On Sparse Phase Recovery Based On Convex Optimization

Most of the information of optical wavefront is encoded in the phase which includes more details of the object. Conventional optical measuring apparatus can only record the intensity of light, but can not measure the phase of light directly. Thus it is important to recover the phase from the intensity measurements of the object.Phase recovery has been widely studied in the past few decades. Now there are many ways to solve the phase retrieval problem, such as traditional iterative phase recovery algorithm, phase recovery algorithm based on Transport of Intensity Equation (TIE) and phase recovery algorithm based on convex optimization. Traditional iterative phase recovery algorithm recovers phase from two intensity measurements on the image, or uses Fourier transform to recover phase Fourier plane in an imaging system. This method has the advantage of iterative speed, but is easy to fall into local solution. While the algorithm based on TIE used to solve TIE to recover the phase in the previous plane by measuring the changes of two light intensity which perpendicular to the axis. In recent years, phase recovery algorithm based on convex optimization is proposed to solve the shortcoming of traditional iterative algorithm which is easy to fall into local solution by converting the phase recovery problem into quadratic programming problem.This paper focus on solving the problem of sparse phase recovery based on convex optimization method. The main work of the paper is as follows:(1) Compares the typical phase recovery method based on convex optimization PhaseLift, PhaseCut and Compressive Phase Retrieval (CPR), and analyzes the advantage and disadvantage.(2) Puts forward a phase retrieval method called compression phase cut retrieval algorithm by combining CPR and PhaseCut method. Firstly, using CPR to solve l1 minimization problem to get a sparse solution of signal’s phase, then set the normalized phase as initial value of PhaseCut to improve the recovery result of CPR by TFOCS toolkit. The experiment shows that it is not only improve the result of CPR But also overcome the defect of PhaseCut which is not conducive to recover the phase of sparse signal.(3) Studied the phase recovery problem while the measuring amplitude is sparse. Currently most phase retrieval method consider the problem of general signal, although CPR method take the sparsity of signal into consideration, there is few discussion of sparsity of measuring amplitude. Experiment verifies that PhaseCut method is easier to recover phase from sparse measuring amplitude in the presence of noise compared to the other algorithm. We improved the PhaseCut algorithm on this basis, it reduced the dimension, speed up the rate, improved the efficiency and recovery effect.