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research
A new ADMM algorithm for the Euclidean median and its application to robust patch regression
Authors
Kunal N. Chaudhury
K. R. Ramakrishnan
Publication date
16 January 2015
Publisher
Doi
Cite
View
on
arXiv
Abstract
The Euclidean Median (EM) of a set of points
Ω
\Omega
Ω
in an Euclidean space is the point x minimizing the (weighted) sum of the Euclidean distances of x to the points in
Ω
\Omega
Ω
. While there exits no closed-form expression for the EM, it can nevertheless be computed using iterative methods such as the Wieszfeld 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.Comment: 5 pages, 3 figures, 1 table. To appear in Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing, April 19-24, 201
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oai:eprints.iisc.ac.in:54288
Last time updated on 08/01/2019
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info:doi/10.1109%2Ficassp.2015...
Last time updated on 01/04/2019