A Nonparametric Bayesian Approach to Image Compressive Sensing on Manifolds with Correlation Constraints

The broad class of manifold models are considered for extending the conventional compressive sensing (CS) to a more general framework. However, although the manifold-based CS approaches using a mixture of factor analyzers can learn latent geometric structures of high-dimensional signals, they have two issues that potentially limit their practical use: First, the manifold modeling does not take account of sharing factors among mixture components and thus misses the chance to enhance statistical strength; Second, introducing correlation constraints may cause intractable model inference. In this paper, we address these issues by: (1) depicting the mixture correlations with a hierarchical Beta process whose upper-layer process is an Indian buffet process in nonparametric Bayesian manner; (2) deriving a combination of collapsed Gibbs sampler and auxiliary-variable-based slice sampler to obtain the model accurate solutions. Experimental results on real dataset demonstrate that our proposed method provides significant performance improvements compared to the sparsity-based CS algorithms, while outperforming the state-of-the-art manifold-based inversion strategies for image reconstruction.