Mean-square analysis of the gradient projection sparse recovery algorithm based on non-uniform norm

With the previously proposed non-uniform norm called lN-norm, which consists of a sequence of l1-norm or l0-norm elements according to relative magnitude, a novel lN-norm sparse recovery algorithm can be derived by projecting the gradient descent solution to the reconstruction feasible set. In order to gain analytical insights into the performance of this algorithm, in this letter we analyze the steady state mean square performance of the gradient projection lN-norm sparse recovery algorithm in terms of different sparsity, as well as additive noise. Numerical simulations are provided to verify the theoretical results.