An Unconstrained q Minimization with 0q≤1 for Sparse Solution of Underdetermined Linear Systems

We study an unconstrained version of the q minimization for the sparse solution of underdetermined linear systems for 0<q≤1. Although the minimization is nonconvex when $q<1$, we introduce a regularization and develop an iterative algorithm. We show that the iterative algorithm converges and that the iterative solutions converge to the sparse solution under some additional assumptions on underdetermined linear systems. Numerical experiments are presented to demonstrate the effectiveness of our approach.