Research On Phase Retrieval Method Under Non-ideal Measurement

The phase retrieval(PR)problem is a classic inverse problem in the field of signal processing.This problem studies how to recover the original signal from amplitude-only linear measurement data.It has attracted much attention because of its wide application background.Although the phase retrieval theory under ideal measurement has been gradually refined,it is often difficult to meet the ideal measurement model in many practical applications.The phase retrieval method under non-ideal measurement is still a topic that needs to be further studied.The reasons for the non-idealization of the measurement can be divided into two categories:(1)the influence of external outliers and noise;(2)the mismatch of the internal model.In this paper,for the influence of external outliers and noise,phase retrieval methods against outliers or noise are proposed for both discrete phase retrieval and continuous phase retrieval problem.Then,for the mismatch of the internal model,the cause and correction will be analyzed,and take the PR-based Inverse Synthetic Aperture Radar(ISAR)imaging application as an example,analyze its model mismatch and propose a specific mismatch correction method.The specific research content is as follows:1.Research the basic model and reconstruction methods of phase retrieval problem,investigate the existing phase retrieval algorithms,master the development history,application background,model classification and reconstruction principle of phase retrieval problem,providing a theoretical basis for the research of phase retrieval problem under non-ideal measurement.2.Research the anti-outlier discrete phase retrieval method.Aiming at the problem that the phase retrieval algorithm in the discrete domain is sensitive to outliers,a new phase retrieval measurement structure is proposed to estimate the rough information of the outliers and use it as a weight to assist the phase retrieval reconstruction.A reconstruction algorithm introduced weight information is proposed to suppress the influence of outliers in the reconstruction to obtain higher reconstruction accuracy.Numerical simulation is performed to verify the outlier robustness of the proposed algorithm.A hardware platform is built to verify the practical feasibility of the proposed measurement structure.3.Research the anti-noise continuous phase retrieval method.Aiming at the problem that the phase retrieval algorithm in continuous domain is sensitive to noise,by analyzing the current phase retrieval theory in the continuous domain in terms of the limitation of scattering function and redundant parameters,an improved parameter estimation method is proposed to relieve the limitation of the scattering function.Eliminating parameter redundancy improves the noise robustness of the continuous phase retrieval method.Numerical simulation is performed to verify the effectiveness of the proposed method.4.Research the correction of phase retrieval model mismatch.Aiming at the problem that the internal model mismatch in practical applications can easily cause the phase retrieval failure,analyze the reasons for the model mismatch and the correction ideas,and take the PR-based ISAR imaging as an example to analyze the internal model mismatch in the measurement process.We propose a more streamlined and accurate phase retrieval ISAR model to eliminate mismatch.To compensate for the increase in the difficulty of solution which caused by the simplicity of the model,a radar signal waveform design scheme is proposed to make the phase retrieval map formed as close as possible to the single shot to obtain the highest possible successful reconstruction rate.Then We integrate the overall imaging framework,and verify the effectiveness of the proposed imaging framework and its sensitivity to key parameter estimation errors through numerical simulation.The performance of the proposed method is evaluated by being compared with the existing ISAR imaging methods.