Research On Phase Retrieval At High Degradation Level

In recent years,with the booming development of deep learning techniques,neural network models have been widely used in various aspects of the real world.In this thesis,a novel solution that combines deep learning techniques with the phase retrieval problem is investigated.The phase retrieval problem refers to the fact that the sensor devices relied on by coherent diffraction imaging techniques can only capture the amplitude information of the diffracted image in practical situations,while the phase information in the captured signal is completely lost.This realistic technical obstacle greatly limits the further development of coherent diffraction techniques and poses a great challenge to generate high-quality phase and amplitude information.To solve the problem,three main works are carried out in this thesis as follows:With the in-depth study of neural network models,researchers have gradually opened up the cross research direction of combining neural network models with various different subfields.Based on this basic idea,this thesis selects phase retrieval,which is an important challenge in the field of optics and new materials,as the entry point for research,and carefully examines the background of the problem and the current technical bottlenecks.By analyzing the characteristics of this problem,we design a novel neural network architecture,named(47)-Net,which can simultaneously separate and reconstruct the phase and amplitude information of the raw mixed signal.Since the design of the(47)-Net architecture takes into account the characteristics of the phase retrieval problem,numerical experiments also show that the network architecture designed in this thesis can obtain more robust and high-quality signal reconstruction results not only in the case of single diffraction,but also in the case of sparse sampling.One of the challenges facing the neural network model is the large number of parameters and the complex structure of the model,which makes the neural network model more like a "black box" and makes the study of its interpretability difficult.In this thesis,we analyze the impact of different types of activation functions on solving the phase retrieval problem and the impact of different number of downsampling layers on the problem,taking the activation function and the number of downsampling layers as the starting point.Since the phase retrieval problem generates a large number of negative pixel values in practice,it is beneficial to design a neural network model with incomplete negative inhibition to solve the problem.Moreover,since the mixed signal contains more information,if the number of downsampling layers is too many,the information will be lost;while too few downsampling layers will cause insufficient condensation of information,which will affect the reconstruction effect of the signal.By analyzing the two characteristics of the above neural network model and the corresponding numerical experimental results,this thesis provides a new design idea for the subsequent design of the network architecture to solve the phase retrieval problem.A large number of mathematical optimization methods have been proposed for the mathematical model abstracted from the phase retrieval problem and have achieved a series of remarkable results.However,model-based optimization algorithms often face problems such as time-consuming and high model complexity.In this thesis,we propose a new solution by combining the neural network model and the mathematical model of the phase retrieval problem with the Plug-and-Play architecture as the general framework: the neural network model is inserted into the phase retrieval model as a regularization term and solved by the alternating direction method of multipliers.The proposed solution can strengthen the interpretability of the neural network model by solving the optimal model on the one hand,and better reconstruct the phase signal and amplitude signal by the data-driven feature of the neural network model on the other hand.Numerical experiments show that the algorithm framework proposed in this thesis has a good reconstruction effect.Through the study of the above problems,this thesis constructs a novel network architecture and algorithm architecture based on deep learning,and also explores the interpretability of deep learning,which has some fundamental role for the subsequent research in this field.