A weakly-convex formulation for phaseless imaging

Abstract

We consider the problem of reconstructing an object given magnitudes of linear measurements. We follow the `lifting' approach, but unlike previous work which use convex relaxations of the unit rank constraint, we use a weakly-convex matrix penalty. We derive a convergent algorithm and show that it is computationally more feasible than those obtained under convex relaxations. We demonstrate numerically that when the signal to noise ratio is high, the proposed algorithm can achieve almost error-free reconstruction with fewer measurements than when convex relaxation is employed.