Abstract

A block compressed sensing ghost imaging reconstruction algorithm based on a block sparse Bayesian is proposed to deal with the problem that the large-size target image limited by the memory space cannot be reconstructed with the existing compressed sensing ghost imaging scheme. The large-size target image is divided into several small-sized image blocks of the same size, which is separately subjected to a compressed sensing reconstruction solution. The reconstructed solutions of each image block can be combined into one whole image, resulting in the target image. The simulation results show that the block compressed sensing ghost imaging reconstruction algorithm with a block sparse Bayesian can perform well even when storage requirements are difficult to realize via reconstructing large-scale target images.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]

2019 (3)

Z. Tan, H. Yu, R. Lu, R. Zhu, S. Yang, and S. Han, “Non-locally coded fourier-transform ghost imaging,” Opt. Express 27(3), 2937–2948 (2019).
[Crossref]

J. Li, W. Gao, J. Qian, Q. Guo, J. Xi, and C. Ritz, “Robust entangled-photon ghost imaging with compressive sensing,” Sensors 19(1), 192 (2019).
[Crossref]

R. Zhu, G. Li, and Y. Guo, “Compressed-sensing-based gradient reconstruction for ghost imaging,” Int. J. Theor. Phys. 58(4), 1215–1226 (2019).
[Crossref]

2018 (1)

X. Yao, X. Liu, L. You, Z. Wang, X. Feng, F. Liu, K. Cui, Y. Huang, and W. Zhang, “Quantum secure ghost imaging,” Phys. Rev. A 98(6), 063816 (2018).
[Crossref]

2016 (2)

Y. Si, L.-J. Kong, Y.-N. Li, C.-H. Tu, and H.-T. Wang, “Ghost imaging with high visibility using classical light source,” Chin. Phys. Lett. 33(3), 034203 (2016).
[Crossref]

X.-B. Song, S.-H. Zhang, D. Cao, J. Xiong, H. Wang, and K. Wang, “Inherent relation between visibility and resolution in thermal light ghost imaging,” Opt. Commun. 365, 38–42 (2016).
[Crossref]

2015 (1)

G. H. Low, T. J. Yoder, and I. L. Chuang, “Quantum imaging by coherent enhancement,” Phys. Rev. Lett. 114(10), 100801 (2015).
[Crossref]

2014 (1)

S. D. Babacan, S. Nakajima, and M. N. Do, “Bayesian group-sparse modeling and variational inference,” IEEE Trans. Acoust., Speech, Signal Process. 62(11), 2906–2921 (2014).
[Crossref]

2013 (3)

Z. Zhang and B. D. Rao, “Extension of sbl algorithms for the recovery of block sparse signals with intra-block correlation,” IEEE Trans. Acoust., Speech, Signal Process. 61(8), 2009–2015 (2013).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87(2), 023820 (2013).
[Crossref]

2012 (3)

2011 (1)

Y. Bai, K. Yang, W. Yang, and X. Yu, “Noise analysis in correlated imaging, quantum and classical,” Optik (Munich, Ger.) 122(20), 1791–1794 (2011).
[Crossref]

2010 (5)

P. Clemente, V. Duran, V. Torrescompany, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. 35(14), 2391–2393 (2010).
[Crossref]

M. N. O’Sullivan, K. W. C. Chan, and R. W. Boyd, “Comparison of the signal-to-noise characteristics of quantum versus thermal ghost imaging,” Phys. Rev. A 82(5), 053803 (2010).
[Crossref]

W. Gong and S. Han, “A method to improve the visibility of ghost images obtained by thermal light,” Phys. Lett. A 374(8), 1005–1008 (2010).
[Crossref]

F. Ferri, D. Magatti, L. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref]

Y. C. Eldar, P. Kuppinger, and H. Bolcskei, “Block-sparse signals: Uncertainty relations and efficient recovery,” IEEE Trans. Acoust., Speech, Signal Process. 58(6), 3042–3054 (2010).
[Crossref]

2009 (2)

Y. C. Eldar and M. Mishali, “Robust recovery of signals from a structured union of subspaces,” IEEE Trans. Inf. Theory 55(11), 5302–5316 (2009).
[Crossref]

X.-H. Chen, Q. Liu, K.-H. Luo, and L.-A. Wu, “Lensless ghost imaging with true thermal light,” Opt. Lett. 34(5), 695–697 (2009).
[Crossref]

2008 (2)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
[Crossref]

L. Meier, S. Van De Geer, and P. Bühlmann, “The group lasso for logistic regression,” J. Royal Stat. Soc. Ser. B (Statistical Methodol.) 70(1), 53–71 (2008).
[Crossref]

2004 (2)

D. P. Wipf and B. D. Rao, “Sparse bayesian learning for basis selection,” IEEE Trans. Acoust., Speech, Signal Process. 52(8), 2153–2164 (2004).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70(1), 013802 (2004).
[Crossref]

1995 (1)

T. Pittman, Y. Shih, D. Strekalov, and A. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

1988 (1)

D. Klyshko, “Combine epr and two-slit experiments: Interference of advanced waves,” Phys. Lett. A 132(6-7), 299–304 (1988).
[Crossref]

Ahmadi-Kandjani, S.

M. Tanha, R. Kheradmand, and S. Ahmadi-Kandjani, “Gray-scale and color optical encryption based on computational ghost imaging,” Appl. Phys. Lett. 101(10), 101108 (2012).
[Crossref]

Astola, J.

Babacan, S. D.

S. D. Babacan, S. Nakajima, and M. N. Do, “Bayesian group-sparse modeling and variational inference,” IEEE Trans. Acoust., Speech, Signal Process. 62(11), 2906–2921 (2014).
[Crossref]

Bache, M.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70(1), 013802 (2004).
[Crossref]

L. A. Lugiato, A. Gatti, E. Brambilla, and M. Bache, “Correlated imaging: classical noise vs. quantum entanglement,” in Fluctuations and Noise in Photonics and Quantum Optics II, vol. 5468 (International Society for Optics and Photonics, 2004), pp. 262–269.

Bai, Y.

Y. Bai, K. Yang, W. Yang, and X. Yu, “Noise analysis in correlated imaging, quantum and classical,” Optik (Munich, Ger.) 122(20), 1791–1794 (2011).
[Crossref]

Bolcskei, H.

Y. C. Eldar, P. Kuppinger, and H. Bolcskei, “Block-sparse signals: Uncertainty relations and efficient recovery,” IEEE Trans. Acoust., Speech, Signal Process. 58(6), 3042–3054 (2010).
[Crossref]

Bowman, A.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Bowman, R.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Boyd, R. W.

M. N. O’Sullivan, K. W. C. Chan, and R. W. Boyd, “Comparison of the signal-to-noise characteristics of quantum versus thermal ghost imaging,” Phys. Rev. A 82(5), 053803 (2010).
[Crossref]

Brambilla, E.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70(1), 013802 (2004).
[Crossref]

L. A. Lugiato, A. Gatti, E. Brambilla, and M. Bache, “Correlated imaging: classical noise vs. quantum entanglement,” in Fluctuations and Noise in Photonics and Quantum Optics II, vol. 5468 (International Society for Optics and Photonics, 2004), pp. 262–269.

Bühlmann, P.

L. Meier, S. Van De Geer, and P. Bühlmann, “The group lasso for logistic regression,” J. Royal Stat. Soc. Ser. B (Statistical Methodol.) 70(1), 53–71 (2008).
[Crossref]

Cao, D.

X.-B. Song, S.-H. Zhang, D. Cao, J. Xiong, H. Wang, and K. Wang, “Inherent relation between visibility and resolution in thermal light ghost imaging,” Opt. Commun. 365, 38–42 (2016).
[Crossref]

Chan, K. W. C.

M. N. O’Sullivan, K. W. C. Chan, and R. W. Boyd, “Comparison of the signal-to-noise characteristics of quantum versus thermal ghost imaging,” Phys. Rev. A 82(5), 053803 (2010).
[Crossref]

Chen, X.-H.

Chuang, I. L.

G. H. Low, T. J. Yoder, and I. L. Chuang, “Quantum imaging by coherent enhancement,” Phys. Rev. Lett. 114(10), 100801 (2015).
[Crossref]

Clemente, P.

Cui, K.

X. Yao, X. Liu, L. You, Z. Wang, X. Feng, F. Liu, K. Cui, Y. Huang, and W. Zhang, “Quantum secure ghost imaging,” Phys. Rev. A 98(6), 063816 (2018).
[Crossref]

Do, M. N.

S. D. Babacan, S. Nakajima, and M. N. Do, “Bayesian group-sparse modeling and variational inference,” IEEE Trans. Acoust., Speech, Signal Process. 62(11), 2906–2921 (2014).
[Crossref]

Duran, V.

Edgar, M. P.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Eldar, Y. C.

Y. C. Eldar, P. Kuppinger, and H. Bolcskei, “Block-sparse signals: Uncertainty relations and efficient recovery,” IEEE Trans. Acoust., Speech, Signal Process. 58(6), 3042–3054 (2010).
[Crossref]

Y. C. Eldar and M. Mishali, “Robust recovery of signals from a structured union of subspaces,” IEEE Trans. Inf. Theory 55(11), 5302–5316 (2009).
[Crossref]

Erkmen, B. I.

Feng, X.

X. Yao, X. Liu, L. You, Z. Wang, X. Feng, F. Liu, K. Cui, Y. Huang, and W. Zhang, “Quantum secure ghost imaging,” Phys. Rev. A 98(6), 063816 (2018).
[Crossref]

Ferri, F.

F. Ferri, D. Magatti, L. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref]

Gao, W.

J. Li, W. Gao, J. Qian, Q. Guo, J. Xi, and C. Ritz, “Robust entangled-photon ghost imaging with compressive sensing,” Sensors 19(1), 192 (2019).
[Crossref]

Gatti, A.

F. Ferri, D. Magatti, L. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70(1), 013802 (2004).
[Crossref]

L. A. Lugiato, A. Gatti, E. Brambilla, and M. Bache, “Correlated imaging: classical noise vs. quantum entanglement,” in Fluctuations and Noise in Photonics and Quantum Optics II, vol. 5468 (International Society for Optics and Photonics, 2004), pp. 262–269.

Gong, W.

W. Gong and S. Han, “A method to improve the visibility of ghost images obtained by thermal light,” Phys. Lett. A 374(8), 1005–1008 (2010).
[Crossref]

Guo, Q.

J. Li, W. Gao, J. Qian, Q. Guo, J. Xi, and C. Ritz, “Robust entangled-photon ghost imaging with compressive sensing,” Sensors 19(1), 192 (2019).
[Crossref]

Guo, Y.

R. Zhu, G. Li, and Y. Guo, “Compressed-sensing-based gradient reconstruction for ghost imaging,” Int. J. Theor. Phys. 58(4), 1215–1226 (2019).
[Crossref]

Han, S.

Z. Tan, H. Yu, R. Lu, R. Zhu, S. Yang, and S. Han, “Non-locally coded fourier-transform ghost imaging,” Opt. Express 27(3), 2937–2948 (2019).
[Crossref]

W. Gong and S. Han, “A method to improve the visibility of ghost images obtained by thermal light,” Phys. Lett. A 374(8), 1005–1008 (2010).
[Crossref]

Hardy, N. D.

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87(2), 023820 (2013).
[Crossref]

Huang, Y.

X. Yao, X. Liu, L. You, Z. Wang, X. Feng, F. Liu, K. Cui, Y. Huang, and W. Zhang, “Quantum secure ghost imaging,” Phys. Rev. A 98(6), 063816 (2018).
[Crossref]

Katkovnik, V.

Kheradmand, R.

M. Tanha, R. Kheradmand, and S. Ahmadi-Kandjani, “Gray-scale and color optical encryption based on computational ghost imaging,” Appl. Phys. Lett. 101(10), 101108 (2012).
[Crossref]

Klyshko, D.

D. Klyshko, “Combine epr and two-slit experiments: Interference of advanced waves,” Phys. Lett. A 132(6-7), 299–304 (1988).
[Crossref]

Kong, L.-J.

Y. Si, L.-J. Kong, Y.-N. Li, C.-H. Tu, and H.-T. Wang, “Ghost imaging with high visibility using classical light source,” Chin. Phys. Lett. 33(3), 034203 (2016).
[Crossref]

Kuppinger, P.

Y. C. Eldar, P. Kuppinger, and H. Bolcskei, “Block-sparse signals: Uncertainty relations and efficient recovery,” IEEE Trans. Acoust., Speech, Signal Process. 58(6), 3042–3054 (2010).
[Crossref]

Lancis, J.

Li, G.

R. Zhu, G. Li, and Y. Guo, “Compressed-sensing-based gradient reconstruction for ghost imaging,” Int. J. Theor. Phys. 58(4), 1215–1226 (2019).
[Crossref]

Li, J.

J. Li, W. Gao, J. Qian, Q. Guo, J. Xi, and C. Ritz, “Robust entangled-photon ghost imaging with compressive sensing,” Sensors 19(1), 192 (2019).
[Crossref]

Li, Y.-N.

Y. Si, L.-J. Kong, Y.-N. Li, C.-H. Tu, and H.-T. Wang, “Ghost imaging with high visibility using classical light source,” Chin. Phys. Lett. 33(3), 034203 (2016).
[Crossref]

Liu, F.

X. Yao, X. Liu, L. You, Z. Wang, X. Feng, F. Liu, K. Cui, Y. Huang, and W. Zhang, “Quantum secure ghost imaging,” Phys. Rev. A 98(6), 063816 (2018).
[Crossref]

Liu, Q.

Liu, X.

X. Yao, X. Liu, L. You, Z. Wang, X. Feng, F. Liu, K. Cui, Y. Huang, and W. Zhang, “Quantum secure ghost imaging,” Phys. Rev. A 98(6), 063816 (2018).
[Crossref]

Low, G. H.

G. H. Low, T. J. Yoder, and I. L. Chuang, “Quantum imaging by coherent enhancement,” Phys. Rev. Lett. 114(10), 100801 (2015).
[Crossref]

Lu, R.

Lugiato, L.

F. Ferri, D. Magatti, L. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref]

Lugiato, L. A.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70(1), 013802 (2004).
[Crossref]

L. A. Lugiato, A. Gatti, E. Brambilla, and M. Bache, “Correlated imaging: classical noise vs. quantum entanglement,” in Fluctuations and Noise in Photonics and Quantum Optics II, vol. 5468 (International Society for Optics and Photonics, 2004), pp. 262–269.

Luo, K.-H.

Magatti, D.

F. Ferri, D. Magatti, L. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref]

Meier, L.

L. Meier, S. Van De Geer, and P. Bühlmann, “The group lasso for logistic regression,” J. Royal Stat. Soc. Ser. B (Statistical Methodol.) 70(1), 53–71 (2008).
[Crossref]

Mishali, M.

Y. C. Eldar and M. Mishali, “Robust recovery of signals from a structured union of subspaces,” IEEE Trans. Inf. Theory 55(11), 5302–5316 (2009).
[Crossref]

Nakajima, S.

S. D. Babacan, S. Nakajima, and M. N. Do, “Bayesian group-sparse modeling and variational inference,” IEEE Trans. Acoust., Speech, Signal Process. 62(11), 2906–2921 (2014).
[Crossref]

O’Sullivan, M. N.

M. N. O’Sullivan, K. W. C. Chan, and R. W. Boyd, “Comparison of the signal-to-noise characteristics of quantum versus thermal ghost imaging,” Phys. Rev. A 82(5), 053803 (2010).
[Crossref]

Padgett, M.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Pittman, T.

T. Pittman, Y. Shih, D. Strekalov, and A. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Qian, J.

J. Li, W. Gao, J. Qian, Q. Guo, J. Xi, and C. Ritz, “Robust entangled-photon ghost imaging with compressive sensing,” Sensors 19(1), 192 (2019).
[Crossref]

Rao, B. D.

Z. Zhang and B. D. Rao, “Extension of sbl algorithms for the recovery of block sparse signals with intra-block correlation,” IEEE Trans. Acoust., Speech, Signal Process. 61(8), 2009–2015 (2013).
[Crossref]

D. P. Wipf and B. D. Rao, “Sparse bayesian learning for basis selection,” IEEE Trans. Acoust., Speech, Signal Process. 52(8), 2153–2164 (2004).
[Crossref]

Ritz, C.

J. Li, W. Gao, J. Qian, Q. Guo, J. Xi, and C. Ritz, “Robust entangled-photon ghost imaging with compressive sensing,” Sensors 19(1), 192 (2019).
[Crossref]

Sergienko, A.

T. Pittman, Y. Shih, D. Strekalov, and A. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Shapiro, J. H.

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87(2), 023820 (2013).
[Crossref]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
[Crossref]

Shih, Y.

T. Pittman, Y. Shih, D. Strekalov, and A. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Si, Y.

Y. Si, L.-J. Kong, Y.-N. Li, C.-H. Tu, and H.-T. Wang, “Ghost imaging with high visibility using classical light source,” Chin. Phys. Lett. 33(3), 034203 (2016).
[Crossref]

Song, X.-B.

X.-B. Song, S.-H. Zhang, D. Cao, J. Xiong, H. Wang, and K. Wang, “Inherent relation between visibility and resolution in thermal light ghost imaging,” Opt. Commun. 365, 38–42 (2016).
[Crossref]

Strekalov, D.

T. Pittman, Y. Shih, D. Strekalov, and A. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Sun, B.

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Opt. Commun. (1)

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Opt. Express (1)

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Optik (Munich, Ger.) (1)

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B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
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J. Li, W. Gao, J. Qian, Q. Guo, J. Xi, and C. Ritz, “Robust entangled-photon ghost imaging with compressive sensing,” Sensors 19(1), 192 (2019).
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Figures (5)

Fig. 1.
Fig. 1. Block-compressed-sensing-based image Reconstruction flow chart.
Fig. 2.
Fig. 2. The flow chart based on sparse Bayesian-compressed sensing ghost imaging schemes.
Fig. 3.
Fig. 3. Two-arm ghost imaging device for a pseudothermal light source. (SLM: Spatial light modulator; BS: Beam splitter; BD: Bucket detector.).
Fig. 4.
Fig. 4. The reconstruction results of Bayesian-compressed reconstruction algorithms for M-many measurements.
Fig. 5.
Fig. 5. Computational time of two BSBL algorithms reconstructions for different sampling rates. (a) Computation time of two BSBL algorithm reconstructions of Cameraman objects. (b) Computation time of two BSBL algorithm reconstructions of house objects.

Tables (1)

Tables Icon

Table 1. PSNR s of images reconstructed by Bayesian-compressed algorithms at different sampling rates.

Equations (18)

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

b = A x ,
b i = A 8 x i ,
A = [ A 8 A 8 A 8 ] .
b = A x + n ,
m i n x 0 , s . t . b A x 2 2 t ,
x ^ = a r g     m i n     α b A x 2 2 + λ x 1 ,
x = ( x 1 , x 2 , , x z 1 ) X 1 T , , ( x z w 1 + 1 , x z w 1 + 2 , , x z w ) X w T .
P ( x i ; s i , Y i ) N ( 0 , s i , Y i ) ,
P ( x i ; { s i , Y i } i = 1 w ) N ( 0 , D 0 ) ,
P ( n ; μ ) N ( 0 , μ I ) ,
P ( x | b ; μ , { s i , Y i } i = 1 w ) N ( k x , D x ) ,
x ^ D 0 A T ( μ I + A D 0 A T ) 1 b .
L ( μ , { s i , Y i } i = 1 w ) = def l g | μ I + A D 0 A T | + b T ( μ I + A D 0 A T ) 1 b .
μ ( b A k x 2 2 + T r ( D x A T A ) ) / M ,
Y i [ D x i + k x i ( k x i ) T ] / s i ,
s i ( k x i ) T Y i 1 k x i T r ( A i ) T ( D b i ) 1 A i Y i ,
s i T r [ Y i 1 ( D x i + k x i ( k x i ) T ) ] / z i .
PSNR = 20 log 10 max k | u 0 [ k ] | 2 / RMSE ,

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