## Speckle-constrained variational methods for image restoration in optical coherence tomography |

JOSA A, Vol. 30, Issue 5, pp. 878-885 (2013)

http://dx.doi.org/10.1364/JOSAA.30.000878

Enhanced HTML Acrobat PDF (638 KB)

### Abstract

A number of despeckling methods for optical coherence tomography (OCT) have been proposed. In these digital filtering techniques, speckle noise is often simplified as additive white Gaussian noise due to the logarithmic compression for the signal. The approximation is not completely consistent with the characteristic of OCT speckle noise, and cannot be reasonably extended to deconvolution algorithms. This paper presents a deconvolution model that combines the variational regularization term with the statistical characteristic constraints of data corrupted by OCT speckle noise. In the data fidelity term, speckle noise is modeled as signal dependent, and the point spread function of OCT systems is included. The regularization functional introduces *a priori* information on the original images, and a regularization term based on block matching 3D modeling is used to construct the variational model in the paper. Finally, the method is applied to the restoration of actual OCT raw data of human skin. The numerical results demonstrate that the proposed deconvolution algorithm can simultaneously enhance regions of images containing detail and remove OCT speckle noise.

© 2013 Optical Society of America

**OCIS Codes**

(100.0100) Image processing : Image processing

(100.1830) Image processing : Deconvolution

(100.3020) Image processing : Image reconstruction-restoration

(110.4500) Imaging systems : Optical coherence tomography

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: November 29, 2012

Revised Manuscript: March 11, 2013

Manuscript Accepted: March 15, 2013

Published: April 15, 2013

**Virtual Issues**

Vol. 8, Iss. 6 *Virtual Journal for Biomedical Optics*

**Citation**

Daiqiang Yin, Ying Gu, and Ping Xue, "Speckle-constrained variational methods for image restoration in optical coherence tomography," J. Opt. Soc. Am. A **30**, 878-885 (2013)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-5-878

Sort: Year | Journal | Reset

### References

- 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, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991). [CrossRef]
- J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999). [CrossRef]
- M. Pircher, E. Gotzinger, R. Leitgeb, A. F. Fercher, and C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8, 565–569 (2003). [CrossRef]
- A. E. Desjardins, B. J. Vakoc, W. Y. Oh, S. M. R. Motaghiannezam, G. J. Tearney, and B. E. Bouma, “Angle-resolved optical coherence tomography with sequential angular selectivity for speckle reduction,” Opt. Express 15, 6200–6209 (2007). [CrossRef]
- T. M. Jorgensen, J. Thomadsen, U. Christensen, W. Soliman, and B. Sander, “Enhancing the signal-to-noise ratio in ophthalmic optical coherence tomography by image registration—method and clinical examples,” J. Biomed. Opt. 12, 041208 (2007). [CrossRef]
- D. A. Caneiro, S. A. Read, and M. J. Collins, “Speckle reduction in optical coherence tomography imaging by affine-motion image registration,” J. Biomed. Opt. 16, 116027 (2011). [CrossRef]
- M. Szkulmowski, I. Gorczynska, D. Szlag, M. Sylwestrzak, A. Kowalczyk, and M. Wojtkowski, “Efficient reduction of speckle noise in optical coherence tomography,” Opt. Express 20, 1337–1359 (2012). [CrossRef]
- D. C. Adler, T. H. Ko, and J. G. Fujimoto, “Speckle reduction in optical coherence tomography images by use of a spatially adaptive wavelet filter,” Opt. Lett. 29, 2878–2880 (2004). [CrossRef]
- S. Chitchian, M. A. Fiddy, and N. M. Fried, “Denoising during optical coherence tomography of the prostate nerves via wavelet shrinkage using dual-tree complex wavelet transform,” J. Biomed. Opt. 14, 014031 (2009). [CrossRef]
- Z. Jian, L. Yu, B. Rao, B. J. Tromberg, and Z. Chen, “Three-dimensional speckle suppression in optical coherence tomography based on the curvelet transform,” Opt. Express 18, 1024–1032 (2010). [CrossRef]
- P. Puvanathasan and K. Bizheva, “Speckle noise reduction algorithm for optical coherence tomography based on interval type II fuzzy set,” Opt. Express 15, 15747–15758 (2007). [CrossRef]
- M. A. Mayer, A. Borsdorf, M. Wagner, J. Hornegger, C. Y. Mardin, and R. P. Tornow, “Wavelet denoising of multiframe optical coherence tomography data,” Biomed. Opt. Express 3, 572–589 (2012). [CrossRef]
- H. M. Salinas and D. C. Fernandez, “Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography,” IEEE Trans. Med. Imaging 26, 761–771 (2007). [CrossRef]
- P. Puvanathasan and K. Bizheva, “Interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in optical coherence tomography images,” Opt. Express 17, 733–746 (2009). [CrossRef]
- R. Bernardes, C. Maduro, P. Serranho, A. Araujo, S. Barbeiro, and J. Cunha-Vaz, “Improved adaptive complex diffusion despeckling filter,” Opt. Express 18, 24048–24059 (2010). [CrossRef]
- L. Fang, S. Li, Q. Nie, J. A. Izatt, C. A. Toth, and S. Farsiu, “Sparsity based denoising of spectral domain optical coherence tomography images,” Biomed. Opt. Express 3, 927–942 (2012). [CrossRef]
- T. S. Ralston, D. L. Marks, F. Kamalabadi, and S. A. Boppart, “Deconvolution methods for mitigation of transverse blurring in optical coherence tomography,” IEEE Trans. Image Process. 14, 1254–1264 (2005). [CrossRef]
- Y. Liu, Y. Liang, G. Mu, and X. Zhu, “Deconvolution methods for image deblurring in optical coherence tomography,” J. Opt. Soc. Am. A 26, 72–77 (2009). [CrossRef]
- R. Prashanth and S. Bhattacharya, “Space variant deconvolution for optical coherence tomography,” Proc. SPIE 8311, 831113 (2011). [CrossRef]
- F. Natterer and F. Wubbeling, Mathematical Methods in Image Reconstruction (SIAM, 2001).
- H. H. Arsenault and G. April, “Properties of speckle integrated with a finite aperture and logarithmically transformed,” J. Opt. Soc. Am. 66, 1160–1163 (1976). [CrossRef]
- G. Aubert and J. Aujol, “A variational approach to remove multiplicative noise,” SIAM J. Appl. Math. 68, 925–946 (2008). [CrossRef]
- J. M. Bioucas-Dias and M. A. T. Figueiredo, “Multiplicative noise removal using variable splitting and constrained optimization,” IEEE Trans. Image Process. 19, 1720–1730 (2010). [CrossRef]
- F. Dong, H. Zhang, and D. X. Kong, “Nonlocal total variation models for multiplicative noise removal using split Bregman iteration,” Math. Comput. Model. 55, 939–954(2012). [CrossRef]
- M. A. T. Figueiredo and J. M. Bioucas-Dias, “Restoration of Poissonian images using alternating direction optimization,” IEEE Trans. Image Process. 19, 3133–3145 (2010). [CrossRef]
- D. Q. Chen and L. Z. Cheng, “Spatially adapted regularization parameter selection based on the local discrepancy function for Poissonian image deblurring,” Inverse Probl. 28, 015004 (2012). [CrossRef]
- A. Danielyan, V. Katkovnik, and K. Egiazarian, “Deblurring of Poissonian images using BM3D frames,” Proc. SPIE 8138, 813812 (2011). [CrossRef]
- K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process. 16, 2080–2095 (2007). [CrossRef]
- A. Danielyan, V. Katkovnik, and K. Egiazarian, “BM3D frames and variational image deblurring,” IEEE Trans. Image Process. 21, 1715–1728 (2012). [CrossRef]
- L. Denis, F. Tupin, J. Darbon, and M. Sigelle, “SAR image regularization with fast approximate discrete minimization,” IEEE Trans. Image Process. 18, 1588–1600 (2009). [CrossRef]
- J. Shi and S. Osher, “A nonlinear inverse scale space method for a convex multiplicative noise model,” SIAM J. Imaging Sci. 1, 294–321 (2008). [CrossRef]
- S. Setzer, “Operator splittings, Bregman methods and frame shrinkage in image processing,” Int. J. Comput. Vis. 92, 265–280 (2011). [CrossRef]
- E. Esser, X. Q. Zhang, and T. F. Chan, “A general framework for a class of first order primal-dual algorithms for convex optimization in imaging science,” SIAM J. Imaging Sci. 3, 1015–1046 (2010). [CrossRef]
- G. Gilboa and S. Osher, “Nonlocal operators with applications to image processing,” Multiscale Model. Simul. 7, 1005–1028 (2009). [CrossRef]
- W. Dong, X. Li, L. Zhang, and G. Shi, “Sparsity-based image denoising via dictionary learning and structural clustering,” in Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 457–464.
- S. Y. Zhao, Y. Gu, P. Xue, J. Guo, T. M. Shen, T. S. Wang, N. Y. Huang, L. Zhang, H. X. Qiu, X. Yu, and X. B. Wei, “Imaging port wine stains by fiber optical coherence tomography,” J. Biomed. Opt. 15, 036020 (2010). [CrossRef]
- Z. Wang, H. Kyonob, H. G. Bezerrab, D. L. Wilson, M. A. Costa, and A. M. Rollins, “Automatic segmentation of intravascular optical coherence tomography images for facilitating quantitative diagnosis of atherosclerosis,” Proc. SPIE 7889, 78890N(2011). [CrossRef]
- K. Zhang and J. U. Kang, “Real-time intraoperative 4D full-range FD-OCT based on the dual graphics processing units architecture for microsurgery guidance,” Biomed. Opt. Express 2, 764–770 (2011). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.