Abstract

Compressive holography is a relatively time-consuming image estimation in convex optimized problem. We propose an efficient block-wise algorithm to limit the searching space and reduce the calculation time while keeping the reconstruction quality. The effective anti-aliasing boundary of the sub-hologram is located to determine the block size for compressive reconstruction in the total-variation two-step iterative shrinkage/thresholding algorithm. Padded sub-holograms could be reconstructed in parallel by using multi-core processors. Compared with the traditional compressive holography, the block-wise algorithm could take approximately 1/50 of the reconstruction time and achieve an improved reconstruction quality.

© 2017 Optical Society of America

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References

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2017 (4)

J. Li, L. Zhong, Q. Zhang, Y. Zhou, J. X. Xiong, J. D. Tian, and X. X. Lu, “Optical image hiding based on dual-channel simultaneous phase-shifting interferometry and compressive sensing,” Appl. Phys. B 123(1), 4 (2017).

Z. Wang, L. Spinoulas, K. He, L. Tian, O. Cossairt, A. K. Katsaggelos, and H. Chen, “Compressive holographic video,” Opt. Express 25(1), 250–262 (2017).
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T. Leportier and M. C. Park, “Holographic reconstruction by compressive sensing,” J. Opt. 19(6), 065704 (2017).

W. Zhang, L. Cao, H. Zhang, H. Zhang, C. Han, G. Jin, and Y. Sheng, “Quantitative study on a resampling mask method for speckle reduction with amplitude superposition,” Appl. Opt. 56(13), F205–F212 (2017).
[PubMed]

2016 (2)

2014 (4)

P. T. Samsheerali, K. Khare, and J. Joseph, “Quantitative phase imaging with single shot digital holography,” Opt. Commun. 319, 85–89 (2014).

P. Memmolo, L. Miccio, F. Merola, O. Gennari, P. A. Netti, and P. Ferraro, “3D morphometry of red blood cells by digital holography,” Cytometry A 85(12), 1030–1036 (2014).
[PubMed]

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516(7529), 74–77 (2014).
[PubMed]

X. Wu, Y. Yu, W. Zhou, and A. Asundi, “4f amplified in-line compressive holography,” Opt. Express 22(17), 19860–19872 (2014).
[PubMed]

2013 (2)

Y. Rivenson, A. Stern, and J. Rosen, “Reconstruction guarantees for compressive tomographic holography,” Opt. Lett. 38(14), 2509–2511 (2013).
[PubMed]

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).

2012 (2)

Y. Liu, L. Tian, J. W. Lee, H. Y. H. Huang, M. S. Triantafyllou, and G. Barbastathis, “Scanning-free compressive holography for object localization with subpixel accuracy,” Opt. Lett. 37(16), 3357–3359 (2012).
[PubMed]

Z. Hao, Q. F. Tan, and G. F. Jin, “Holographic display system of a three-dimensional image with distortion-free magnification and zero-order elimination,” Opt. Eng. 51(7), 075801 (2012).

2011 (1)

2010 (2)

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nat. Photonics 4(12), 833–839 (2010).

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).

2009 (3)

K. Ori, B. Yaron, and S. Yaron, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).

T. W. Su, S. Seo, A. Erlinger, and A. Ozcan, “High-throughput lensfree imaging and characterization of a heterogeneous cell solution on a chip,” Biotechnol. Bioeng. 102(3), 856–868 (2009).
[PubMed]

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17(15), 13040–13049 (2009).
[PubMed]

2007 (2)

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

M. E. Gehm, R. John, D. J. Brady, R. M. Willett, and T. J. Schulz, “Single-shot compressive spectral imaging with a dual-disperser architecture,” Opt. Express 15(21), 14013–14027 (2007).
[PubMed]

2006 (2)

E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).

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

1978 (1)

A. J. Devaney, “Nonuniqueness in the inverse scattering problem,” J. Math. Phys. 19(7), 1526–1531 (1978).

Asundi, A.

Barbastathis, G.

Bioucas-Dias, J. M.

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

Boss, D.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).

Brady, D. J.

Bryanston-Cross, P.

Candes, E. J.

E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).

Cao, L.

Chapman, H. N.

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nat. Photonics 4(12), 833–839 (2010).

Chen, H.

Choi, K.

Claus, D.

Cossairt, O.

Cotte, Y.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).

Depeursinge, C.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).

Devaney, A. J.

A. J. Devaney, “Nonuniqueness in the inverse scattering problem,” J. Math. Phys. 19(7), 1526–1531 (1978).

Donoho, D. L.

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

Endo, Y.

Erlinger, A.

T. W. Su, S. Seo, A. Erlinger, and A. Ozcan, “High-throughput lensfree imaging and characterization of a heterogeneous cell solution on a chip,” Biotechnol. Bioeng. 102(3), 856–868 (2009).
[PubMed]

Ferraro, P.

P. Memmolo, L. Miccio, F. Merola, O. Gennari, P. A. Netti, and P. Ferraro, “3D morphometry of red blood cells by digital holography,” Cytometry A 85(12), 1030–1036 (2014).
[PubMed]

Figueiredo, M. A. T.

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

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(7529), 74–77 (2014).
[PubMed]

Garcia, J.

Gehm, M. E.

Gennari, O.

P. Memmolo, L. Miccio, F. Merola, O. Gennari, P. A. Netti, and P. Ferraro, “3D morphometry of red blood cells by digital holography,” Cytometry A 85(12), 1030–1036 (2014).
[PubMed]

Han, C.

Hao, Z.

Z. Hao, Q. F. Tan, and G. F. Jin, “Holographic display system of a three-dimensional image with distortion-free magnification and zero-order elimination,” Opt. Eng. 51(7), 075801 (2012).

He, K.

Horisaki, R.

Huang, H. Y. H.

Iliescu, D.

Ito, T.

Javidi, B.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).

Jin, G.

Jin, G. F.

Z. Hao, Q. F. Tan, and G. F. Jin, “Holographic display system of a three-dimensional image with distortion-free magnification and zero-order elimination,” Opt. Eng. 51(7), 075801 (2012).

John, R.

Joseph, J.

P. T. Samsheerali, K. Khare, and J. Joseph, “Quantitative phase imaging with single shot digital holography,” Opt. Commun. 319, 85–89 (2014).

Jourdain, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).

Kakue, T.

Katsaggelos, A. K.

Khare, K.

P. T. Samsheerali, K. Khare, and J. Joseph, “Quantitative phase imaging with single shot digital holography,” Opt. Commun. 319, 85–89 (2014).

Lee, J. W.

Leportier, T.

T. Leportier and M. C. Park, “Holographic reconstruction by compressive sensing,” J. Opt. 19(6), 065704 (2017).

Li, C.

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516(7529), 74–77 (2014).
[PubMed]

Li, J.

J. Li, L. Zhong, Q. Zhang, Y. Zhou, J. X. Xiong, J. D. Tian, and X. X. Lu, “Optical image hiding based on dual-channel simultaneous phase-shifting interferometry and compressive sensing,” Appl. Phys. B 123(1), 4 (2017).

Liang, J.

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516(7529), 74–77 (2014).
[PubMed]

Lim, S.

Liu, Y.

Lu, X. X.

J. Li, L. Zhong, Q. Zhang, Y. Zhou, J. X. Xiong, J. D. Tian, and X. X. Lu, “Optical image hiding based on dual-channel simultaneous phase-shifting interferometry and compressive sensing,” Appl. Phys. B 123(1), 4 (2017).

Magistretti, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).

Marks, D. L.

Marquet, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).

Memmolo, P.

P. Memmolo, L. Miccio, F. Merola, O. Gennari, P. A. Netti, and P. Ferraro, “3D morphometry of red blood cells by digital holography,” Cytometry A 85(12), 1030–1036 (2014).
[PubMed]

Merola, F.

P. Memmolo, L. Miccio, F. Merola, O. Gennari, P. A. Netti, and P. Ferraro, “3D morphometry of red blood cells by digital holography,” Cytometry A 85(12), 1030–1036 (2014).
[PubMed]

Miccio, L.

P. Memmolo, L. Miccio, F. Merola, O. Gennari, P. A. Netti, and P. Ferraro, “3D morphometry of red blood cells by digital holography,” Cytometry A 85(12), 1030–1036 (2014).
[PubMed]

Mico, V.

Netti, P. A.

P. Memmolo, L. Miccio, F. Merola, O. Gennari, P. A. Netti, and P. Ferraro, “3D morphometry of red blood cells by digital holography,” Cytometry A 85(12), 1030–1036 (2014).
[PubMed]

Nugent, K. A.

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nat. Photonics 4(12), 833–839 (2010).

Ori, K.

K. Ori, B. Yaron, and S. Yaron, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).

Ozcan, A.

T. W. Su, S. Seo, A. Erlinger, and A. Ozcan, “High-throughput lensfree imaging and characterization of a heterogeneous cell solution on a chip,” Biotechnol. Bioeng. 102(3), 856–868 (2009).
[PubMed]

Park, M. C.

T. Leportier and M. C. Park, “Holographic reconstruction by compressive sensing,” J. Opt. 19(6), 065704 (2017).

Patorski, K.

Pavillon, N.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).

Rivenson, Y.

Y. Rivenson, A. Stern, and J. Rosen, “Reconstruction guarantees for compressive tomographic holography,” Opt. Lett. 38(14), 2509–2511 (2013).
[PubMed]

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).

Romberg, J. K.

E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).

Rosen, J.

Samsheerali, P. T.

P. T. Samsheerali, K. Khare, and J. Joseph, “Quantitative phase imaging with single shot digital holography,” Opt. Commun. 319, 85–89 (2014).

Schulz, T. J.

Seo, S.

T. W. Su, S. Seo, A. Erlinger, and A. Ozcan, “High-throughput lensfree imaging and characterization of a heterogeneous cell solution on a chip,” Biotechnol. Bioeng. 102(3), 856–868 (2009).
[PubMed]

Sheng, Y.

Shimobaba, T.

Spinoulas, L.

Stern, A.

Y. Rivenson, A. Stern, and J. Rosen, “Reconstruction guarantees for compressive tomographic holography,” Opt. Lett. 38(14), 2509–2511 (2013).
[PubMed]

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).

Su, T. W.

T. W. Su, S. Seo, A. Erlinger, and A. Ozcan, “High-throughput lensfree imaging and characterization of a heterogeneous cell solution on a chip,” Biotechnol. Bioeng. 102(3), 856–868 (2009).
[PubMed]

Tan, Q. F.

Z. Hao, Q. F. Tan, and G. F. Jin, “Holographic display system of a three-dimensional image with distortion-free magnification and zero-order elimination,” Opt. Eng. 51(7), 075801 (2012).

Tao, T.

E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).

Tian, J. D.

J. Li, L. Zhong, Q. Zhang, Y. Zhou, J. X. Xiong, J. D. Tian, and X. X. Lu, “Optical image hiding based on dual-channel simultaneous phase-shifting interferometry and compressive sensing,” Appl. Phys. B 123(1), 4 (2017).

Tian, L.

Toy, F.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).

Triantafyllou, M. S.

Trusiak, M.

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(7529), 74–77 (2014).
[PubMed]

Wang, Z.

Willett, R. M.

Wu, X.

Xiong, J. X.

J. Li, L. Zhong, Q. Zhang, Y. Zhou, J. X. Xiong, J. D. Tian, and X. X. Lu, “Optical image hiding based on dual-channel simultaneous phase-shifting interferometry and compressive sensing,” Appl. Phys. B 123(1), 4 (2017).

Yaron, B.

K. Ori, B. Yaron, and S. Yaron, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).

Yaron, S.

K. Ori, B. Yaron, and S. Yaron, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).

Yu, Y.

Zhang, H.

Zhang, Q.

J. Li, L. Zhong, Q. Zhang, Y. Zhou, J. X. Xiong, J. D. Tian, and X. X. Lu, “Optical image hiding based on dual-channel simultaneous phase-shifting interferometry and compressive sensing,” Appl. Phys. B 123(1), 4 (2017).

Zhang, W.

Zhong, L.

J. Li, L. Zhong, Q. Zhang, Y. Zhou, J. X. Xiong, J. D. Tian, and X. X. Lu, “Optical image hiding based on dual-channel simultaneous phase-shifting interferometry and compressive sensing,” Appl. Phys. B 123(1), 4 (2017).

Zhou, W.

Zhou, Y.

J. Li, L. Zhong, Q. Zhang, Y. Zhou, J. X. Xiong, J. D. Tian, and X. X. Lu, “Optical image hiding based on dual-channel simultaneous phase-shifting interferometry and compressive sensing,” Appl. Phys. B 123(1), 4 (2017).

Appl. Opt. (2)

Appl. Phys. B (1)

J. Li, L. Zhong, Q. Zhang, Y. Zhou, J. X. Xiong, J. D. Tian, and X. X. Lu, “Optical image hiding based on dual-channel simultaneous phase-shifting interferometry and compressive sensing,” Appl. Phys. B 123(1), 4 (2017).

Appl. Phys. Lett. (1)

K. Ori, B. Yaron, and S. Yaron, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).

Biotechnol. Bioeng. (1)

T. W. Su, S. Seo, A. Erlinger, and A. Ozcan, “High-throughput lensfree imaging and characterization of a heterogeneous cell solution on a chip,” Biotechnol. Bioeng. 102(3), 856–868 (2009).
[PubMed]

Commun. Pure Appl. Math. (1)

E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).

Cytometry A (1)

P. Memmolo, L. Miccio, F. Merola, O. Gennari, P. A. Netti, and P. Ferraro, “3D morphometry of red blood cells by digital holography,” Cytometry A 85(12), 1030–1036 (2014).
[PubMed]

IEEE Trans. Image Process. (1)

J. M. Bioucas-Dias and M. A. T. 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 (1)

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

J. Disp. Technol. (1)

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).

J. Math. Phys. (1)

A. J. Devaney, “Nonuniqueness in the inverse scattering problem,” J. Math. Phys. 19(7), 1526–1531 (1978).

J. Opt. (1)

T. Leportier and M. C. Park, “Holographic reconstruction by compressive sensing,” J. Opt. 19(6), 065704 (2017).

Nat. Photonics (2)

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7(2), 113–117 (2013).

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nat. Photonics 4(12), 833–839 (2010).

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(7529), 74–77 (2014).
[PubMed]

Opt. Commun. (1)

P. T. Samsheerali, K. Khare, and J. Joseph, “Quantitative phase imaging with single shot digital holography,” Opt. Commun. 319, 85–89 (2014).

Opt. Eng. (1)

Z. Hao, Q. F. Tan, and G. F. Jin, “Holographic display system of a three-dimensional image with distortion-free magnification and zero-order elimination,” Opt. Eng. 51(7), 075801 (2012).

Opt. Express (5)

Opt. Lett. (3)

Other (1)

J. R. Fienup, “Coherent lensless imaging,” in Imaging Systems, Optical Society of America (2010), paper P.IMD2.

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Figures (10)

Fig. 1
Fig. 1 (a) 3-D distribution of the layered object. (b) Phase of propagation kernel at different layers. (c) Reconstructed layers with traditional back-propagation (TBP) algorithm. (d) Reconstructed layers with traditional compressive holography (TCH) algorithm.
Fig. 2
Fig. 2 (a) Time of reconstruction versus the number of reconstructed voxels of 3-D object datacube by using the TwIST algorithm. (b) Stacked chart of consuming time for 500 iterations.
Fig. 3
Fig. 3 (a) Maximum recording angle of image sensor determined by the pixel pitch. (b) Maximum diffraction angle of the hologram when reconstruction. (c) The two-points object with the size of 1 μm. (d) The hologram sampled by an image sensor with the pixel size of 1 μm. (e) The hologram sampled by an image sensor with the pixel size of 8 μm. (f) The reconstructed results from the hologram with the pixel size of 1 μm without occluding the rectangular region. (f) The reconstructed results from the hologram with the pixel size of 1 μm with occluding the rectangular region. (h) The reconstructed results from the hologram with the pixel size of 8 μm with occluding the rectangular region.
Fig. 4
Fig. 4 The diagram of the proposed block-wise compressive holographic algorithm.
Fig. 5
Fig. 5 The parallel frame of Single-Program-Multiple-Data based on block-wise compressive holography (BCH).
Fig. 6
Fig. 6 The compressive holographic reconstructions. (a) z = 16 mm, with TCH algorithm, (b) z = 56 mm, with TCH algorithm, (c) z = 16 mm, with proposed BCH algorithm, (d) z = 56 mm, with proposed BCH algorithm.
Fig. 7
Fig. 7 The optical set-up for imaging the layered object.
Fig. 8
Fig. 8 (a) The captured in-line hologram with multi-layer objects (b) The top view of experimental set-up (c) The side view of experimental set-up.
Fig. 9
Fig. 9 Reconstructed layers with (a) TBP algorithm, (b) TCH algorithm and (c) BCH algorithm.
Fig. 10
Fig. 10 The cross section of different reconstructions by (a) TBP algorithm, (b) TCH algorithm and (a) BCH algorithm. Profiles of the reconstructed pattern by (d) TBP algorithm, (e) TCH algorithm and (f) BCH algorithm.

Tables (1)

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Table 1 Image contrasts of reconstruction at different layers with TBP, TCH, and BCH algorithms.

Equations (14)

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I ( x , y ) = U A * + U * A + A A * + U U * = 2 Re ( U ) + n
U ( x , y ) = i s ( x , y ; z i ) P S F ( x , y ; z i )
z i < N Δ 2 / λ ,
U m n = i F - 1 { s ˜ m ' n ' i e i 2 π z i λ 2 ( m ' Δ f ) 2 ( n ' Δ f ) 2 }
g = 2 Re ( T F - 1 P F S ) + n = 2 Re ( H S ) + n ,
S = arg min g 2 R e ( H S ) 2 2 + τ ϒ T V ( S )
ϒ T V ( S ) = j i ( | Δ i h S | + | Δ j v S | )
f i = sin β i / λ
f i < 1 2 f m a x
sin β i < λ / 2 Δ p i x e l
β m a x = arc sin ( λ / 2 Δ p i x e l ) .
sin θ = λ / 2 Δ p i x e l
A = 2 z tan θ ,
K = I max I min I max + I min

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