Sparse Bayesian Dictionary Learning with a Gaussian Hierarchical Model
This is an incremental improvement for applications like image denoising and feature extraction, offering enhanced dictionary learning accuracy in data-scarce scenarios.
The paper tackles dictionary learning for sparse signal representation by proposing a new hierarchical Bayesian model with a Gaussian-inverse Gamma prior to promote sparsity, and it shows that the methods achieve better accuracy than existing ones, especially with limited training signals.
We consider a dictionary learning problem whose objective is to design a dictionary such that the signals admits a sparse or an approximate sparse representation over the learned dictionary. Such a problem finds a variety of applications such as 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 priors are also placed on the dictionary and the noise variance such that they can be reasonably inferred 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 \emph{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.