Sparse Bayesian dictionary learning with a Gaussian hierarchical model

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• 作者：Linxiao Yang^a ; Jun Fang^a ; ^{JunFang@uestc.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{201321190224@std.uestc.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Hong Cheng^b ; ^{hcheng@uestc.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Hongbin Li^c ; ^{Hongbin.Li@stevens.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Dictionary learning ; Gaussian-inverse Gamma prior ; Variational Bayesian ; Gibbs sampling
• 刊名：Signal Processing
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：130
• 期：Complete
• 页码：93-104
• 全文大小：3267 K

文摘

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 variance 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.