Research On Reconstruction Methods Of Sparse CT Based On Compressed Sensing

The CT(Computed Tomography) technology is one of the most important detection means in the medical diagnosis field. The number of the global CT exams increases every year. The X-ray radiation in the process of CT has become the major radiation source of the modern people. Too much radiation can lead to the increased risk for cancer. Therefore, reducing the radiation dose in the CT process has become a global consensus.CS(Compressed Sensing) technology is one of the most popular signal processing paradigms in recent years. CS can provide an accurate reconstruction of the target signal with fewer measurements than the Nyquist-Shannon sampling theorem required. Introduction of CS into CT will help to reduce the CT projection ray numbers, thus to reduce the radiation dose, which has very important research and application value for human health. This dissertation focuses on the research of the sparse CT reconstruction methods, which can use the CS technology to reduce the CT projection ray numbers while maintaining the quality of the reconstructed CT images.The main points of this dissertation are shown as below:1. The information in the two spaces before and after the Fourier transform has special correspondence. By analyzing this correspondence, the phenomenon of two different sampling models in the Fourier space resulting in different reconstructions is analyzed theoretically. Thus, we propose to design the sampling model based on the structure of the sparsifying bases, which can maximize the information utilization in the sparsifying bases.2. By fusing the a prior information of the projection direction and image sparseness, the MDATV(Multi-Direction Anisotropic Total Variation) norm is proposed. The ART(Algebraic Reconstruction Technique) + MDATV algorithm framework is proposed for MDATV. The synthetic simulation and real data experiments verify the effectiveness and robustness of the algorithm.3. The NESTA(Nesterov’s algorithm) is proposed for minimizing the objective function, which can overcome the step-size instability of the GD(Gradient Descent) method. The NESTA algorithm flow is simplified for the objective function thus to improve the stability. The synthetic simulation and real data experiments verify the effectiveness and stability of the algorithm.4. According to the noise features in CT, the denoise reconstruction models based on the Euclidean norm inequality and the infinity norm inequality were proposed. The corresponding solving algorithms were designed. The theoretical derivation indicates that the denoise model based on the Euclidean norm is better than that based on the infinity norm, and the iterative reconstruction algorithms have the ability of denoising. The synthetic simulation experiments verify the correctness of the conclusions.