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A NEW ADMM ALGORITHM FOR THE EUCLIDEAN MEDIAN AND ITS APPLICATION TO ROBUST PATCH REGRESSION

Chaudhury, Kunal N and Ramakrishnan, KR (2015) A NEW ADMM ALGORITHM FOR THE EUCLIDEAN MEDIAN AND ITS APPLICATION TO ROBUST PATCH REGRESSION. In: 40th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), APR 19-24, 2014, Brisbane, AUSTRALIA, pp. 1603-1607.

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Abstract

The Euclidean Median (EM) of a set of points Omega in an Euclidean space is the point x minimizing the (weighted) sum of the Euclidean distances of x to the points in Omega. While there exits no closed-form expression for the EM, it can nevertheless be computed using iterative methods such as the Weiszfeld algorithm. The EM has classically been used as a robust estimator of centrality for multivariate data. It was recently demonstrated that the EM can be used to perform robust patch-based denoising of images by generalizing the popular Non-Local Means algorithm. In this paper, we propose a novel algorithm for computing the EM (and its box-constrained counterpart) using variable splitting and the method of augmented Lagrangian. The attractive feature of this approach is that the subproblems involved in the ADMM-based optimization of the augmented Lagrangian can be resolved using simple closed-form projections. The proposed ADMM solver is used for robust patch-based image denoising and is shown to exhibit faster convergence compared to an existing solver.

Item Type: Conference Proceedings
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Additional Information: Copy right for this article belongs to the IEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA
Keywords: Image denoising; patch-based algorithm; robustness; Euclidean median; variable splitting; augmented Lagrangian; alternating direction method of multipliers (ADMM); convergence
Department/Centre: Division of Electrical Sciences > Electrical Engineering
Date Deposited: 19 Aug 2016 09:17
Last Modified: 19 Aug 2016 09:17
URI: http://eprints.iisc.ernet.in/id/eprint/54288

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