Compressive Sensing Reconstruction Method Based On Bayesian Theory

Compressive Sensing is a new sampling theory, which has received universal attention in the theory and application. Sparse signal reconstruction is one of the core problems in Compressive Sensing. And there have been many algorithms about it. However, how to effectively improve the quality of signal reconstruction in presence of noise is always one of the issues to be resolved. Therefore, according to this problem, the paper introduces Bayesian estimation into the CS reconstruction and has studied the CS reconstruction algorithm. And as the wavelet basis is not enough sparse which lead to the Bayesian recovery effect is not ideal, the novel adaptive sparse representation is introduced to the BCS. At the same time, the paper puts forward the reconstruction combined the Adaptive sparse representation with Sparse Bayesian Learning. In this paper, the main research work is as follow:1. As sparse prior model is a major problem in BCS, this paper gives a detailed introduction on Relevance Vector Machine hierarchical model and Laplace hierarchical model.In order to verify the algorithm, the simulation experiment is done, using the Maximum A Posteriori estimation to analyze Wavelet coefficients of the image in the two sparse prior model. The paper compared the reconstruction effect of proposed algorithm with that of OMP algorithm and GPSR algorithm. The simulation results show that BCS reconstruction based on two kind of sparse prior gets better results in the larger observation noise situation.2. For the same scenes or the same graphics, multitasking Bayesian Compressive Sensing can achieve good reconstruction by less sampling compared with the single task. The paper combines multi-tasks with Bayesian compressive sensing using joint sparse approximate idea, and tasks share a common a prior model. As improper initial selection of the noise parameters is the key issue affecting the algorithm performance, the parameters in the Posteriori likelihood function can be replaced with multivariate Student-t distribution, instead of the multivariate Gaussian distribution, which can avoid the estimation of noise parameters. And only the sparse parameters are needed to estimate in the iterative. As the sampling rate is 20%, Reconstruction experiments take three tasks, whose PSNR average increases about 3d B, compared to the single task.3. As the problem of wavelet basis is not sparse enough, the studies a method combined adaptive dictionary learning with Sparse Bayesian Learning reconstruction method. The method uses the idea of alternate iteration to converge to the solution step by step. And a more accurate image is obtained after several iterations. In each iteration, the paper divides the image into small blocks, and utilizes these blocks to get a dictionary which is the sparse basis of this reconstruction. Then, a sparse recovery model is build. At last, the paper solves this module using by SBL. Simulation results show that compared to BCS reconstruction algorithm based on wavelet, the proposed algorithm can get better results.