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The Scientific World Journal
Volume 2014, Article ID 852978, 8 pages
Research Article

An Analysis Dictionary Learning Algorithm under a Noisy Data Model with Orthogonality Constraint

1Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China
2Centre for Vision, Speech and Signal Processing, University of Surrey, Guildford GU2 7XH, UK

Received 25 January 2014; Revised 13 June 2014; Accepted 26 June 2014; Published 13 July 2014

Academic Editor: Francesco Camastra

Copyright © 2014 Ye Zhang 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.


Two common problems are often encountered in analysis dictionary learning (ADL) algorithms. The first one is that the original clean signals for learning the dictionary are assumed to be known, which otherwise need to be estimated from noisy measurements. This, however, renders a computationally slow optimization process and potentially unreliable estimation (if the noise level is high), as represented by the Analysis K-SVD (AK-SVD) algorithm. The other problem is the trivial solution to the dictionary, for example, the null dictionary matrix that may be given by a dictionary learning algorithm, as discussed in the learning overcomplete sparsifying transform (LOST) algorithm. Here we propose a novel optimization model and an iterative algorithm to learn the analysis dictionary, where we directly employ the observed data to compute the approximate analysis sparse representation of the original signals (leading to a fast optimization procedure) and enforce an orthogonality constraint on the optimization criterion to avoid the trivial solutions. Experiments demonstrate the competitive performance of the proposed algorithm as compared with three baselines, namely, the AK-SVD, LOST, and NAAOLA algorithms.