Study On Statistical Iterative Reconstruction Methods For Low-dose X-ray CT

Along with the rapid development of modern medical imaging technology, X-ray computed tomography imaging technology has become a routine clinical diagnosis and treatment. At present, in the situation to minimize the X-ray radiation, how to obtain CT images with high density, clear anatomical information, and good lesion presentation is the most urgent demand in clinical practice. Therefore, the development of low-dose X-ray CT imaging technology has drawn more and more attention. The strategies include reducing the X-ray dose, improving the imaging hardware system and designing high-quality imaging algorithms. To overcome quality degradation of CT image caused by X-ray attenuation, the research reported in this dissertation is to gain better performance of low-dose X-ray CT imaging by using advanced algorithms. Through in-depth study in the three aspects, such as projection data filtering, statistical iterative reconstruction, and CT image processing, the main innovative work are summarized as follows:1. Based on the statistical characteristics of low-dose X-ray CT projections, two filtering methods for projection data were proposed,(1) It is always difficult to distinguish edges and flat areas in a sinogram, which may result in excessive smoothing. To solve this problem, first of all, considering the fuzziness of projections, the gradient magnitude and intuition fuzzy entropy are simultaneously used as indicators for the edges to construct an indicator function. Furthermore, with the proposed edge indicator function as the diffusion coefficient, a regularization Perona-Malik equation sinogram smoothing model based on intuitionistic fuzzy entropy was presented. The model overcomes the shortage of traditional Perona-Malik equation. Meanwhile, it could perform diffusion with different directions and intensity in different regions of the sinogram. Finally,the optimal solution to the proposed model is obtained using the additional operator splittingmethod. Experimental results show that the proposed method is faster, and able to retain important edges while smoothing the noise.(2) For the facts that traditional projection data restoration algorithms could not preserve important image edges when smoothing the noise, a joint prior constrained maximum a posterior projection data recovery model was proposed. Its advantage lies in that the method constructs a joint prior which is composed of median root prior and the sinogram sparse representation based on over complete redundancy dictionary. Because the median root prior can better smooth the noise and the sparse representation of sinogram can effectively perceive boundaries and structure information, the joint prior would reach a good balance between noise smoothing and edge-reservation. To complete the optimal estimation of the new algorithm model, this paper applies alternating iterative method to decompose the mentioned joint estimation into two sub-problems to be estimated. Then these two sub-optimization estimation were resolved respectively with the separable paraboloidal surrogates method and the orthogonal matching pursuit method. Finally, good visualization and quantitative analysis of the imaging results verify the feasibility and effectiveness of the proposed algorithm.2. On the basis of statistical modeling for Low-dose X-ray CT projection data, two improved statistical iterative reconstruction algorithms were proposed by design of regularizations that could better characterize the image prior information,(1) To overcome the “piecewise constant” problem in total variation regularization,firstly, total generalized variation(TGV) was introduced into Markov Random Field(MRF).The TGV is convex, rotation invariant, lower semi continuous and could approximate any polynomial function. Secondly, a modified statistical iterative reconstruction algorithm based on MRF prior constrained was proposed. To optimize the new algorithm model, two steps were needed. The first step is to solve the joint problem by alternating iterative method. The second step is to solve the two sub problems with the separable paraboloidal surrogates method and the first order primal dual method. Finally, the simulation experiment was carried out using the complete projection data, and the reconstruction images could be obtained,in which edge and details can be clearly distinguished.(2) To overcome quality degradation in reconstruction image resulted from incomplete projections, we proposed a statistical iterative reconstruction algorithm based on joint sparseprior regularization. The main characteristics of image could be represented by the sparse representation. When the regularization is more sparse, it can better reflect the important characteristics of image. In this dissertation, we constructed a joint sparse prior model through image transforming with the joint sparse. The joint sparse transformation consists of the image shear wave conversion, the amplitude transformation of image gradient, and the difference amplitude alternation of the image and estimated auxiliary vector. In order to further optimize the proposed model, this paper adopted two solution schemes, i.e., the alternating direction multiplier method and conjugate gradient method. In the end, we carried out simulation experiments with incomplete projection data, and the experimental results showed that the new algorithm is feasible and effective.3. To minimize the artifacts appeared in Low-dose X-ray CT images, an adaptive TGV regularized image restoration algorithm based on strict intuition entropy was proposed in this dissertation. First, according to the fuzziness of low-dose CT images, a new diffusion coefficient function that could adaptively distinguish the edge and flat region of image was proposed by constructing strict intuition entropy of CT images. Furthermore, we established an adaptive TGV regularized image restoration model based on the proposed diffusion coefficient. There are two challenges in the optimization estimation for the new model, i.e.,the solution to diffusion coefficients of implicit adaptive estimation and the solution to the TGV regularization joint estimation model containing the dual variable. This dissertation used particle swarm optimization and the first order primal dual algorithms to solve them respectively. Finally, this dissertation analyzed numerical experiment results with three different stripe artifacts distribution feature, showing that the proposed algorithm could suppress noise and artifacts, meanwhile preserving important boundaries of images.