Nonconvex Optimization with Alternating Direction Method of Multipliers for Tensor-Based Compressed Sensing with Group Sparsity

Tensor-based compressive sensing (CS) can preserve the intrinsic multidimensional structures with a reduced computational complexity. However, its recovery performance is degraded by simple sparsity. This paper proposes an efficient recovery algorithm GT-ADMM to solve a nonconvex optimization problem for tensor-based CS with group sparsity. Group-sparse representations of tensors is derived based on the Kronecker product of adaptively trained basis. The proposed algorithm incorporates alternating direction method of multipliers (ADMM) to obtain desirable recovery quality with improved efficiency. It requires few degrees of freedom to achieve tensor recovery with a guarantee of minimized approximation error. Experimental results demonstrate that the proposed algorithm outperforms state-of-the-art tensor-based methods in compressive video sampling.