A nonparametric Bayesian approach to joint multiple dictionary learning with separate image sources

Nonparametric Bayesian approach is considered for learning appropriate dictionaries in sparse image representations. However, for images from multiple separate sources, existing methods have two issues that potentially limit their practical implements: first, learning one unified dictionary is not optimal for representing image samples in different subspaces; second, the required number of dictionaries and their correlations are unknown in advance. In this paper, we address these issues by: 1) modeling multiple dictionaries using a Dirichlet process which can automatically infer the latent dictionary number needed to fit the image data; 2) placing a hierarchical Beta process prior to depict the dictionary correlations. To make the Bayesian model inference tractable, we further derive a combination of collapsed Gibbs sampler and auxiliary-variable-based slice sampler. Experimental results demonstrate that our proposed inference approach can achieve an optimized set of dictionaries for multiple source images, while exhibiting performance improvements in the context of image compressive sensing reconstruction.