The Research Of Compressed Sensing And Phase Retrieval Algorithms Based On Adaptive Sparse Representation

Acquiring,processing and transmitting the information efficiently is of great importance to the scientific progress.As a carrier of information,the image is usually sampled by a high sampling rate in the traditional sampling process to guarantee the perfect reconstruction of the image.However,much measurement data not only increases the complexity of the sampling side but also increases the pressure of data transmission,processing and storage.How to reconstruct high quality images from less measurement data is a challenge.To address this issue,the adaptive sparse representation technique is utilized in this paper to study the algorithms of reconstructing images with high quality from less measurement data,which lacks the information seriously.The efficient compressed sensing magnetic resonance imaging(CSMRI)algorithm and phase retrieval(PR)algorithm are focused.The concrete research contents and innovative achievements are as follows:Firstly,to address the low reconstruction quality issue of previous CSMRI algorithms at the low sampling rate,the CSMRI algorithm based on first order approximation dictionary learning and the CSMRI algorithm of fusing the local sparsity and the plug-and-play prior are proposed.The dictionary learning method is important for image reconstruction.A first order approximation for the product of the dictionary and the coefficient in the cost function of traditional dictionary learning is performed in this paper,and a first order approximation dictionary learning method which can capture the image information efficiently is proposed.Moreover,an effective CSMRI algorithm of utilizing this dictionary learning method is proposed.According to the principle that the image should approximate its denoised version,the plug-and-play regularization model is constructed.This model is incorporated into the CSMRI based on the first order approximation dictionary learning to exploit a variety of prior knowledge for image reconstruction.The experiments validate the effectiveness of this algorithm.Secondly,to address the low reconstruction quality issue of previous PR algorithms at the low oversampling rate,the PR algorithms based on tight frame,adaptive orthogonal dictionary are proposed.The measurement data of the traditional PR contains less structure information about the underlying image.Additional image prior information is needed to guarantee the recovery of high quality images.Therefore,an algorithm based on the sparsity of the image under the TIHP(Translation Invariant Haar Pyramid)tight frame is proposed for phase retrieval.Due to the non-adaptiveness of the tight frame,the reconstruction quality of the aforementioned algorithm is low at low oversampling rates.To address this issue,the PR algorithm of exploiting the adaptive dictionary is proposed.The orthogonal structure is utilized to constrain the dictionary for reducing the computation complexity of the algorithm.The algorithm can optimize the dictionary and the image jointly only via the Fourier magnitude,and the experiments validate the effectiveness of the algorithm.Thirdly,a transfer orthogonal sparsifying transform learning algorithm is proposed,and this method is utilized for phase retrieval.Since the initial image of phase retrieval is usually random,the estimated image at the initial iteration usually contains a lot of noise.Image patches of this estimated image as training samples are bad for dictionary learning.To address this issue,the regularization term of the sparsifying transform is constructed to measure the similarity between the underlying sparsifying transform and the known sparsifying transform.The transfer orthogonal sparsifying transform learning method is proposed,and the PR optimization problem is formulated by utilizing this method.The alternating directions method of multipliers method is utilized to solve the problem effectively.Finally,for the coded diffraction pattern(CDP)sampling model,PR algorithms based on tight frame learning,group sparsifying dictionary learning are proposed to address the issues that the low reconstruction quality and the bad de-noise ability of previous PR algorithms at the few CDPs case.For the case that the data is contaminated by Gauss noise,a PR algorithm of utilizing unnatural sparse representation model,tight frame learning model for image reconstruction is proposed.The unnatural l0 sparse measure function is utilized in this algorithm to measure the sparsity of the image under the adaptive tight frame to suppress the noise component in the estimated image.For Poisson noise,a robust PR algorithm which utilizes a variety of prior knowledge for image reconstruction is proposed.The local sparsity and non-local similarity are incorporated into the image reconstruction via the group-based sparse representation,and the sparsity of the image in gradient domain is fused for image reconstruction.The utilization of a variety of prior knowledge leads to the result that the algorithm can recover the image efficiently from few CDPs.