Research On Phase Retrieval Algorithms Based On Optimization Theory

Phase Retrieval(PR)refers to reconstructing the phase and the original signal from only the amplitude or intensity measurement of the signal,which appears in many fields of science and engineering.Wireless signals are propagated through electromagnetic waves as a carrier,including amplitude and phase.For a general signal,the structural information carried by its phase is much greater than its amplitude.Therefore,it is of great practical significance to recover the phase information of the signal.Among the many PR algorithms,the amplitude-based PR algorithms have obvious advantages in terms of recovery rate and computational complexity.However,this type of algorithms still have problems such as changes in gradient components,slow processing of large-scale data,poor recovery of sparse signals,and poor recovery near the limit of information theory.Based on the amplitude flow PR algorithms,this dissertation adopts an optimization theoretical framework,combined with convex optimization theory and statistical signal processing,to carry out further research on PR algorithms.This dissertation has contributions to the performance improvement of PR algorithms,large-scale signal recovery and sparse signal recovery,mainly including the following:(1)Stochastic PR algorithm based on reweighted amplitude flow is proposed.As the scale of data continues to increase,existing algorithms can no longer meet the requirements for accurate recovery and rapid convergence.Based on the in-depth study of the reweighted amplitude flow,a stochastic PR algorithm based on the reweighted amplitude flow is proposed.This algorithm improves the initialization method through the stochastic variance reduction algorithm,and combines the stochastic gradient method and the reweighted gradient descent method to realize the rapid recovery of the signal phase,and finally improves the overall performance of the algorithm.Comparative experiments verify the effectiveness and superiority of the improved stochastic reweighted amplitude flow algorithm in terms of recovery rate,convergence speed and robustness.(2)PR algorithm based on smoothed amplitude flow is proposed.This algorithm first proposes a smoothing scheme for amplitude flow based on the non-convex and non-smooth characteristics of PR loss function;secondly,obtains the initial estimated value through the maximum correlation initialization algorithm;finally develops an adaptive gradient descent method to obtain the global optimal value.A large number of comparative experiments show that the smoothed amplitude flow algorithm has obvious advantages in terms of recovery rate,convergence speed and computational complexity.(3)Stochastic PR algorithm based on smoothed amplitude flow is proposed.Aiming at the characteristics of large-scale data environment,a stochastic smoothed amplitude flow PR algorithm is improved on the basis of the smoothed amplitude flow algorithm.The stochastic gradient method is combined with the smoothed amplitude flow to effectively avoid the algorithm falling into a saddle point or local optimal value.A large number of comparative experiments show that the stochastic smoothed amplitude flow algorithm performs well in terms of recovery success rate,iteration speed and computational complexity.(4)Sparse PR algorithm based on greedy autocorrelation is proposed.Based on the in-depth analysis of the greedy sparse PR algorithm,an improved greedy autocorrelation Fourier PR algorithm is proposed.The iterative process is promoted by combining the Levenberg-Marquardt algorithm and the alternate algorithm,and the best estimate is finally obtained.Compared with the original algorithm,the greedy autocorrelation sparse PR algorithm has good performance in terms of recovery probability,robustness to noise and stability.(5)Sparse PR algorithm based on smoothed amplitude flow is proposed.Based on smoothed amplitude flow,a PR algorithm in a sparse environment is proposed.Through the estimation of the support,the maximum correlation initialization method and the gradient descent method with hard threshold,the sparse estimation value is finally obtained.The comparative experiment proves that compared with the existing sparse PR algorithm,the recovery performance and convergence speed of the sparse smoothed algorithm are significantly improved,and it has good robustness.