Image Compressed Sensing Reconstruction Based On Nonlocal Self-similartity Model

Compressed sensing theory is a more concise image sampling compression tool,which breaks the sampling ratio limitation of traditional Nyquist sampling theorem.For the sparse signal or the sparse representation signal,the signal is sampled at a ratio much less than the signal bandwidth by 2 times.It accurately reconstructs the original signal by obtaining a small number of measurements and according to the corresponding reconstruction optimization algorithm.The way to reconstruct the original image from a small number of measurements is an ill-posed inverse problem.With the utilization of the priori model of the natural image,the solution space can be regularized and constrained to approximate the real solution.In particular,image prior information plays a key role in the reconstruction algorithm.Therefore,this thesis focus on the compressed sensing reconstruction algorithm from the nonlocal self-similarity prior model of the image.The specific research contents are as follows:1.To solve the problem that the traditional compressed sensing algorithm based on total variation model cannot effectively restore details and texture of image,which leads to over-smoothing of reconstructed image,an image CS reconstruction algorithm based on structural group total variation model is proposed.The proposed algorithm utilizes the nonlocal self-similarity and structural sparsity of image,and converts the CS recovery problem into the total variation minimization problem of the structural group constructed by nonlocal self-similarity image blocks.In addition,the optimization model of the proposed algorithm is built with regularization constraint of the structural group total variation model,and utilizes the split Bregman iterative method to separate the algorithm into two sub-problems,and then employs the steepest gradient descent algorithm and the primal-dual algorithm respectively to solve them.The proposed algorithm makes full use of the information and structural sparsity of image to protect the image details and texture.The experimental results demonstrate that the proposed algorithm achieves significant performance improvements over the state-of-the-art total variation based algorithm in both PSNR and visual perception.2.Most existing image compressed sensing reconstruction algorithms make the sparse representation of signal by using fixed basis function,which ignore the non-stationary nature of natural images and lack adaptability,so the image cannot be properly sparse represented.Thus,these algorithms do not perform well on image detail and texture protection.To solve the above problems,this thesis proposes an adaptive image compression sensing reconstruction algorithm based on nonlocal regularization.A more efficient nonlocal regularization model is constructed by using the nonlocal self-similarity of the image.In addition,an effective adaptive dictionary learning method in the sparse representation model is used to characterize the local sparsity of the image.The algorithm constructs the objective function with the nonlocal regularization model and the sparse representation model as constraints,and the efficient solution process of the algorithm is given by using the split Bregman iteration method.The experimental results demonstrate that the proposed algorithm is more superior and has better reconstruction performance than the current mainstream algorithms.