Abstract

For optical coherence tomography (OCT), ultrasound, synthetic-aperture radar, and other coherent ranging methods, speckle can cause spurious detail that detracts from the utility of the image. It is a problem inherent to imaging densely scattering objects with limited bandwidth. Using a method of regularization by minimizing Csiszar’s I-divergence measure, we derive a method of speckle minimization that produces an image that both is consistent with the known data and extrapolates additional detail based on constraints on the magnitude of the image. This method is demonstrated on a test image and on an OCT image of a Xenopus laevis tadpole.

© 2005 Optical Society of America

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    [Crossref]
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    [Crossref]
  5. D. L. Snyder, J. A. O’Sullivan, M. I. Miller, “The use of maximum likelihood estimation in forming images of diffuse radar targets from delay-doppler data,” IEEE Trans. Inf. Theory 35, 536–548 (1989).
    [Crossref]
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  7. P. Moulin, J. A. O’Sullivan, D. L. Synder, “A method of sieves for multiresolution spectrum estimation and radar Imaging,” IEEE Trans. Inf. Theory 38, 801–813 (1992).
    [Crossref]
  8. M. Cetin, W. C. Karl, “Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization,” IEEE Trans. Image Process. 10, 623–631 (2001).
    [Crossref]
  9. M. D. Kulkarni, C. W. Thomas, J. A. Izatt, “Image enhancement in optical coherence tomography using deconvolution,” Electron. Lett. 33, 1365–1367 (1997).
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  10. S. R. DeGraaf, “SAR imaging via modern 2-D spectral estimation methods,” IEEE Trans. Image Process. 7, 729–761 (1998).
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2004 (1)

2003 (1)

2002 (1)

H. Lanteri, M. Roche, C. Aime, “Penalized maximum likelihood image restoration with positivity constraints: multiplicative algorithms,” Inverse Probl. 18, 1397–1419 (2002).
[Crossref]

2001 (1)

M. Cetin, W. C. Karl, “Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization,” IEEE Trans. Image Process. 10, 623–631 (2001).
[Crossref]

2000 (2)

J. Rogowska, M. E. Brezinski, “Evaluation of the adaptive speckle suppresion filter for coronary optical coherence tomography imaging,” IEEE Trans. Med. Imaging 14, 1261–1266 (2000).
[Crossref]

M. Bashkansky, J. Reintjes, “Statistics and reduction of speckle in optical coherence tomography,” Opt. Lett. 25, 545–547 (2000).
[Crossref]

1999 (3)

K. M. Yung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
[Crossref] [PubMed]

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[Crossref] [PubMed]

X. Hao, S. Gao, X. Gao, “A novel multiscale nonlinear thresholding method for ultrasonic speckle supressing,” IEEE Trans. Med. Imaging 18, 787–794 (1999).
[Crossref] [PubMed]

1998 (3)

J. M. Schmitt, “Restoration of optical coherence images of living tissue using the CLEAN algorithm,” J. Biomed. Opt. 3, 66–75 (1998).
[Crossref] [PubMed]

S. R. DeGraaf, “SAR imaging via modern 2-D spectral estimation methods,” IEEE Trans. Image Process. 7, 729–761 (1998).
[Crossref]

B. R. Frieden, D. J. Graser, “Closed-form maximum entropy image restoration,” Opt. Commun. 146, 79–84 (1998).
[Crossref]

1997 (2)

M. D. Kulkarni, C. W. Thomas, J. A. Izatt, “Image enhancement in optical coherence tomography using deconvolution,” Electron. Lett. 33, 1365–1367 (1997).
[Crossref]

J. M. Schmitt, “Array detection for speckle reduction in optical coherence microscopy,” Phys. Med. Biol. 42, 1427–1439 (1997).
[Crossref] [PubMed]

1995 (1)

D. L. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory 41, 613–627 (1995).
[Crossref]

1992 (5)

P. C. Hansen, “Numerical tools for analysis and solution of Fredholm integral equations of the first kind,” Inverse Probl. 8, 849–872 (1992).
[Crossref]

M. L. Reis, N. C. Roberty, “Maximum entropy algorithms for image reconstruction from projections,” Inverse Probl. 8, 623–644 (1992).
[Crossref]

B. Borden, “Maximum entropy regularization in inverse synthetic aperture radar imagery,” IEEE Trans. Signal Process. 40, 969–973 (1992).
[Crossref]

P. Moulin, J. A. O’Sullivan, D. L. Synder, “A method of sieves for multiresolution spectrum estimation and radar Imaging,” IEEE Trans. Inf. Theory 38, 801–813 (1992).
[Crossref]

C. L. Byrne, “Iterative image reconstruction algorithms based on cross-entropy minimization,” IEEE Trans. Image Process. 2, 96–103 (1992).
[Crossref]

1991 (3)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

I. Csiszar, “Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems,” Ann. Stat. 19, 2032–2066 (1991).
[Crossref]

X. Zhuang, R. M. Haralick, Y. Zhao, “Maximum entropy image restoration,” IEEE Trans. Signal Process. 39, 1478–1480 (1991).
[Crossref]

1989 (1)

D. L. Snyder, J. A. O’Sullivan, M. I. Miller, “The use of maximum likelihood estimation in forming images of diffuse radar targets from delay-doppler data,” IEEE Trans. Inf. Theory 35, 536–548 (1989).
[Crossref]

1986 (1)

Adler, D. C.

Aime, C.

H. Lanteri, M. Roche, C. Aime, “Penalized maximum likelihood image restoration with positivity constraints: multiplicative algorithms,” Inverse Probl. 18, 1397–1419 (2002).
[Crossref]

Bashkansky, M.

Bertero, M.

M. Bertero, P. Bocacci, Introduction to Inverse Problems in Imaging (IOP, 1998).
[Crossref]

Bocacci, P.

M. Bertero, P. Bocacci, Introduction to Inverse Problems in Imaging (IOP, 1998).
[Crossref]

Boppart, S. A.

Borden, B.

B. Borden, “Maximum entropy regularization in inverse synthetic aperture radar imagery,” IEEE Trans. Signal Process. 40, 969–973 (1992).
[Crossref]

Brezinski, M. E.

J. Rogowska, M. E. Brezinski, “Evaluation of the adaptive speckle suppresion filter for coronary optical coherence tomography imaging,” IEEE Trans. Med. Imaging 14, 1261–1266 (2000).
[Crossref]

Byrne, C. L.

C. L. Byrne, “Iterative image reconstruction algorithms based on cross-entropy minimization,” IEEE Trans. Image Process. 2, 96–103 (1992).
[Crossref]

Cetin, M.

M. Cetin, W. C. Karl, “Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization,” IEEE Trans. Image Process. 10, 623–631 (2001).
[Crossref]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Cover, T. M.

T. M. Cover, J. A. Thomas, Elements of Information Theory (Wiley, 1991).
[Crossref]

Csiszar, I.

I. Csiszar, “Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems,” Ann. Stat. 19, 2032–2066 (1991).
[Crossref]

DeGraaf, S. R.

S. R. DeGraaf, “SAR imaging via modern 2-D spectral estimation methods,” IEEE Trans. Image Process. 7, 729–761 (1998).
[Crossref]

Donoho, D. L.

D. L. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory 41, 613–627 (1995).
[Crossref]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Frieden, B. R.

B. R. Frieden, D. J. Graser, “Closed-form maximum entropy image restoration,” Opt. Commun. 146, 79–84 (1998).
[Crossref]

Fujimoto, J. G.

D. C. Adler, T. H. Ko, J. G. Fujimoto, “Speckle reduction in optical coherence tomography by use of a spatially adaptive wavelet filter,” Opt. Lett. 29, 2878–2880 (2004).
[Crossref]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Gao, S.

X. Hao, S. Gao, X. Gao, “A novel multiscale nonlinear thresholding method for ultrasonic speckle supressing,” IEEE Trans. Med. Imaging 18, 787–794 (1999).
[Crossref] [PubMed]

Gao, X.

X. Hao, S. Gao, X. Gao, “A novel multiscale nonlinear thresholding method for ultrasonic speckle supressing,” IEEE Trans. Med. Imaging 18, 787–794 (1999).
[Crossref] [PubMed]

Goodman, J.

J. Goodman, Statistical Optics (Wiley, 1985).

Graser, D. J.

B. R. Frieden, D. J. Graser, “Closed-form maximum entropy image restoration,” Opt. Commun. 146, 79–84 (1998).
[Crossref]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Gull, S. F.

Hansen, P. C.

P. C. Hansen, “Numerical tools for analysis and solution of Fredholm integral equations of the first kind,” Inverse Probl. 8, 849–872 (1992).
[Crossref]

Hao, X.

X. Hao, S. Gao, X. Gao, “A novel multiscale nonlinear thresholding method for ultrasonic speckle supressing,” IEEE Trans. Med. Imaging 18, 787–794 (1999).
[Crossref] [PubMed]

Haralick, R. M.

X. Zhuang, R. M. Haralick, Y. Zhao, “Maximum entropy image restoration,” IEEE Trans. Signal Process. 39, 1478–1480 (1991).
[Crossref]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Izatt, J. A.

M. D. Kulkarni, C. W. Thomas, J. A. Izatt, “Image enhancement in optical coherence tomography using deconvolution,” Electron. Lett. 33, 1365–1367 (1997).
[Crossref]

Karl, W. C.

M. Cetin, W. C. Karl, “Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization,” IEEE Trans. Image Process. 10, 623–631 (2001).
[Crossref]

Ko, T. H.

Kulkarni, M. D.

M. D. Kulkarni, C. W. Thomas, J. A. Izatt, “Image enhancement in optical coherence tomography using deconvolution,” Electron. Lett. 33, 1365–1367 (1997).
[Crossref]

Lanteri, H.

H. Lanteri, M. Roche, C. Aime, “Penalized maximum likelihood image restoration with positivity constraints: multiplicative algorithms,” Inverse Probl. 18, 1397–1419 (2002).
[Crossref]

Lee, S. L.

K. M. Yung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
[Crossref] [PubMed]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Mandel, L.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
[Crossref]

Marks, D. L.

Miller, M. I.

D. L. Snyder, J. A. O’Sullivan, M. I. Miller, “The use of maximum likelihood estimation in forming images of diffuse radar targets from delay-doppler data,” IEEE Trans. Inf. Theory 35, 536–548 (1989).
[Crossref]

Moulin, P.

P. Moulin, J. A. O’Sullivan, D. L. Synder, “A method of sieves for multiresolution spectrum estimation and radar Imaging,” IEEE Trans. Inf. Theory 38, 801–813 (1992).
[Crossref]

Newton, T. J.

O’Sullivan, J. A.

P. Moulin, J. A. O’Sullivan, D. L. Synder, “A method of sieves for multiresolution spectrum estimation and radar Imaging,” IEEE Trans. Inf. Theory 38, 801–813 (1992).
[Crossref]

D. L. Snyder, J. A. O’Sullivan, M. I. Miller, “The use of maximum likelihood estimation in forming images of diffuse radar targets from delay-doppler data,” IEEE Trans. Inf. Theory 35, 536–548 (1989).
[Crossref]

Oldenburg, A. L.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Reintjes, J.

Reis, M. L.

M. L. Reis, N. C. Roberty, “Maximum entropy algorithms for image reconstruction from projections,” Inverse Probl. 8, 623–644 (1992).
[Crossref]

Reynolds, J. J.

Roberty, N. C.

M. L. Reis, N. C. Roberty, “Maximum entropy algorithms for image reconstruction from projections,” Inverse Probl. 8, 623–644 (1992).
[Crossref]

Roche, M.

H. Lanteri, M. Roche, C. Aime, “Penalized maximum likelihood image restoration with positivity constraints: multiplicative algorithms,” Inverse Probl. 18, 1397–1419 (2002).
[Crossref]

Rogowska, J.

J. Rogowska, M. E. Brezinski, “Evaluation of the adaptive speckle suppresion filter for coronary optical coherence tomography imaging,” IEEE Trans. Med. Imaging 14, 1261–1266 (2000).
[Crossref]

Schmitt, J. M.

K. M. Yung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
[Crossref] [PubMed]

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[Crossref] [PubMed]

J. M. Schmitt, “Restoration of optical coherence images of living tissue using the CLEAN algorithm,” J. Biomed. Opt. 3, 66–75 (1998).
[Crossref] [PubMed]

J. M. Schmitt, “Array detection for speckle reduction in optical coherence microscopy,” Phys. Med. Biol. 42, 1427–1439 (1997).
[Crossref] [PubMed]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Snyder, D. L.

D. L. Snyder, J. A. O’Sullivan, M. I. Miller, “The use of maximum likelihood estimation in forming images of diffuse radar targets from delay-doppler data,” IEEE Trans. Inf. Theory 35, 536–548 (1989).
[Crossref]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Synder, D. L.

P. Moulin, J. A. O’Sullivan, D. L. Synder, “A method of sieves for multiresolution spectrum estimation and radar Imaging,” IEEE Trans. Inf. Theory 38, 801–813 (1992).
[Crossref]

Thomas, C. W.

M. D. Kulkarni, C. W. Thomas, J. A. Izatt, “Image enhancement in optical coherence tomography using deconvolution,” Electron. Lett. 33, 1365–1367 (1997).
[Crossref]

Thomas, J. A.

T. M. Cover, J. A. Thomas, Elements of Information Theory (Wiley, 1991).
[Crossref]

Wolf, E.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
[Crossref]

Xiang, S. H.

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[Crossref] [PubMed]

Yung, K. M.

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[Crossref] [PubMed]

K. M. Yung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
[Crossref] [PubMed]

Zhao, Y.

X. Zhuang, R. M. Haralick, Y. Zhao, “Maximum entropy image restoration,” IEEE Trans. Signal Process. 39, 1478–1480 (1991).
[Crossref]

Zhuang, X.

X. Zhuang, R. M. Haralick, Y. Zhao, “Maximum entropy image restoration,” IEEE Trans. Signal Process. 39, 1478–1480 (1991).
[Crossref]

Ann. Stat. (1)

I. Csiszar, “Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems,” Ann. Stat. 19, 2032–2066 (1991).
[Crossref]

Appl. Opt. (2)

Electron. Lett. (1)

M. D. Kulkarni, C. W. Thomas, J. A. Izatt, “Image enhancement in optical coherence tomography using deconvolution,” Electron. Lett. 33, 1365–1367 (1997).
[Crossref]

IEEE Trans. Image Process. (3)

S. R. DeGraaf, “SAR imaging via modern 2-D spectral estimation methods,” IEEE Trans. Image Process. 7, 729–761 (1998).
[Crossref]

C. L. Byrne, “Iterative image reconstruction algorithms based on cross-entropy minimization,” IEEE Trans. Image Process. 2, 96–103 (1992).
[Crossref]

M. Cetin, W. C. Karl, “Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization,” IEEE Trans. Image Process. 10, 623–631 (2001).
[Crossref]

IEEE Trans. Inf. Theory (3)

P. Moulin, J. A. O’Sullivan, D. L. Synder, “A method of sieves for multiresolution spectrum estimation and radar Imaging,” IEEE Trans. Inf. Theory 38, 801–813 (1992).
[Crossref]

D. L. Snyder, J. A. O’Sullivan, M. I. Miller, “The use of maximum likelihood estimation in forming images of diffuse radar targets from delay-doppler data,” IEEE Trans. Inf. Theory 35, 536–548 (1989).
[Crossref]

D. L. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory 41, 613–627 (1995).
[Crossref]

IEEE Trans. Med. Imaging (2)

J. Rogowska, M. E. Brezinski, “Evaluation of the adaptive speckle suppresion filter for coronary optical coherence tomography imaging,” IEEE Trans. Med. Imaging 14, 1261–1266 (2000).
[Crossref]

X. Hao, S. Gao, X. Gao, “A novel multiscale nonlinear thresholding method for ultrasonic speckle supressing,” IEEE Trans. Med. Imaging 18, 787–794 (1999).
[Crossref] [PubMed]

IEEE Trans. Signal Process. (2)

X. Zhuang, R. M. Haralick, Y. Zhao, “Maximum entropy image restoration,” IEEE Trans. Signal Process. 39, 1478–1480 (1991).
[Crossref]

B. Borden, “Maximum entropy regularization in inverse synthetic aperture radar imagery,” IEEE Trans. Signal Process. 40, 969–973 (1992).
[Crossref]

Inverse Probl. (3)

H. Lanteri, M. Roche, C. Aime, “Penalized maximum likelihood image restoration with positivity constraints: multiplicative algorithms,” Inverse Probl. 18, 1397–1419 (2002).
[Crossref]

P. C. Hansen, “Numerical tools for analysis and solution of Fredholm integral equations of the first kind,” Inverse Probl. 8, 849–872 (1992).
[Crossref]

M. L. Reis, N. C. Roberty, “Maximum entropy algorithms for image reconstruction from projections,” Inverse Probl. 8, 623–644 (1992).
[Crossref]

J. Biomed. Opt. (3)

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[Crossref] [PubMed]

J. M. Schmitt, “Restoration of optical coherence images of living tissue using the CLEAN algorithm,” J. Biomed. Opt. 3, 66–75 (1998).
[Crossref] [PubMed]

K. M. Yung, S. L. Lee, J. M. Schmitt, “Phase-domain processing of optical coherence tomography images,” J. Biomed. Opt. 4, 125–136 (1999).
[Crossref] [PubMed]

Opt. Commun. (1)

B. R. Frieden, D. J. Graser, “Closed-form maximum entropy image restoration,” Opt. Commun. 146, 79–84 (1998).
[Crossref]

Opt. Lett. (2)

Phys. Med. Biol. (1)

J. M. Schmitt, “Array detection for speckle reduction in optical coherence microscopy,” Phys. Med. Biol. 42, 1427–1439 (1997).
[Crossref] [PubMed]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Other (4)

J. Goodman, Statistical Optics (Wiley, 1985).

M. Bertero, P. Bocacci, Introduction to Inverse Problems in Imaging (IOP, 1998).
[Crossref]

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[Crossref]

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[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Images of Lena to demonstrate a naïve Gaussian deblurring algorithm. (a) Original Lena image. (b) Speckled Lena image reconstructed with a Tikhonov-regularized least-squares algorithm. (c) Amplitude of the image of (b) blurred with a Gaussian window as in Eq. (5). (d) Image corrected with the I-divergence algorithm. Inset in each part, magnified image of Lena’s right eye.

Fig. 2
Fig. 2

OCT images of Xenopus laevis tadpole processed in various ways. The image size is 1000 μ m transverse by 600 μ m axial. (a) Original, unprocessed amplitude data. (b) Tikhonov-regularized least-squares solution for the image. (c) Reference image that is the Gaussian blurred amplitude of (b). (d) Despeckled using I-divergence minimization from the reference image. The upper dotted box in each image corresponds to the magnified area in Fig. 3; the lower dotted box in each image corresponds to the magnified area in Fig. 4.

Fig. 3
Fig. 3

Magnified OCT images of a Xenopus laevis tadpole that correspond to the upper dotted box in each image of Fig. 2. The image size is 240 μ m transverse by 150 μ m axial. (a) Original, unprocessed amplitude data. (b) Tikhonov-regularized least-squares solution for the image. (c) Reference image that is the Gaussian blurred amplitude of (b). (d) Despeckled using I-divergence minimization from the reference image. Note how the image in (d) retains the detail of the least-squares solution of (b) but includes the smoothed amplitude of the reference image of (c).

Fig. 4
Fig. 4

Magnified OCT images of a Xenopus laevis tadpole that correspond to the lower dotted box in each image of Fig. 2. The image size is 240 μ m transverse by 130 μ m axial. (a) Original, unprocessed amplitude data. (b) Tikhonov-regularized least-squares solution for the image. (c) Reference image that is the Gaussian blurred amplitude of (b). (d) Despeckled using I-divergence minimization from the reference image. The uniform intensity areas of the reference image of (c) are “filled in” with the detail of the least-squares solution of (b) to form the despeckled image. Consistency helps to ensure that the despeckled image retains the detail provided by the data.

Equations (5)

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L = y A x 2 + λ i [ x i 2 log x i u i 2 x i 2 + u i 2 ] .
L x i = L Re { x i } Re { x i } x i + L Im { x i } Im { x i } x i = L Re { x i } i L Im { x i } = 2 { A A x A y } i + 4 λ x i log x i u i ,
x i ( n + 1 ) = x i ( n ) 2 ϵ [ { A A x ( n ) A y } i + 2 λ x i ( n ) log x i ( n ) u i ] .
L = y A x 2 + λ i x i 2 = y A x 2 + λ x 2 ,
u ( r ) γ = ( π w 2 ) N 2 η x Tik ( r ) γ exp ( r r 2 w 2 ) d N r .

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