Abstract

We present preliminary experimental results for implementing the “blurred trajectories” method on three parallel optics (PO) systems. The “main” system and “auxiliary” optics were simple laboratory graded lenses attached to an iris diaphragm. When applying the blurred trajectories method we first show an improvement in the matrix condition, as the matrix condition number decreased in a range of factors of 3 to 418 relative to the main system. Following that, image restoration by weak regularization was performed so that the system matrix condition dominated the restoration process. It was shown that the restoration results of the PO are better than those of the main system and the auxiliary optics separately. In addition, the quality of the restoration follows the system’s matrix condition. The improvement in the matrix condition achieved by the PO system improved the immunity to detection noise. Finally, a comparison to Wiener filtering restoration shows that it is also generally inferior to the proposed method.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. M. K. Singh, U. S. Tiwary, and Y. Kim, “An adaptively accelerated Lucy-Richardson method for image deblurring,” EURASIP J. Adv. Signal Process. V2008, 365021 (2008).
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    [CrossRef]
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  16. I. Klapp, N. Sochen, and D. Mendlovic, “Trajectories in parallel optics,” J. Opt. Soc. Am. A 28, 2014–2025 (2011).
    [CrossRef]
  17. I. Klapp and D. Mendlovic, “Trajectories by a blurred auxiliary lens,” J. Opt. Soc. Am. A 28, 1796–1804 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. A. K. Jain, Fundamentals of Digital Image Processing(Prentice-Hall, 1989), Chap. 3.6.
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  25. M. R. Banham and A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag.24–41 (1997).
    [CrossRef]
  26. I. Klapp and D. Mendlovic, “Optical design for improving the matrix condition—experiment,” in Frontiers in OpticsOSA Technical Digest (CD) (Optical Society of America, 2010), paper FTuD5.

2011

2010

M. Kieweg, H. Gross, T. Sievers, and L. Müller, “Ill-posedness of space variant image deconvolution,” Proc. SPIE 7800, 78000K (2010).
[CrossRef]

2009

2008

M. Rerabek and P. Pata, “The space variant PSF for deconvolution of wide field astronomical images,” Proc. SPIE 7015, 70152G (2008).
[CrossRef]

M. K. Singh, U. S. Tiwary, and Y. Kim, “An adaptively accelerated Lucy-Richardson method for image deblurring,” EURASIP J. Adv. Signal Process. V2008, 365021 (2008).

2005

T. A. Cheema, I. M. Qureshi, and A. Hussain, “Blind Image deconvolution using space-variant neural network approach,” Electron. Lett. 41, 308–309 (2005).
[CrossRef]

2004

S. Kavusi, H. Kakavand, and A. El Gamal, “Quantitative study of high dynamic range sigma delta-based focal plane array architectures, Proc. SPIE 5406, 341–350 (2004).
[CrossRef]

1997

M. R. Banham and A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag.24–41 (1997).
[CrossRef]

1992

N. P. Galatsanos and A. K. Katsaggelos, “Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation,” IEEE Trans. Image Process. 1, 322–336 (1992).
[CrossRef]

1976

H. C. Andrews and C. L. Paterson, “Singular value decomposition and digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 24, 26–53 (1976).
[CrossRef]

1975

1973

M. P. Ekstrom, “A spectral characterization of the ill conditioning in numerical deconvolution,” IEEE Trans. Audio Electroacoust. 21, 344–348 (1973).
[CrossRef]

Andrews, H. C.

H. C. Andrews and C. L. Paterson, “Singular value decomposition and digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 24, 26–53 (1976).
[CrossRef]

Banham, M. R.

M. R. Banham and A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag.24–41 (1997).
[CrossRef]

Cheema, T. A.

T. A. Cheema, I. M. Qureshi, and A. Hussain, “Blind Image deconvolution using space-variant neural network approach,” Electron. Lett. 41, 308–309 (2005).
[CrossRef]

Deng, L.

L. Deng and R. Lu, “A blind image restoration method based on genetic algorithm and the fuzzy control,” in International Conference on Audio, Language and Image Processing, 2008 (ICALIP 2008) (IEEE, 2008), pp. 330–334.

Dutta, S.

M. Sabbarao, Y. Kang, S. Dutta, and X. Tue, “Localized and computationally efficient approach to shift-variant image deblurring,” in Proceedings of IEEE International Conference on Image Processing, 2008 (ICIP 2008) (IEEE, 2008), pp. 657–660.

Ekstrom, M. P.

M. P. Ekstrom, “A spectral characterization of the ill conditioning in numerical deconvolution,” IEEE Trans. Audio Electroacoust. 21, 344–348 (1973).
[CrossRef]

El Gamal, A.

S. Kavusi, H. Kakavand, and A. El Gamal, “Quantitative study of high dynamic range sigma delta-based focal plane array architectures, Proc. SPIE 5406, 341–350 (2004).
[CrossRef]

Elad, M.

M. Elad, “Introduction to image processing,” Lecture Notes (Technion, 1999) (in Hebrew). http://www.cs.technion.ac.il/~elad/publications/Various/Book_ImageProcessing.pdf .

Fujii, Y.

T. Ito, H. Hoshino, Y. Fujii, and N. Ohta, “Measurements of space variant PSF and its application to restoring severely degraded images,” in Proceedings of ICROS-SICE International Joint Conference 2009 (IEEE, 2009), pp. 2301–2304.

Galatsanos, N. P.

N. P. Galatsanos and A. K. Katsaggelos, “Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation,” IEEE Trans. Image Process. 1, 322–336 (1992).
[CrossRef]

Golob, G. H.

G. H. Golob and C. F. Van-Loan, Matrix Computations (North Oxford Academic, 1983).

Gross, H.

M. Kieweg, H. Gross, T. Sievers, and L. Müller, “Ill-posedness of space variant image deconvolution,” Proc. SPIE 7800, 78000K (2010).
[CrossRef]

Hansen, P. C.

P. C. Hansen and J. G. Nagy, Deblurring Images: Matrices, Spectra, and Filtering (SIAM, 2006), Chap. 1.4.

Hoshino, H.

T. Ito, H. Hoshino, Y. Fujii, and N. Ohta, “Measurements of space variant PSF and its application to restoring severely degraded images,” in Proceedings of ICROS-SICE International Joint Conference 2009 (IEEE, 2009), pp. 2301–2304.

Hussain, A.

T. A. Cheema, I. M. Qureshi, and A. Hussain, “Blind Image deconvolution using space-variant neural network approach,” Electron. Lett. 41, 308–309 (2005).
[CrossRef]

Ito, T.

T. Ito, H. Hoshino, Y. Fujii, and N. Ohta, “Measurements of space variant PSF and its application to restoring severely degraded images,” in Proceedings of ICROS-SICE International Joint Conference 2009 (IEEE, 2009), pp. 2301–2304.

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing(Prentice-Hall, 1989), Chap. 3.6.

Jun, S.

Y. Yoo, S. Jun, J. Shin, and J. Paik, “Regularized iterative restoration of combined optical and color filter array degradation,” in Second International Conference on Future Generation Communication and Networking Symposia, 2008 (FGCNS 2008) (IEEE, 2008), pp. 197–202.

Kakavand, H.

S. Kavusi, H. Kakavand, and A. El Gamal, “Quantitative study of high dynamic range sigma delta-based focal plane array architectures, Proc. SPIE 5406, 341–350 (2004).
[CrossRef]

Kang, Y.

M. Sabbarao, Y. Kang, S. Dutta, and X. Tue, “Localized and computationally efficient approach to shift-variant image deblurring,” in Proceedings of IEEE International Conference on Image Processing, 2008 (ICIP 2008) (IEEE, 2008), pp. 657–660.

Katsaggelos, A. K.

M. R. Banham and A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag.24–41 (1997).
[CrossRef]

N. P. Galatsanos and A. K. Katsaggelos, “Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation,” IEEE Trans. Image Process. 1, 322–336 (1992).
[CrossRef]

Kavusi, S.

S. Kavusi, H. Kakavand, and A. El Gamal, “Quantitative study of high dynamic range sigma delta-based focal plane array architectures, Proc. SPIE 5406, 341–350 (2004).
[CrossRef]

Kieweg, M.

M. Kieweg, H. Gross, T. Sievers, and L. Müller, “Ill-posedness of space variant image deconvolution,” Proc. SPIE 7800, 78000K (2010).
[CrossRef]

Kim, Y.

M. K. Singh, U. S. Tiwary, and Y. Kim, “An adaptively accelerated Lucy-Richardson method for image deblurring,” EURASIP J. Adv. Signal Process. V2008, 365021 (2008).

Klapp, I.

I. Klapp and D. Mendlovic, “Trajectories by a blurred auxiliary lens,” J. Opt. Soc. Am. A 28, 1796–1804 (2011).
[CrossRef]

I. Klapp, N. Sochen, and D. Mendlovic, “Trajectories in parallel optics,” J. Opt. Soc. Am. A 28, 2014–2025 (2011).
[CrossRef]

I. Klapp and D. Mendlovic, “Improvement of matrix condition of hybrid, space variant optics by the means of parallel optics design,” Opt. Express 17, 11673–11689(2009).
[CrossRef]

I. Klapp and D. Mendlovic, “Optical design for improving matrix condition,” in Signal Recovery and SynthesisOSA Technical Digest (CD) (Optical Society of America, 2009), paper STuA7.

I. Klapp and D. Mendlovic, “Optical design for improving the matrix condition—experiment,” in Frontiers in OpticsOSA Technical Digest (CD) (Optical Society of America, 2010), paper FTuD5.

Kopeika, N. S.

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998), Chap. 18.

Liu, X.

X. Liu, “CMOS image sensors dynamic range and SNR enhancement via statistical signal processing,” Ph.D. dissertation (Stanford, 2002).

Lu, R.

L. Deng and R. Lu, “A blind image restoration method based on genetic algorithm and the fuzzy control,” in International Conference on Audio, Language and Image Processing, 2008 (ICALIP 2008) (IEEE, 2008), pp. 330–334.

Mendlovic, D.

I. Klapp, N. Sochen, and D. Mendlovic, “Trajectories in parallel optics,” J. Opt. Soc. Am. A 28, 2014–2025 (2011).
[CrossRef]

I. Klapp and D. Mendlovic, “Trajectories by a blurred auxiliary lens,” J. Opt. Soc. Am. A 28, 1796–1804 (2011).
[CrossRef]

I. Klapp and D. Mendlovic, “Improvement of matrix condition of hybrid, space variant optics by the means of parallel optics design,” Opt. Express 17, 11673–11689(2009).
[CrossRef]

I. Klapp and D. Mendlovic, “Optical design for improving matrix condition,” in Signal Recovery and SynthesisOSA Technical Digest (CD) (Optical Society of America, 2009), paper STuA7.

I. Klapp and D. Mendlovic, “Optical design for improving the matrix condition—experiment,” in Frontiers in OpticsOSA Technical Digest (CD) (Optical Society of America, 2010), paper FTuD5.

Müller, L.

M. Kieweg, H. Gross, T. Sievers, and L. Müller, “Ill-posedness of space variant image deconvolution,” Proc. SPIE 7800, 78000K (2010).
[CrossRef]

Nagy, J. G.

P. C. Hansen and J. G. Nagy, Deblurring Images: Matrices, Spectra, and Filtering (SIAM, 2006), Chap. 1.4.

Ohta, N.

T. Ito, H. Hoshino, Y. Fujii, and N. Ohta, “Measurements of space variant PSF and its application to restoring severely degraded images,” in Proceedings of ICROS-SICE International Joint Conference 2009 (IEEE, 2009), pp. 2301–2304.

Paik, J.

Y. Yoo, S. Jun, J. Shin, and J. Paik, “Regularized iterative restoration of combined optical and color filter array degradation,” in Second International Conference on Future Generation Communication and Networking Symposia, 2008 (FGCNS 2008) (IEEE, 2008), pp. 197–202.

Pata, P.

M. Rerabek and P. Pata, “The space variant PSF for deconvolution of wide field astronomical images,” Proc. SPIE 7015, 70152G (2008).
[CrossRef]

Paterson, C. L.

H. C. Andrews and C. L. Paterson, “Singular value decomposition and digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 24, 26–53 (1976).
[CrossRef]

Peyrovian, M. J.

Qureshi, I. M.

T. A. Cheema, I. M. Qureshi, and A. Hussain, “Blind Image deconvolution using space-variant neural network approach,” Electron. Lett. 41, 308–309 (2005).
[CrossRef]

Rerabek, M.

M. Rerabek and P. Pata, “The space variant PSF for deconvolution of wide field astronomical images,” Proc. SPIE 7015, 70152G (2008).
[CrossRef]

Sabbarao, M.

M. Sabbarao, Y. Kang, S. Dutta, and X. Tue, “Localized and computationally efficient approach to shift-variant image deblurring,” in Proceedings of IEEE International Conference on Image Processing, 2008 (ICIP 2008) (IEEE, 2008), pp. 657–660.

Sawchuk, A. A.

Shin, J.

Y. Yoo, S. Jun, J. Shin, and J. Paik, “Regularized iterative restoration of combined optical and color filter array degradation,” in Second International Conference on Future Generation Communication and Networking Symposia, 2008 (FGCNS 2008) (IEEE, 2008), pp. 197–202.

Sievers, T.

M. Kieweg, H. Gross, T. Sievers, and L. Müller, “Ill-posedness of space variant image deconvolution,” Proc. SPIE 7800, 78000K (2010).
[CrossRef]

Singh, M. K.

M. K. Singh, U. S. Tiwary, and Y. Kim, “An adaptively accelerated Lucy-Richardson method for image deblurring,” EURASIP J. Adv. Signal Process. V2008, 365021 (2008).

Sochen, N.

Tiwary, U. S.

M. K. Singh, U. S. Tiwary, and Y. Kim, “An adaptively accelerated Lucy-Richardson method for image deblurring,” EURASIP J. Adv. Signal Process. V2008, 365021 (2008).

Tue, X.

M. Sabbarao, Y. Kang, S. Dutta, and X. Tue, “Localized and computationally efficient approach to shift-variant image deblurring,” in Proceedings of IEEE International Conference on Image Processing, 2008 (ICIP 2008) (IEEE, 2008), pp. 657–660.

Van-Loan, C. F.

G. H. Golob and C. F. Van-Loan, Matrix Computations (North Oxford Academic, 1983).

Wilkinson, J. H.

J. H. Wilkinson, Rounding Errors in Algebraic Processes (Her Majesty’s Stationery Office, 1963), Chap. 3, p. 91.

Yoo, Y.

Y. Yoo, S. Jun, J. Shin, and J. Paik, “Regularized iterative restoration of combined optical and color filter array degradation,” in Second International Conference on Future Generation Communication and Networking Symposia, 2008 (FGCNS 2008) (IEEE, 2008), pp. 197–202.

Electron. Lett.

T. A. Cheema, I. M. Qureshi, and A. Hussain, “Blind Image deconvolution using space-variant neural network approach,” Electron. Lett. 41, 308–309 (2005).
[CrossRef]

EURASIP J. Adv. Signal Process.

M. K. Singh, U. S. Tiwary, and Y. Kim, “An adaptively accelerated Lucy-Richardson method for image deblurring,” EURASIP J. Adv. Signal Process. V2008, 365021 (2008).

IEEE Signal Process. Mag.

M. R. Banham and A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag.24–41 (1997).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process.

H. C. Andrews and C. L. Paterson, “Singular value decomposition and digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 24, 26–53 (1976).
[CrossRef]

IEEE Trans. Audio Electroacoust.

M. P. Ekstrom, “A spectral characterization of the ill conditioning in numerical deconvolution,” IEEE Trans. Audio Electroacoust. 21, 344–348 (1973).
[CrossRef]

IEEE Trans. Image Process.

N. P. Galatsanos and A. K. Katsaggelos, “Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation,” IEEE Trans. Image Process. 1, 322–336 (1992).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Express

Proc. SPIE

M. Rerabek and P. Pata, “The space variant PSF for deconvolution of wide field astronomical images,” Proc. SPIE 7015, 70152G (2008).
[CrossRef]

M. Kieweg, H. Gross, T. Sievers, and L. Müller, “Ill-posedness of space variant image deconvolution,” Proc. SPIE 7800, 78000K (2010).
[CrossRef]

S. Kavusi, H. Kakavand, and A. El Gamal, “Quantitative study of high dynamic range sigma delta-based focal plane array architectures, Proc. SPIE 5406, 341–350 (2004).
[CrossRef]

Other

X. Liu, “CMOS image sensors dynamic range and SNR enhancement via statistical signal processing,” Ph.D. dissertation (Stanford, 2002).

T. Ito, H. Hoshino, Y. Fujii, and N. Ohta, “Measurements of space variant PSF and its application to restoring severely degraded images,” in Proceedings of ICROS-SICE International Joint Conference 2009 (IEEE, 2009), pp. 2301–2304.

A. K. Jain, Fundamentals of Digital Image Processing(Prentice-Hall, 1989), Chap. 3.6.

M. Elad, “Introduction to image processing,” Lecture Notes (Technion, 1999) (in Hebrew). http://www.cs.technion.ac.il/~elad/publications/Various/Book_ImageProcessing.pdf .

I. Klapp and D. Mendlovic, “Optical design for improving the matrix condition—experiment,” in Frontiers in OpticsOSA Technical Digest (CD) (Optical Society of America, 2010), paper FTuD5.

I. Klapp and D. Mendlovic, “Optical design for improving matrix condition,” in Signal Recovery and SynthesisOSA Technical Digest (CD) (Optical Society of America, 2009), paper STuA7.

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998), Chap. 18.

G. H. Golob and C. F. Van-Loan, Matrix Computations (North Oxford Academic, 1983).

J. H. Wilkinson, Rounding Errors in Algebraic Processes (Her Majesty’s Stationery Office, 1963), Chap. 3, p. 91.

M. Sabbarao, Y. Kang, S. Dutta, and X. Tue, “Localized and computationally efficient approach to shift-variant image deblurring,” in Proceedings of IEEE International Conference on Image Processing, 2008 (ICIP 2008) (IEEE, 2008), pp. 657–660.

Y. Yoo, S. Jun, J. Shin, and J. Paik, “Regularized iterative restoration of combined optical and color filter array degradation,” in Second International Conference on Future Generation Communication and Networking Symposia, 2008 (FGCNS 2008) (IEEE, 2008), pp. 197–202.

L. Deng and R. Lu, “A blind image restoration method based on genetic algorithm and the fuzzy control,” in International Conference on Audio, Language and Image Processing, 2008 (ICALIP 2008) (IEEE, 2008), pp. 330–334.

P. C. Hansen and J. G. Nagy, Deblurring Images: Matrices, Spectra, and Filtering (SIAM, 2006), Chap. 1.4.

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Figures (21)

Fig. 1.
Fig. 1.

Block diagram for a hybrid system.

Fig. 2.
Fig. 2.

Parallel optics block schema.

Fig. 3.
Fig. 3.

Trajectories methods.

Fig. 4.
Fig. 4.

Relation between the image shift and the trajectories matrix in a 6×6 matrix.

Fig. 5.
Fig. 5.

Postprocessing step. In the 3×2 field, there are 15 available translations and an auxiliary system image.

Fig. 6.
Fig. 6.

Layout of the experimental optical setup.

Fig. 7.
Fig. 7.

Object and illumination branch: (a) typical object (example B), (b) illumination source housing with LED and collimation lens, (c) diffuser, and (d) pinhole.

Fig. 8.
Fig. 8.

Imaging branch: (e) lens housing and simple lens, (f) iris diaphragm, (g) window, and (h) imager.

Fig. 9.
Fig. 9.

Illumination and pinhole: (e) illumination source housing with led and collimation lens, and (i) pinhole.

Fig. 10.
Fig. 10.

Experimental objects: A is a point object, B is a smiley, and C is a five points object.

Fig. 11.
Fig. 11.

Typical PSF measurements (example B): (a) main system PSF and (b) auxiliary optics PSF. The x and y axis are in [pixels] unit.

Fig. 12.
Fig. 12.

Main system singular values and target auxiliary system matrix (example B): (a) main system singular values, and (b) target auxiliary system matrix composed of some of the singular matrices of the main system, which are associated with the Θ range of singular values.

Fig. 13.
Fig. 13.

Point object (example A): main and auxiliary optics channel signal.

Fig. 14.
Fig. 14.

Smiley (example B): main and auxiliary optics channel signal.

Fig. 15.
Fig. 15.

Five-points (example C): main and auxiliary optics channel signal.

Fig. 16.
Fig. 16.

Point object (example A): imaging and restoration.

Fig. 17.
Fig. 17.

Point object (example A): imaging and restoration 3D restoration in low regularization λ=1e8.

Fig. 18.
Fig. 18.

Smiley (example B): imaging and restoration.

Fig. 19.
Fig. 19.

Five-points (example C): imaging and restoration.

Fig. 20.
Fig. 20.

Bottom left point of the five-points object (example C): restoration as a function of the regularization coefficient. Rows 1, 2, and 3 are the image restoration of the bottom left point object. In each column, we give the restoration results for a different regularization coefficient, which decreases from left to right. In the bottom left, we give the object blurred image before restoration as a reference.

Fig. 21.
Fig. 21.

Comparison between restoration by regularization of the main and PO systems to the restoration by WF of the main system in all three study cases.

Tables (4)

Tables Icon

Table 1. Experimental Conditions

Tables Icon

Table 2. Improvement in the Matrix Condition

Tables Icon

Table 3. Measured Data Statistics

Tables Icon

Table 4. SNR Values in Decibels

Equations (27)

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

IL×1image=HL×L·IL×1obj+IL×1noise,
I^L×1res=(IL×1obj+ΔIL×1obj)=HL×L1·(IL×1image+IL×1noise),
ΔIL×1obj2IL×1obj2k2H·IL×1noise2IL×1image2.
k2H=σ1/σn.
H=USVt=i=1Lσi·Mi.
Mi=ui·vit,
H1=U(S1)Vt=U(S+ΔS)Vt=H+O.
O=U(ΔS)Vt=iΘΔS(i,i)·Mi.
IL×1image=H1L×L·IL×1object=HL×L·IL×1obj+O·IL×1obj+IL×1noise.
IL×1image=HL×L·IL×1obj+O˜·IL×1obj+IL×1noise.
Ol(i,j;Δm,Δn)=Tl{Δm,Δn,I}.
O^l(i,j;Δm,Δn)=Ol(i,j;Δm,Δn)·Haux(i,j).
O˜=l=1QWl·O^l=l=1QLl,
Wl=1Nli=1Lj=1LOt°O^l(i,j;Δm,Δn),
Nl=i=1Lj=1LOl(i,j;Δm,Δn)·Haux(i,j).
IL×1auxiliary_sys=O˜·IL×1obj,
Iauxiliary_sys=i=1QWl·Ol·Iaux=i=1QWl·O^l·IL×1obj.
IL×1trajl=O^l·IL×1obj.
IL×1auxiliary_sys=Wl·IL×1trajl.
IL×1image=HL×L·IL×1obj+i=1QWl·O^l·IL×1obj+IL×1noise.
Iresn=(H1H1)·Iimage,
SNR=σsignal2σnoise2,
SNR[dB]=10log(σsignal2/σnoise2).
I^L×1res=(Ht·H+λ·I)1·Ht·IL×1image,
I^L×1res-MAP=argminIobj{Probnoise(Iimage/Iobj)·Probobj(Iobj)},
λ=1/SNR.
I^resw(x,y)=FT1{OTF*(fx,fy)|OTF*(fx,fy)|2+λFT{Iimage(x,y)}},

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