Research On Novel Models And Algorithms For Phase Retrieval Of Structured Signals

The research on phase retrieval problems begins in the middle age of the 20th cen-tury,which has quite a long history.Due to the complexity of the problem,there is no satisfactory solutions to the problem in the theoretic or algorithmic ways.In recent,it is an innovate and effective routine to utilize priors of signals such like sparsity,smooth-ness to construct models and algorithms.We propose three novel phase retrieval models which are specified for reconstructing generalized sparse binary signals,natural image and sparse signals.The Simulated Annealing Sparse PhAse Recovery?SASPAR?algorithm for recon-structing sparse binary signals from their phaseless magnitudes of the Fourier transform is presented.Sufficient numeric simulations indicate that the method is quite effective and suggest the binary model is robust.The SASPAR algorithm seems competitive to the existing methods for its efficiency and high recovery rate even with fewer Fourier measurements.We also presents a novel generalized phase retrieval model for natural images regu-larized by the anisotropic TV regularizer.The efficient and carefully implemented alter-nating stochastic coordinate descent?ASCD?algorithm is proposed for this model.The proposed regularizer,as the prior,results in natural image signals being able to be approx-imated with fewer measurements but also brings in bias to the model.Therefore,based on the results of simulations,an empirically adaptive penalty strategy is given to enhance the convergence speed and accuracy significantly.One of the efficient methods for reconstructing signals from its phaseless measure-ments is phaselift with L₁ regularizer to convert the original problem to a semi-definite programming problem.In order to reduce the modeling bias brought by L₁ regularizer,we introduce the phaselift model with the partial L₁ regularizer.Existence,uniqueness and stability are also proved.