The Uniqueness and Greedy Method for Quadratic Compressive Sensing

Abstract

Quadratic compressive sensing, as a nonlinear extension of compressive sensing, has attracted considerable attention in optical image, X-ray crystallography, transmission electron microscopy, etc. We introduce the concept of uniform s-regularity to study the uniqueness in quadratic compressive sensing and propose a greedy algorithm for the corresponding numerical optimization. Moreover, we prove the convergence of the proposed algorithm under the uniform s-regularity condition. Finally, we present numerical results to demonstrate the efficiency of the proposed method.