Regularized Classic Phase Retrieval From Noise Pollution Measurements

The phase and the magnitudes of the signal or image are the important basis for the researchers to determine the correct signals.But practically,the general optical detection devices can only measure the magnitudes of the Fourier transform of the signal or image,which is often polluted by noise.This affects the researchers accuracy in judging the signals.This paper aims to recover the phase from Fourier transform data,which is contaminated by white Gaussia.n noise.This paper is divided into two parts:The first part is the regularized phase retrieval from white Gaussian noise pollution measurements for real-valued images.Based on the intensity mea-surements,the least square model and the total variation regularization model are established,which are referred to as "LSB" and "TV" respectively.The proposed models can be solved effi-ciently by an Alternating direction method of multipliers(ADMM).which is convergent under the weaker conditions with the help of the advanced optimization theory.Finally,the correctness of the proposed methods is verified by a large number of numerical examples,and it is also proved that the model can fully recover the high-quality image from the noise data.The second part is the regularized phase retrieval from white Gaussian noise measurements in the complex field.Previously,the researchers demonstrated that three sets of data were needed to fully recover the real-valued image.However,it takes four sets of data to restore a complex image in the complex domain.This paper aims to restore a high-quality complex image by using three sets of data.Two models in the complex domain are established:the LS model and the TVB model.In order to reduce the computational cost of the algorithm,the proximal ADMM algorithm is used to solve the TVB model.Finally,numerical examples are used to verify the validity of the conclusion that only three sets of data can be sufficient to restore a higher-quality complex image.