The Research Of Phase Retrieval Algorithm Based On Non-convex Optimization And Deep Learning

Non-convex optimization is the research frontier of optimization,recent years have seen a flurry of activities in designing provably efficient non-convex procedures for solving statistical estimation and machine learning problems.In addition,the rise of deep learning has greatly improved the accuracy and speed of algorithms based on supervised learning in computer vision.As a typical non-convex problem,how to combine nonconvex optimization with deep learning to construct an effective solving algorithm has always been a difficult problem in this field.The concrete research contents and innovative achievements are as follows:Firstly,in order to solve the phase retrieval problem in the coded diffraction model,the proposed method,named Two-Agent Consensus Equilibrium(TACE),is a coded diffraction imaging algorithm based on consensus equation.In this algorithm,the proximal operator of the corresponding data fidelity term in the coded diffraction model and blind denoising operator are placed in the consensus equation as the optimization equation to be solved.The iterative algorithm results the proximal operator of the data fidelity term and the blind denoiser tend to nash equilibrium point.Multi-Agent Consensus Equilibrium(MACE)is guaranteed to converge under mild conditions.The numerical and visual experiments show that the algorithm can recover more details,textures,etc.information and has obvious advantages in reconstructing real images.Secondly,in order to solve the phase retrieval problem faced to large-scale coded diffraction patterns,the proposed method,named Consensus Equilibrium with Stochastic Optimization(SOCE),is an accelerated coded diffraction imaging algorithm based on first-order stochastic optimization.The algorithm utilizes the separable features of the observations and solves them using the first-order stochastic optimization algorithm,selecting a subset of coded diffraction patterns randomly at each iteration to calculate the gradient of the data fidelity term,which can be seen as an accelerated version of the TACE algorithm.The results of numerical and visual experiments show that the algorithm can effectively deal with large-scale coded diffraction patterns.Finally,in order to solve the problem of low reconstruction quality of existing compressive phase retrieval algorithms under under-sampling rate,the proposed method,named Deep Phase Retrieval with Regularization by Denoising(DPR-RED),is a compressive phase retrieval algorithm based on Deep Image Prior fused Regularization by Denoising(RED)term.The algorithm adds the displayed RED prior as a regular term to the implicit deep image prior loss function and uses the Alternating Direction Method of Multipliers(ADMM)algorithm to solve it effectively.The numerical and visual experiments show that the algorithm can reconstruct high-quality images under the under-sampling rate and is robust to Gaussian and Poisson noises.