 8(2), 1–8 (2016).

IEEE Signal Process. Mag. (3)

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. Kittle, “Compressive coded aperture spectral imaging: An introduction,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).

R. G. Baraniuk, T. Goldstein, A. C. Sankaranarayanan, C. Studer, A. Veeraraghavan, and M. B. Wakin, “Compressive video sensing: algorithms, architectures, and applications,” IEEE Signal Process. Mag. 34(1), 52–66 (2017).

R. G. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24(4), 118–121 (2007).

IEEE Trans. Comp. Imag. (1)

M. S. Asif, A. Ayremlou, A. Sankaranarayanan, A. Veeraraghavan, and R. Baraniuk, “Flatcam: thin, bare-sensor cameras using coded aperture and computation,” IEEE Trans. Comp. Imag. 3(3), 384–397 (2017).

IEEE Trans. Image Process. (3)

O. Cossairt, M. Gupta, and S. K. Nayar, “When does computational imaging improve performance?” IEEE Trans. Image Process. 22(2), 447–458 (2013).
[PubMed]

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: From theory to applications,” IEEE Trans. Image Process. 59(9), 4053–4085 (2011).

J. M. Bioucas-Dias and M. A. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
[PubMed]

IEEE Trans. Inf. Theory (2)

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).

J. Adv. Sig. Proc. (1)

J. Y. Park and M. B. Wakin, “A geometric approach to multi-view compressive imaging,” J. Adv. Sig. Proc. 37, 1–15 (2012).

J. Mod. Opt. (1)

D. Thapa, K. Raahemifar, and V. Lakshminarayanan, “Less is more: compressive sensing in optics and image science,” J. Mod. Opt. 62(6), 415–429 (2015).

Nat. Protoc. (1)

G. Komis, M. Mistrik, O. Šamajová, M. Ovečka, J. Bartek, and J. Šamaj, “Superresolution live imaging of plant cells using structured illumination microscopy,” Nat. Protoc. 10(8), 1248–1263 (2015).
[PubMed]

Opt. Eng. (3)

L. Liu, C. Guo, and Y. He, “Single exposure superresolution restoration for optical sparse aperture based on random convolution,” Opt. Eng. 56(7), 073102 (2017).

R. M. Willett, R. F. Marcia, and J. M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial,” Opt. Eng. 50(7), 072601 (2011).

M. J. DeWeert and B. P. Farm, “Lensless coded-aperture imaging with separable Doubly-Toeplitz masks,” Opt. Eng. 54(2), 023102 (2015).

Opt. Express (6)

Opt. Lett. (1)

Phys. Med. Biol. (1)

J. Tang, B. E. Nett, and G. H. Chen, “Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms,” Phys. Med. Biol. 54(19), 5781–5804 (2009).
[PubMed]

Proc. SPIE (6)

R. Voelkel and K. J. Weible, “Laser beam homogenizing: limitations and constraints,” Proc. SPIE 7102, 71020J (2008).

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Figures (11)

Fig. 1
Fig. 1 Computational imaging architectures for compressive optical imaging. (a) Image-plane coding (IPC) with the mask at a conjugate image plane. (b) Fourier-plane coding (FPC) with the mask at a Fourier plane in the imaging path. (c) Double random phase encoding uses separate random phase masks placed at object and Fourier planes. (d) Structured illumination architectures use image-plane coding with the mask at a conjugate image plane in the illumination path. (e) Fourier ptychography architectures use masks at a Fourier plane in the illumination path. (f) Lensless CS architectures use only a mask between the sensor and the object to modulate light emanating from the object. (g) Mask-based light field imaging architecture with the mask slightly in front of the sensor.
Fig. 2
Fig. 2 Illustration of CS forward models for a single observation. (Top row) Illustration of our IPC model as defined in Eq. (1). (Middle row) Illustration of our FPC model with coherent light as defined in Eq. (3). (Bottom row) Illustration of our FPC model with incoherent light as defined in Eq. (5).
Fig. 3
Fig. 3 Masks for FPC with incoherent light. (Top row) Random binary masks displayed at the Fourier plane have corresponding image domain equivalents with very large DC components, which reduces observational diversity across different masks. (Middle row) Low-throughput Gabor masks contain few non-zero elements, which reduces the DC component in relation to other components and increases diversity of observations. (Bottom row) High-throughput Gabor masks behave closer to random binary masks and result in lower observational diversity. Images are scaled for visualization.
Fig. 4
Fig. 4 Photo of the benchtop compressive imaging platform displaying beam paths for the IPC arm (solid line) and the FPC arm (dashed line). The high-resolution “witness” camera takes ground truth images of the object for comparison to computationally reconstructed images (dotted line).
Fig. 5
Fig. 5 Alignment techniques for IPC and FPC imaging. (a,b) For IPC alignment, a central group of 16 mask elements is set in the “on” position and the DMD is translated until light is primarily confined to the central 4 CCD pixels (b). (c,d) For FPC alignment, a central group of mask elements are set in the “off” position and the DMD is translated until the mask produces a high-pass filter effect in the acquired image (d).
Fig. 6
Fig. 6 “No mask” images of a 1951 USAF resolution target with the witness camera, FPC, and IPC arms under coherent and incoherent illumination. The arrows in panels (a-c) indicate the origin of the intensity line profiles extending vertically across the group 3 elements for each image. Scale bar in (a) represents 1 mm for all images.
Fig. 7
Fig. 7 Plots of the modulation transfer function (MTF) for each system arm; witness arm (black), IPC arm (red), FPC arm (blue). Line style indicates the illumination setting; coherent (solid), incoherent narrowband (dashed), or incoherent broadband (dot-dashed).
Fig. 8
Fig. 8 CS reconstructions vs. bicubic interpolation under incoherent illumination. Top row: Bicubic interpolation. Middle row: CS reconstructions. Bottom row: Line profiles across the group 3 elements. Outlined in red are digitally zoomed regions with arrows indicating the origin of vertical line profiles across the group 3 elements; blue corresponds to bicubic interpolation and red to CS reconstruction. Scale bar in (a) represents 1 mm for all images.
Fig. 9
Fig. 9 CS reconstructions vs. bicubic interpolation under coherent illumination. Outlined in red are digitally zoomed regions of the group 3 elements with arrows indicating the origin of vertical line profiles; blue for bicubic interpolation and red for CS reconstructions. Scale bar in (a) represents 1 mm for all images.
Fig. 10
Fig. 10 CS reconstructions with different numbers of coded mask elements mapped to each camera pixel, for the FPC and IPC arms under incoherent narrowband illumination. Mask sizes of 240 × 240, 480 × 480, and 960 × 960 mapped to a 120 × 120 pixel region on the camera correspond to mask element to pixel ratios of 4, 16, and 64, respectively.
Fig. 11
Fig. 11 Application of IPC CS to imaging biological tissue. (a) H&E stained histopathology section of the colon with digitally zoomed region (d). Scale bar in (a) represents 1 mm. (b) Image of the same tissue section from the IPC arm after bicubic interpolation, and corresponding digital zoom (e). 480 x 480 pixel IPC CS reconstruction from 120 x 120 pixel observations (d = 16) with corresponding zoomed region (f). All images were captured with incoherent broadband illumination. Scale bar in (a) represents 1 mm for images (a) – (c).

Equations (6)

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Y i = D r [ H( M i X ) ] D c
y i =D T H Λ M i x
Y i = D r [ H | F 1 { M i F( X ) } | 2 ] D c
y i =D T H | F 1 { Λ M i F( x ) } | 2
Y i = D r [ H{ | F 1 ( M i ) | 2 X } ] D c
y i =D T H T M i x

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