Enhanced low-rank + sparsity decomposition for speckle reduction in optical coherence tomography," J. Abstract. Speckle artifacts can strongly hamper quantitative analysis of optical coherence tomography (OCT), which is necessary to provide assessment of ocular disorders associated with vision loss. Here, we introduce a method for speckle reduction, which leverages from low-rank + sparsity decomposition (LRpSD) of the logarithm of intensity OCT images. In particular, we combine nonconvex

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... ization-based low-rank approximation of an original OCT image with a sparsity term that incorporates the speckle. State-of-the-art methods for LRpSD require a priori knowledge of a rank and approximate it with nuclear norm, which is not an accurate rank indicator. As opposed to that, the proposed method provides more accurate approximation of a rank through the use of nonconvex regularization that induces sparse approximation of singular values. Furthermore, a rank value is not required to be known a priori. This, in turn, yields an automatic and computationally more efficient method for speckle reduction, which yields the OCT image with improved contrast-to-noise ratio, contrast and edge fidelity. The source code will be available at www.mipav.net/English/research/research.html. Kopriva, Shi, and Chen: Enhanced low-rank + sparsity decomposition for speckle reduction in optical. . . Downloaded From: http://biomedicaloptics.spiedigitallibrary.org/ on 07/18/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Suggested value for the penalty parameter β in Eq. (16): β ¼ 1. Suggested value for constant a in Eqs. (9) to (13): a ¼ 0.6∕λ. 1. L ð0Þ ¼ X; S ð0Þ ¼ 0; Λ ð0Þ ¼ 0; t ¼ 1. 2. while not converge do 3. Execute SVD Eq. (21). 4. Update L using Eq. (20). 5. Update S using Eq. (22). 6. Update Λ using Eq. (19). 7. t←t þ 1 8. end while Output: L←L ðt þ1Þ , S←S ðt þ1Þ . Kopriva, Shi, and Chen: Enhanced low-rank + sparsity decomposition for speckle reduction in optical. . . Downloaded From: http://biomedicaloptics.spiedigitallibrary.org/ on 07/18/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Ivica Kopriva received his PhD in electrical engineering from the University of Zagreb, Croatia, in 1998, with the topic on blind source separation. He is a senior scientist at the Rud¯er Bošković Institute, Zagreb, Croatia. He has coauthored over 40 papers in internationally recognized journals, one book, and holds three US patents. His current research is focused on structured decompositions of empirical data with applications in imaging, spectroscopy, and variable selection.