Fully Decomposable Compressive Sampling With Joint Optimization for Multidimensional Sparse Representation

Abstract

Conventional compressive sampling methods cannot efficiently exploit structured sparsity for sampling multidimensional signals like video sequences. In this paper, we propose a fully decomposable compressive sampling model that adopts the Kronecker product framework to exploit the structured sparsity spanning multidimensional signals. It enables efficient sampling in a progressive fashion by retaining the block-diagonal feature of Kronecker products. A synthetic sensing matrix is developed for joint optimization over sampling signals with multiple dimensions. Instead of adjusting global Gram matrix, separable minimization of mutual coherence in multiple dimensions is jointly formulated for a stable recovery with enhanced convergence rate. Sampling rate allocation is considered to improve recovery performance based on the decomposable compressive sampling. The proposed model is employed in video acquisition for temporal sparsity along motion trajectory. Experiment results show that the proposed model can improve the recovery performance with a reduced number of necessary samples in comparison to the state-of-the-art methods.