A NONCONVEX ALGORITHM FOR SIMULTANEOUSLY SPARSE AND LOW-RANK MATRIX RECONSTRUCTION

This paper considers the reconstruction of simultaneously sparse and low-rank matrices with a limited number of random measurements. The use of convex approximations of the sparsity level and the matrix rank enables one to apply well-developed convex optimization techniques. However, owing to the approximation, a convex approach may fail when the global minimum of the cost function is not equal to the generative sparse and low-rank matrix, and there is nothing one can do to avoid this structural error for convex approaches from the perspective of algorithmic development. Instead of using the convex ℓ
₁
norm and the nuclear norm to promote sparsity and low rank, a new approach with nonconvex and nonseparable regularization is proposed to solve the reconstruction problem in this paper. Experimental results shows that in comparison to the existing approaches, the proposed approach achieves significantly improved performance for recovering simultaneously sparse and low-rank matrices.