A NEW HYBRID lp-l2 MODEL FOR SPARSE SOLUTIONS WITH APPLICATIONS TO IMAGE PROCESSING

Finding sparse solutions to a linear system has many real-world applications. In this paper, we study a new hybrid of the l(p) quasi-norm (0 < p < 1) and l(2) norm to approximate the l(0) norm and propose a new model for sparse optimization. The optimality conditions of the proposed model are carefully analyzed for constructing a partial linear approximation fixed-point algorithm. A convergence proof of the algorithm is provided. Computational experiments on image recovery and deblurring problems clearly confirm the superiority of the proposed model over several state-of-the-art models in terms of the signal-to-noise ratio and computational time.