On Phase Retrieval Algorithm Via Non-convex Optimization

It has been shown that the main information in the imaging object is encoded in the phase of the light wave.However,the phase information cannot be collected directly by the existing optical measurements equipment,but the intensity information in the light wave can be recorded.Phase retrieval is to study how to use the measured intensity or amplitude information to reconstruct the phase information of the light wave.At present,the phase retrieval has been widely applied in holographic imaging,electron microscopy,signal restoration and other scientific fields.After years of research and development,various effective algorithms for phase retrieval have been developed,which mainly includes early Gerchberg-Saxton(GS)algorithm based on iterative optimization and its improved algorithms.Phaselift,and Phasecut algorithms based on convex optimization,and Wirtinger Flow(WF)and Truncated Wirtinger Flow(TWF)algorithms based on non-convex optimization proposed in recent years.This thesis mainly studies and improves the non-convex optimized phase retrieval algorithm based on Wirtinger Flow.The main research work is as follows:(1)The performance of the existing non-convex optimization phase retrieval algorithms based on WF framework is analyzed and compared,and a phase recovery algorithm based on Conjugate Reweighted Amplitude Flow(CRAF)is developed.The algorithm uses the conjugate gradient of the amplitude-based objective function,and linearly combines the derivative with the previous search direction,by using adaptive optimization learning rate instead of fixed learning rate.Numerical experimental results show that the required number of measurements and iterations of this algorithm are significantly less than other common algorithms.Moreover,it can effectively process the signal with a certain amount of noise.(2)In order to solve the problem that the recovery effect of the existing of algorithms is unsatisfactory when the measurements are destroyed by the arbitrary outliers,a phase retrieval algorithm based on Median Smooth Amplitude Flow(median-SAF)is proposed.In the process of initialization and iterative update,the truncation rules related to the sample median value is added to eliminate the influence of outliers on the recovery result.Numerical experiments show that the presented algorithm can successfully recover signals whose measurement values are destroyed by arbitrary outliers,and the convergence speed,success rate,and the proportion of outliers accommodated are significantly better than other median-based algorithms.