Research On Image Reconstruction Algorithms Based On Compressive Sensing

Compressive sensing is a novel paradigm for acquiring signals and has a wide range of applications. The basic assumption is that one can recover a sparse or compressible signal from far fewer measurements than traditional methods. The difficulty lies in the construction of efficient recovery algorithms. In this thesis, we review two main approaches for solving the sparse recovery problem in compressive sensing: l 1-minimization methods and greedy methods.In this paper, properties of the Compressive Sensing theory and the existing reconstruction algorithms are firstly analyzed. Based on that, the main contributions of this paper are summarized as follows. An improvement scheme for Approximate Message Passing algorithm is given, and one new scheme is presented to solve sparse reconstruction with noise measurement. Approximate Message Passing algorithm is presented by introducing both message passing algorithm and iterative thresholding algorithm to solve sparse reconstruction problem without noise measurements. Such schemes can have very low per-iteration cost, low storage requirements and low error. This paper improvements the iterative thresholding function by adaptive thresholding method. More effective thresholding point could to be found in the new algorithm. The algorithm has quickly rate of convergence, shorten the running time and lower the running error.Next, a new Random Coordinate Descent Algorithm is presented to solve sparse reconstruction. Base on both pathwise coordinate descent algorithm and greedy coordinate descent, the new algorithm is presented by introducing random update variables on huge-scale optimization problems. Random coordinate descent algorithm is good suitable on huge-scale optimization sparse reconstructions of compressive sensing. We prove the global estimates for the rate of convergence on compressive sensing. For certain huge-scale of objective functions, our results are better than the other algorithm, and confirms a high efficiency of random on problems of very big size.