The Research Of Compressed Sensing Algorithm And Application Based On The Cosparse Analysis Model

Using more prior knowledge of the image to improve the reconstructed image quality is still a crucial issue of compressed sensing. At present, overcomplete sparse representation of the image consists of two models: the synthesis sparse model and the cosparse analysis model. This paper focuses on learning two sparse representation models and reconstruction algorithms of compressed sensing. The main contents are as follows:First, combining synthesis sparse model and cosparse analysis model, the paper proposes a novel reconstruction algorithm based on the sparsity of image over a synthesis dictionary and an analysis dictionary, and respectively uses l0-norm, l1-norm and lp-norm(0<p<1) as the measure of sparsity. The experimental results show that the algorithm fused two sparse priors is better than the algorithm used only a single prior.Secondly, taking into account the adaptive problem between image and sparse dictionary, the paper proposes a reconstruction algorithm based on the adaptive dictionary and two sparse models. The algorithm uses the observations of image to learn adaptive dictionary and utilizes the sparsity of patches in any position of th e image. It overcomes the blocking artifact and improves the quality of image reconstruction effectively.Finally, the synthesis model and the cosparse analysis model are applied to the reconstruction of MR image. A novel algorithm based on adaptive dictionary and two sparse models is proposed. In this algorithm, the influence of noise is also considered. The experimental results show that the algorithm can effectively improve the quality of MR image reconstruction, and has certain robustness in case of noise.