Research Of Phase Retrieval Algorithms Based On Non-linear Compressed Sensing And Deep Priors

Phase Retrieval(PR)refers to the problem of recovering signal from noisy amplitude--only of its Fourier transform,or other linear transform.It is an urgent problem to be solved in the fields of diffraction imaging,X-ray crystallography and astronomy.However,imaging system can only measure the amplitude and intensity of the Fourier spectrum,and cannot capture the phase information,which contains most of the structure information in the image.Due to the lack of phase information in the observed measurements,the PR problem is a typical ill-posed problem.How to solve this problem effectively has always been an important research direction.The existing PR algorithms can reconstruct high-quality images in an ideal environment,but in low sampling rate and the presence of noise,there are problems of low quality reconstructed images and sensitivity to noise.Therefore,based on non-linear compressing sensing theory and deep learning technology,this dissertation focuses on the research of effective PR algorithms by exploiting image priors knowledge to reconstruct high-quality images from low sampling rate or noisy measurements.The concrete research contents and innovative achievements are as follows:Firstly,to address the problem of low resolution and serious artifacts of the reconstructed image when the high frequency interference fringe information of measurement data is missing in coherent diffraction imaging,a resolution enhanced phase retrieval algorithm is proposed based on sparsity.The proposed algorithm poses the sparse priors of the image itself as the regularization term and utilizes the mask to expand the restricted record region in imaging system to reconstruct the missing high-frequency component information and phase information during the iterative optimization process,and then realizes the reconstruction of high-resolution images from the phase-free measurement data with missing high-frequency interference fringe information.Simulation and optical experiments verify the effectiveness of the proposed algorithm.Secondly,aiming at the problem that the hand-crafted prior is not accurate to depict the natural image,utilizing the powerful representation capabilities and universal approximation characteristics of convolutional neural networks,the dual priors approach is proposed to solve the PR problem based on deep priors and total variation(TV).Firstly,a phase retrieval model based on the mixed regularization term is constructed,and an optimization algorithm is utilized to solve the model.To further improve reconstruction performance,we propose a two-stage dual priors PR algorithm.The proposed algorithm first utilizes the internal gradient sparsity of the image to recover the edge information and contour parts of the image.Then,an external image priors from deep denoiser is implicitly utilized to further recover richer details of the image based on a plug-and-play framework.The proposed algorithms utilize the ability of TV to model edge and contour information and the potential of deep convolutional neural network to model local information,and realize the effective fusion of internal priors and external priors through the two-stage framework.The experimental results show that the reconstruction performance using double prior algorithm is better than those based on any single prior algorithm.Thirdly,aiming at the problem that deep denoiser prior is lack of adaptability to content in practical application,an efficient hybrid model-based and data-driven approach is proposed to solve the PR problem with adaptive learned deep priors.The proposed approach replaces the prior projection operator in alternating projection with the elaborated trainable convolution neural network,and truncates and unfolds the iterative process into a deep network HIONet.The prior projection module in HIONet adaptively learns the inherent image priors from large-scale training data,promoting the phase retrieval network to reconstruct the high-quality image.In addition,the expression capability of the network is enhanced by exploiting feature fusion,and the improved network HIONet~+is proposed.Experiment results confirm the reconstruction performance and robustness of the phase retrieval networks.Finally,aiming at the problem of low reconstruction quality and poor robustness to noise under low sampling rate,a zero-shot phase retrieval algorithm based on the diffusion prior is proposed,namely Diff MPR.The proposed algorithm utilizes the image manifold prior implicit in the unconditional pre-trained diffusion model to improve the reconstruction quality of noisy measurement data with low sampling rate.The consistency constraint of the measurements is introduced into the sampling process of the diffusion model,and the reverse diffusion of the denoising diffusion model is guided to generate some natural images conforming to the constraints of the measurement subspace,and a high-quality reconstructed image is generated by iterative sampling.Experimental results demonstrate that the proposed algorithm is effective and robust to noise for the reconstruction task of coding diffraction pattern with low sampling rate.The effectiveness of the proposed algorithms are verified by a large number of experiments on public general image datasets.Experimental results show that compared with traditional optimization methods and deep learning methods,the proposed algorithms have obvious advantages in reconstruction quality and robustness to noise.