Exploiting Block-sparsity for Hyperspectral Kronecker Compressive Sensing: a Tensor-based Bayesian Method

Bayesian methods are attracting increasing attention in the field of compressive sensing (CS), as they are applicable to recover signals from random measurements. However, these methods have limited use in many tensor-based cases such as hyperspectral Kronecker compressive sensing (HKCS), because they exploit the sparsity in only one dimension. In this paper, we propose a novel Bayesian model for HKCS in an attempt to overcome the above limitation. The model exploits multi-dimensional block-sparsity such that the information redundancies in all dimensions are eliminated. Laplace prior distributions are employed for sparse coefficients in each dimension, and their coupling is consistent with the multi-dimensional block-sparsity model. Based on the proposed model, we develop a tensor-based Bayesian reconstruction algorithm, which decouples the hyperparameters for each dimension via a low-complexity technique. Experimental results demonstrate that the proposed method is able to provide more accurate reconstruction than existing Bayesian methods at a satisfactory speed. Additionally, the proposed method can not only be used for HKCS, it also has the potential to be extended to other multi-dimensional CS applications and to multi-dimensional block-sparse-based data recovery.