The Research Of Phase Retrieval Algorithm Based On Nonlinear Compressed Sensing

Nonlinear compressed sensing,namely,recovers a signal from its nonlinear observation data.Phase retrieval is a particular case of nonlinear compressed sensing problem,in other words,it utilizes the magnitude of the Fourier transform,or any other linear transform to recover the signal.Due to the detector can only record the magnitude,lose phase information after the signal transform,phase retrieval is ill-posed.In this paper,we study how to use the observation data of less information to recover the original signal,the main contents are follows:Firstly,in the near field,a phase retrieval algorithm which exploits the statistical characteristic of the higher-order Markov random fields,also called the Fields of Experts(FoE)model is proposed based on the Fo E regularization.The algorithm incorporates the FoE regularizations into the phase retrieval problem which contains amplitude constraints and support constraints.Experimental results show that the algorithm can reconstruct the real image and the phase image,as well as improve the quality of the complex image in low sampling rate.Secondly,to enable prefect reconstruction of the complex images in the coded diffraction imaging system,this paper persents some different methods including the complex image regularization,only the amplitude of the image regularization as well as the amplitude and phase of the image regularization to construct the minimization problem based on the prior of Fo E separately.Moreover,the Heavy-Ball algorithm is utilized for solving the corresponding non-convex optimization problem.Experimental results show that when the data fidelity term combines magnitude regularization as well as phase regularization as cost function,the reconstructed image quality is best.This algorithm improves the reconstructed image quality and is robust to noise.And it also reduces the amount of observation data and the time of observation data effectively.Finally,in view of the observation data by poisson noise,considering the sparsity of image under the dual-tree complex wavelet transform as prior,a phase retrieval algorithm is presented based on dual-tree complex wavelet transform.The algorithm incorporates the data fidelity term and the regularizations to construct the minimization problem.The IPIANO algorithm and the ADMM algorithm are used to slove the optimization problem.Experimental results show that the proposed algorithm can keep more marginal structures and detail information of the real image.