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Sparse Bayesian dictionary learning with a Gaussian hierarchical model
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DOI：10.1016/j.sigpro.2016.06.016.png)
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Abstract
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We consider a dictionary learning problem aimed at designing a dictionary such that the signals admit a sparse or an approximate sparse representation over the learnt dictionary. The problem finds a variety of applications including image denoising, feature extraction, etc. In this paper, we propose a new hierarchical Bayesian model for dictionary learning, in which a Gaussian-inverse Gamma hierarchical prior is used to promote the sparsity of the representation. Suitable non-informative priors are also placed on the dictionary and the noise variance such that they can be reliably estimated from the data. Based on the hierarchical model, a variational Bayesian method and a Gibbs sampling method are developed for Bayesian inference. The proposed methods have the advantage that they do not require the knowledge of the noise valiance a priori. Numerical results show that the proposed methods are able to learn the dictionary with an accuracy better than existing methods, particularly for the case where there is a limited number of training signals. (C) 2016 Elsevier B.V. All rights reserved.
Keywords:
Dictionary learning
Gaussian-inverse Gamma prior
Variational Bayesian
Gibbs sampling
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