A NEW APPROACH FOR SPARSE PHASE RETRIEVAL BASED ON SUPPORT LIFTING AND LEAST SQUARE ESTIMATION

Abstract

To recover a signal x from the magnitude of a possible linear transform of it, problem known as Phase Retrieval (PR), signal sparsity property has been used to guide the uniqueness of the solution. This paper presents herein a new method for sparse phase retrieval (SPR). Based on a lifting operation, we reduce the problem of SPR to solving a linear system with regards to a vectorized version of xx T. We then use the struc-tured sparsity property of this vectorized form to interpret this operation rather as a lifting operation of the signal support. The signal support is identified iteratively using the gradient pursuit principle in conjunction with subsequent refinements aiming to control the stability of the updated solution. A simple least square estimation on the lifted support is then brought out, iteratively and if required, to determine the lifted solution; from which a rank−1 decomposition is achieved to recover the signal of interest. Simulation results confirm the efficiency of the so-called Greedy Support-Lifting Based algorithm (GSuLA) with acceptable complexity. Robustness of the algorithm is also assured for noisy measurements