A Study Of Compressed Sensing Algorithm For CT Image Reconstruction

As one of the most important tools for modern clinic imaging, computed tomography is able to reconstruct the tomographic image inside human body. It has also widely been used in many fields such as industrial detection, safety inspection. As the core of CT, image reconstruction problem is always a hot topic for engineers and scholars in this area. The CT image reconstruction algorithms with incomplete projection data conditions can reduce the radiation dose, shorten the scan time,and hence reduce the radiation injury caused by X-ray which is very important for human body. The traditional analytical algorithms have been the mainstream in CT field for decades due to the advantages of small computation, fast speed, but increasingly unable to meet the radiation dose requirement in modern medical imaging. Meanwhile, the traditional iterative methods can not meet the accuracy and speed requirements for the medical diagnosis. Compressed sensing therory proposed by Candes et al. has mathematically proved that, one can sample the signal in the low dimensional space based on sparsity prior information and then reconstruct the original signal accurately. CT reconstruction algorithms based on compressed sensing theory, are often able to reconstruct the image with higher quality by using fewer projections.In this paper, the CT imaging principle and several image reconstruction algorithm are studied with the widely used third-generation CT scanner as the model. First, the introduction of CT development and imaging principle is presented, and the traditional analytic reconstruction algorithms are reviewed. Then the basic principles of iterative reconstruction and a few algorithms are introduced. Consider the problem that huge projection matrix is not easily stored and processed, an optimization storage scheme based on sparse matrix is proposed and then proved to be efficient with the experiments. At last, the CT image reconstruction problems in the context of compressed sensing are studied, and an improved first-order algorithm based on NESTA using the Bregman method is proposed and applied to sove the CT reconstruction problem.Experimental results show that, the proposed algorithm can reconstruct high-resolution images with only a small amount of projection data when applied to solve fan-beam CTimage reconstruction problem in sparse-view condition. What’s important, the new algorithm has better convergence guarantee with comparison to the original algorithm.