Research On Compressed Sensing Image Reconstruction Algorithms Based On Nonlocal Similarity

Traditional signal acquisition theorem points out that in order to achieve undistorted recovery of the original signal,the signal acquisition rate must be more than twice the bandwidth of the signal to be sampled.However,with the rapid development of modern information science and technology,the bandwidth of the signal to be processed becomes wider and the amount of information is increasing,which undoubtedly brings great challenges to signal sampling,transmission and storage.Compressed sensing is a pioneering theory of signal acquisition.The basic idea of this theory is to project sparse or compressible high-dimensional signals into low-dimensional observations through appropriate observation matrices,and restore the original signals completely by designing reconstruction algorithms.The great advantages of compressed sensing theory lie in: 1)there is no requirement for sampling rate,and the original signal can be recovered from the lower observation value,which reduces the requirement for acquisition hardware,and also reduces the pressure of data storage and processing after acquisition;2)the combination of signal sampling and compression process improves the efficiency of signal acquisition.The emergence of compressed sensing theory has caused a sensation in the field of signal processing,and has rapidly become a research hotspot.There are three key steps in the process of compressed sensing: the sparse representation of signals,the design of observation matrix and the design of reconstruction algorithm.As the core part of compressed sensing,the reconstruction algorithm directly affects the quality of signal recovery,and relates to whether compressed sensing can be applied in practice.Image restoration has always been a research hotspot in the field of signal processing.The emergence of compressed sensing theory further promotes the research of image restoration.As a special signal,the internal structure of the image has strong correlation.Making full use of the structural characteristics of the image as prior information can improve the quality of image reconstruction.The image has self-similarity in the non-local region,and the image reconstruction algorithm based on the non-local self-similarity has achieved good image reconstruction results.Based on the self-similarity of non-local regions of images,this thesis mainly studies the mathematical model and algorithm of image reconstruction.Essentially,in the process of solving the mathematical model of non-local low-rank compressed sensing image reconstruction,the general approach is to transform the image reconstruction process into solving the rank minimization problem of similar block matrices.The rank minimization of matrices is a very difficult problem,and people usually use the approximate rank function of the kernel norm to solve it.However,when the singular value is large,the nuclear norm approximation will lead to a large deviation of the results.In this paper,a compact inverse tangent function and hyperbolic tangent function are used to approximate rank function.A non-local low-rank compressed sensing image reconstruction algorithm based on compact rank approximation is proposed.A large number of simulation result show that the proposed algorithm is effective.Regardless of subjective vision or objective evaluation criterion PSNR,the quality of reconstructed image is better than the current representative compression sensing reconstruction algorithm.Furthermore,considering that the current reconstruction algorithms based on nonlocal similarity of image blocks do not perform well in noise environment.In order to improve the reconstruction performance of non-local low-rank algorithm,a measurement noise minimization term is added to the non-local self-similarity model.In this thesis,a low-rank compressed sensing image reconstruction model of non-local similar blocks with additional noise terms is established,and an algorithm for solving the model is given.According to the different distribution of measurement noise,different noise models are used to fit measurement noise.By reserving space for measurement noise,the restored image can approach the original image more closely.The results show that the proposed algorithm can reconstruct many natural images with complex texture details and different structures from a small number of observations under different types and different levels of measurement noise.Compared with the main image reconstruction algorithms,the proposed algorithm has better reconstruction performance in noisy environment.