title: Improving the Incoherence of a Learned Dictionary via Rank Shrinkage.
abstract: This letter considers the problem of dictionary learning for sparse signal representation whose atoms have low mutual coherence. To learn such dictionaries, at each step, we first update the dictionary using the method of optimal directions (MOD) and then apply a dictionary rank shrinkage step to decrease its mutual coherence. In the rank shrinkage step, we first compute a rank 1 decomposition of the column-normalized least squares estimate of the dictionary obtained from the MOD step. We then shrink the rank of this learned dictionary by transforming the problem of reducing the rank to a nonnegative garrotte estimation problem and solving it using a path-wise coordinate descent approach. We establish theoretical results that show that the rank shrinkage step included will reduce the coherence of the dictionary, which is further validated by experimental results. Numerical experiments illustrating the performance of the proposed algorithm in comparison to various other well-known dictionary learning algorithms are also presented.
authors.affiliation: Department of Computer Science and Engineering, University of Minnesota, Twin Cities, MN 55455, U.S.A. ubaru001@umn.edu.
authors.forename: Shashanka
authors.initials: S
authors.lastname: Ubaru
authors.affiliation: Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne 3010, Victoria, Australia abd-krim.seghouane@unimelb.edu.au.
authors.forename: Abd-Krim
authors.initials: AK
authors.lastname: Seghouane
authors.affiliation: Department of Computer Science and Engineering, University of Minnesota, Twin Cities, MN 55455, U.S.A. saad@cs.umn.edu.
authors.forename: Yousef
authors.initials: Y
authors.lastname: Saad