Truncated tensor-based Bayesian recovery for multidimensional compressive sensing

Bayesian methods are widely used to recover sparse signals from their incomplete measurements with Gaussian white noise. However, while recovering multidimensional signals, these methods are limited by their considerable computational complexities. To address this problem, we develop the truncated Bayesian recovery algorithm for compressive sensing (CS) of multidimensional signals, such as hyperspectral remote sensing images. For each dimension of multidimensional sparse signal, the entries are modeled by the type-II Laplacian prior, such that the support is indicated by the largest variance hyperparameters. The entries of noise tensor are assumed to be independent and Gaussian with zero mean. We approximately estimate the hyperparameters using the maximum a posteriori (MAP) process to determine the supports for each dimension. Based on the supports, the recovered sparse signal is obtained through the tensor-based least square strategy. The required number of iterative cycles can be significantly reduced, compared with conventional method that iterates the MAP process until convergence. Experimental results on synthetic data, hyperspectral images, and hyperspectral remote sensing images demonstrate that the proposed algorithm can obviously speed up multidimensional Bayesian CS recovery.