Research On Image Compressed Sensing Reconstruction Algorithm Based On Prior Regularization

Compressed Sensing(CS)theory is a more efficient image compression technology by sampling and compressing images at a low sampling rate at the same time and recovering the original images with a small amount of observed values.The CS theory points out that on the premise of image sparsity,the observation matrix irrelevant to the sparse basis can be used to observe the image,and then the original image can be recovered by the reconstruction algorithm.Since CS reconstruction is an ill-posed inverse problem,if a prior regularization constraint term is added to the reconstruction model,the unique solution can be obtained through the space of the constrained model solution.Therefore,the reconstruction algorithm is the key to guarantee the accurate reconstruction of images,and the prior information of images is the key to guarantee the excellent performance of the reconstruction algorithm.Therefore,this thesis conducts an in-depth study on image CS reconstruction algorithm based on image prior information.The main research contents and innovation work are as follows:1.In order to reconstruct the original image efficiently from the damaged data,this thesis proposes an image CS reconstruction algorithm based on hybrid weighted total variation and nonlocal low rank.Based on the prior information of local smoothness and nonlocal self-similarity,this algorithm improves the traditional hybrid total variation model.First,the first-order total variation model is weighted by using the weight coefficient of differential curvature construction.At the same time,the average curvature is used to construct the edge detection operator,and a term of the first-order and second-order total variations is selected through the threshold value adaptively,acting on the image edge region and the smooth region respectively,so as to protect the image edge and avoid the occurrence of the staircase effect.Then,the prior regularization terms are constructed with the improved hybrid weighted total variation and nonlocal low-rank as constraints to improve the applicability of the reconstruction algorithm.Simulation results show that compared with the classical CS reconstruction algorithms,the proposed algorithm has better image structure protection performance and noise resistance.2.In view of the problem that traditional image CS reconstruction algorithm based on nonlocal low-rank ignores the differences between image patches and image structure features,which leads to poor image reconstruction effect,this thesis proposes an image CS reconstruction algorithm based on adaptive nonlocal low-rank.This algorithm proposes an adaptive construction method of low-rank matrix,which is to construct an appropriate data matrix of similar patches based on the number of similar patches adaptive matching,search window adaptive matching and new similar patch matching for different structural regions of the image,so as to improve the low-rank characteristic of the data matrix.In addition,the weighted Schatten p-norm is used to approximate the original rank function to obtain the optimal solution of the low-rank matrix optimization problem.Simulation results show that the proposed algorithm has better reconstruction performance than the comparison algorithms.