| Phase retrieval refers to the problem of restoring the phase of the original signal by measuring the magnitude without any phase information.Regarding the loss problem of the phase information during the actual signal observation and transmission process,two algorithms for a one-dimensional long signal and image based on the uniqueness of short-time Fourier transform magnitude measurement are proposed.The main research contents are as follows:(1)For the problem that the STFTPR phase retrieval algorithm can only recover one-dimensional short signal,a phase retrieval algorithm of a long signal based on the STFT magnitude is proposed.The goal of this algorithm is to recover the phase vales of long signal without any phase information.First,the one-dimensional long signal is converted into multi-length short signals.Then the initial iteration value of the gradient descent method(GD)is obtained.And each group of convex loss functions is minimized,and eventually converges to the global minimum.This algorithm is a non-convex optimal phase retrieval algorithm.At the same time,the penalty term is introduced into the derivation process of the algorithm,and the over-fitting degree of the objective function is reduced by the constrained optimization after the weighted processing.At the same time,the generalization index of the function is improved.The experimental results show that the algorithm has a good performance by comparing with the classical phase retrieval algorithm based on STFT magnitude measurement.The phase retrieval performance of the algorithm has been improved obviously.The final RRMSE(n=1000 and SNR=25d B)is relatively less.(2)On the basis of the phase retrieval algorithm of the one-dimensional long signal based on STFT magnitude measurement,considering the wide application of phase retrieval in real life,a phase retrieval image algorithm based on the STFT magnitude measurement is proposed.Compared with convex phase retrieval algorithms of Phase Lift and Phase Lamp,the proposed algorithm can recover the phase information of the images with clearer contours,and hold stronger robustness and higher peak signal-to-noise ratio.At the same time,NL-means algorithm is introduced into the algorithm,which image restoration can get preferable results by weighting the adjacent area blocks of the image after phase retrieval. |
