Alternating Direction Method Of Multipliers For Phase Retrieval With TV And Wavelet

Thephaseretrievalproblemistorecoverthesignalfromthesignal’sFouriertrans-form module. This problem is widely used in the felds of X ray difraction imaging,astronomical imaging and optics. Being lack of the phase information, this inverseproblemisillposed, butwithenoughFouriertransformmodulusmeasurements,phaseinformation can be recovered by solving a series of equations. To recover the signal,there is a non-zero compact support in real space, the support set constraint and theFourier module constraint combine to make a feasible algorithm to solve this problem.The simplest is ER and the alternating projection method proposed by Gerchberg andSaxton, these methods have been widely expanded. The most signifcant developmentis the HIO algorithm proposed by Fienup, which is still widely used. Bauschke, Com-bettes and Luke discovered the relationship between ER, HIO and classical convexoptimization algorithms and proposed the HPR algorithm. Luke put forward RAARalgorithm, which is more efective than HIO and HPR. Other methods include saddlepointoptimizationalgorithmproposedbyElseranddiferencemapalgorithmproposedby Machesini.Ptychographic phase retrieval problem is a new difraction tomography technolo-gy, which can be used to restore the original image from a group of difraction patterngenerated from moving the probe. The probe can detect a portion of the image oncea time. When the overlap region of the probe’s detection images is large enough, wecan use phase recovery methods or unconstrained optimization algorithms to solve thisproblem.In order to solve these two problems, this paper adds total variation and waveletto the objective function on the basis of the existing algorithm, and then uses the AD- MM to solve the problem. The improvement increases the algorithm’s tolerance tonoise, ensures the recovered signal’s smoothness and sparsity. Finally, the numericalexperiments verify the efectiveness of this improvement.