Research On Robust Phase Retrieval Algorithms Towards Coded Diffraction Imaging System

The phase information of recorded measurements is lost in coded diffraction imaging system,which contains most of structural information of the image.Due to the phase retrieval problem is ill-posed,how to reconstruct the original image from measurements without phase information is a challenging task.In this paper,we explore the priors of images to construct regularization models,in order to address the issue of the poor image quality reconstructed by the existing phase retrieval algorithms.The main contents are as follows:Firstly,we propose a phase retrieval algorithm based on orthogonal dictionary learning,utilizing the sparse representation of natural images over orthogonal dictionary.The algorithm can learn the adaptive orthogonal dictionary that matches the image to be reconstructed through orthogonal dictionary learning,and reconstruct the target image by the strategy of alternate updating.Experimental results show that the algorithm can still reconstruct high-quality images by one coded diffraction pattern,though the measurements is contaminated by Gaussian noise.Secondly,because the ability of single dictionary to represent image blocks is limited,image blocks are clustered into several groups by K-means algorithm.Dictionaries are trained corresponding for different groups,which can exploit extra information from image database.When solving phase retrieval optimization problem with Poisson noise removal,the best sub-dictionary is selected by maximizing the projection energy,so that the error of samples represented over dictionary is reduced.Moreover the inverse problem is solved by half-quadratic splitting method.Experimental results show that the algorithm can achieve high image quality and has strong robustness under the few coded diffraction patterns.Finally,in order to improve the adaptability of multi-models in image reconstruction,the optimal parameters of Gaussian mixture model(GMM)can be trained by expectation maximization(EM)algorithm,and then an image patch can be represented optimally by choosing one of components in GMM.Based on the insight,we propose the phase retrieval optimization problem which fuses the statistical properties of GMM and datafidelity term.Moreover,accelerated proximal gradient method is utilized to solve this problem.The experiments show that the proposed method has obvious advantages at the case of measurements under various Gaussian and Poisson noises level.