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Mathematical Problems in Engineering
Volume 2016, Article ID 5737381, 11 pages
http://dx.doi.org/10.1155/2016/5737381
Research Article

An Efficient Algorithm for Learning Dictionary under Coherence Constraint

College of Information Engineering, Zhejiang University of Technology, Hangzhou, Zhejiang 310023, China

Received 30 March 2016; Revised 8 June 2016; Accepted 23 June 2016

Academic Editor: Srdjan Stankovic

Copyright © 2016 Huang Bai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Dictionary learning problem has become an active topic for decades. Most existing learning methods train the dictionary to adapt to a particular class of signals. But as the number of the dictionary atoms is increased to represent the signals much more sparsely, the coherence between the atoms becomes higher. According to the greedy and compressed sensing theories, this goes against the implementation of sparse coding. In this paper, a novel approach is proposed to learn the dictionary that minimizes the sparse representation error according to the training signals with the coherence taken into consideration. The coherence is constrained by making the Gram matrix of the desired dictionary approximate to an identity matrix of proper dimension. The method for handling the proposed model is mainly based on the alternating minimization procedure and, in each step, the closed-form solution is derived. A series of experiments on synthetic data and audio signals is executed to demonstrate the promising performance of the learnt incoherent dictionary and the superiority of the learning method to the existing ones.