On Phase Retrieval Via Momentum Reweighted Amplitude Flow

As we all know,the main physical quantities used to describe the characteristics of the light wave field are amplitude,wavelength,and phase.According to research,most of the information is encoded in the phase.However,existing optical measurement equipment that converts photons into electrons can only record the amplitude or intensity information of the signal,and cannot obtain the phase information of the signal by direct measurement.Therefore,it is necessary to calculate the phase of the object by measuring amplitude or intensity,that is,Phase Retrieval.Phase retrieval has been widely used in science and engineering,including electron microscopy,diffraction imaging,X-ray crystallography,etc.The phase retrieval problem has received extensive attention from researchers in recent years.Many scholars have proposed various solutions to the phase retrieval problem.Earlier,the phase retrieval algorithms were mainly non-convex optimization algorithms,such as Gerchberg-Saxton(GS).Later,the phase retrieval algorithms were mainly convex optimization algorithms including PhaseLift.Recently,the phase retrieval algorithms mainly include nonconvex optimization algorithms based on Wirtinger Flow(WF).The WF algorithm not only overcomes the shortcomings of traditional non-convex optimization algorithms that easily converge to a local optimal solution,but also solves the problem that convex optimization algorithms have high computational complexity and are difficult to recover large-scale twodimensional signals.Therefore,it has received more and more attention in recent years.In this thesis,the framework of WF algorithm is studied and some improvements are proposed.The main work and innovations are as follows:(1)Some existing phase retrieval algorithms such as Wirtinger Flow and Truncated Wirtinger Flow are briefly introduced and analyzed.And it is compared through simulation experiments to analyze and verify its advantages and disadvantages.(2)Combining momentum gradient descent,this thesis designs a phase retrieval algorithm based on Momentum Reweighted Amplitude Flow(MRAF).The algorithm first uses the amplitude loss function to effectively reduce the number of measurements required during the recovery process.Then,the acceleration and robustness of momentum are used to reduce the number of iterations required by the algorithm in the recovery process and improve the recovery success rate of the algorithm.Finally,this thesis verifies the effectiveness of the algorithm through simulation experiments,and proves that the algorithm needs fewer measurements and has faster convergence speed.(3)Introducing the median value into the Momentum Reweighted Amplitude Flow phase retrieval algorithm.This thesis designs a phase retrieval algorithm based on Median Momentum Reweighted Amplitude Flow(median-MRAF).It solves the problem that the existing algorithms are not ideal for recovering signals with outliers.This algorithm takes advantage of the fact that the median cannot be arbitrarily disturbed unless the outliers dominate the inner.The median correlation is used to trim samples during initialization and each iteration to remove the effect of outliers on signal recovery.Experimental results show that compared with some existing algorithms under the same conditions,the algorithm in this thesis has the characteristics of fewer measurements,faster convergence,more tolerable outliers,and higher success rates.