Nonuniform norm based method for sparse signal recovery

Nonuniform norm constraint (NNC)-based methods have numerous potential applications for sparse signal recovery from a small number of measurements. In this study, we propose a novel NNC sparse recovery algorithm. First, a particular solution is attained by the gradient-descent-like method, which searches for the minimum NNC solution. Second, general solutions can be derived in the framework of underdetermined linear systems, wherein the pseudo-inverse matrix can be obtained using the QR decomposition via Givens rotations. Numerical simulations are conducted to verify the superior results with regard to sparsity adaptability, computation time, and recovered signal-to-noise ratio.