On Phase Retrieval Via Reweighted Gradient Descent

It is shown that most of the information of optical wavefront is encoded in the phase.However,the existing optical measuring devices have certain limitations,and it is impossible to directly measure the phase information of the object,and only the intensity information can be recorded.Therefore,it is very important to study how to recover the phase from the intensity information of an object.This problem is known as the phase recovery problem,which is widely found in the fields of X-ray crystallography,optical imaging,wireless communication,and power system monitoring.In recent years,Many different solutions have been proposed by researchers to solve phase recovery problems,including convex optimization and non-convex optimization.The phase recovery algorithm based on convex optimization is commonly used in algorithms such as PhaseLift and CPRL(Compression Phase Retrieval via Lifting).The computational complexity of these algorithms is high,and the recovery efficiency for two-dimensional signals is low.Phase recovery algorithms based on non-convex optimization include Gerchberg-Saxton(GS),Error-Reduction(ER),and Hybrid Input-Output(HIO)algorithms etal.Since the constraints of this type of algorithm are non-convex,the local optimal solution is often obtained.In order to make up for their shortcomings,Candes et al.proposed a non-convex optimization algorithm based on Wirtinger Flow,which uses an effective means to obtain good initial estimates,and selects the appropriate iterative format based on it,and finally obtains convergence results.Experiment show that the algorithm has faster convergence and lower computational complexity.In this thesis,the research based on non-convex optimized phase retrieval algorithm is carried out,and some improvements are proposed based on the Wirtinger Flow algorithm framework.The main research work and results of the thesis are as follows:(1)Several non-convex optimization algorithms such as Wirtinger Flow,Truncated Wirtinger Flow,Truncated Amplitude Flow and Incremental Truncated Wirtinger Flow are compared by simulation experiments,and their advantages and disadvantages are briefly analyzed.(2)Based on the Wirtinger Flow algorithm framework,an incremental gradient descent scheme and reweighting are used to design a phase recovery algorithm called Incremental Reweighted Gradient Descent(IRGD).The proposed algorithm uses incremental gradient descent to solve large-scale signal recovery problems effectively,and uses heavy weighting to improve its recovery performance and reduce the number of measurements required.Simulation results show that the algorithm can recover the original phase with faster convergence speed and fewer measurement times than some common algorithms.(3)Aiming at the problem that some existing algorithms have poor recovery effect on noisy signals,this thesis integrates the filtering algorithm and the unwrapping algorithm into the IRGD algorithm,and proposes an improved algorithm,the unwrapping filtering IRGD algorithm.The algorithm firstly uses initialization and loop iteration to obtain preliminary results,and then filters the amplitude and the real phase obtained by unwrapping in the frequency domain.In this way,most of the noise in the signal can be effectively eliminated,and the recovery effect of the algorithm is improved.Finally,the simulation experiment results show the the effectiveness and noise robustness of the unwrapping filtering IRGD method.