Research On The Iterative Reconstruction Algorithms Based On Compressed Sensing

In the field of industrial nondestructive detection, limited to the object size, shape,scanning conditions and other factors, we can’t get the complete projection data. In themedical CT examination, there is also a hot issue which is how to reduce the radiation byreducing the number of projection sampling in the premise of ensuring the image quality.Because of the theory of compressed sensing, it is possible to reconstruct the image by usingless projection data. The theory uses the sparse prior information of images to improve theimage quality.Major research in the paper is as follows:(1) Based on discrete gradient sparse transform, the image reconstruction model ofcompressed sensing is given. To solve theL1minimization problem, Split-Bregmanalgorithm is introduced. There are two intermediate variables in Split-Bregman algorithm.The algorithm is useful to solve the problem ofL1minimization model. This paperdescribed the process of Split-Bregman algorithm minimizing the TV problem in imagereconstruction field. Sheep-Logan model is given to verify the feasibility of the algorithm.(2) In order to get the sparser solution, the norm in the reconstruction model isreplaced by theL p(0p1)norm to reconstruct images. Because theL p(0p1)regularization problem is a nonconvex optimization problem, the problem is converted to aregularization problem and solved by a reweighted iterative algorithm. FISTA method isused to accelerate the convergence speed. the experimental results show the influence ofoperators on reconstruction quality and the effectiveness of the algorithm.