Research On The Medical Image Reconstruction Algorithm Based On The Non-local Total Variation

Computed tomography(CT)is one of the most widely used medical imaging technologies.CT reconstruction algorithm has a great influence on the quality of reconstructed images.The reconstruction algorithms of commercial CT have been dominated by analytic reconstruction algorithms in the past three decades.But the current dilemma is that the analytic reconstruction algorithms have a high requirement on the completeness of the projection data for reconstruction.The accurate reconstruction of CT scanner under spare sampling conditions has a wide range of promising applications.It can not only reduce the radiation dose received by patients and accelerate the reconstruction speed,but also play an important role in the scanning of requirements of unusual locations.An effective strategy for reducing the radiation dose is sampling the projection data sparsely,which requires advanced algorithms that can accurately reconstruct images.The optimization algorithm based on compressed sensing(CS)has been proved to be an effective class of high-precision sparse reconstruction algorithms,and some algorithms have been applied to practical commercial CT systems.Total Variation(TV)minimum algorithm is a classical reconstruction algorithm based on compressed sensing.It has demonstrated the highprecision sparse reconstruction capability under the CT modes such as fan beam CT,cone beam CT,c-arm CT and special breast CT.However,in some cases,the reconstruction results of TV constrained algorithms will introduce some block artifacts.Therefore,it is of great theoretical and practical significance to explore advanced algorithms that can suppress block artifacts.The nonlocal total variation(NLTV)model based on the nonlocal operator and spectral graph theory effectively improves some defects of the local TV model.In order to deeply analyze the mechanism of NLTV model,this thesis systematically researches the NLTV-based reconstruction algorithm.The main research contents of this thesis are outlined as follows:(1)Based on the Siddon algorithm,we introduced the matrix representation of the iterative algorithms and the modeling approaches of the projection system matrix.And we using the adaptive steepest descent projection onto convex sets(ASD-POCS)algorithm to realize the image reconstruction.(2)We analyzed the possible defects of the reconstruction algorithm based on TV model.We studied the mechanism of NLTV model which is based on the nonlocal similarity principle.And we also compared some optimization algorithms used to solving the NLTV constrained problems to clarify their advantages and disadvantages.(3)We designed a constrained NLTV minimum image reconstruction model.And we also proposed a way to combine the Split Bregman algorithm with the ASD-POCS algorithm.We designed some simulation experiments to compare the TV model and the NLTV model.And the experimental results shown the superiority of the NLTV model in preserving the fine structure and texture of the reconstructed image.In the end,we introduced the parameter selection method and the impact of the algorithm parameters on the reconstructed image.Based on the physics and mathematical principles of computed tomography,this thesis focuses on the regularized reconstruction algorithm under the condition of sparse sampling.We compared the TV model and the NLTV model and the derived NLTV-based iterative reconstruction algorithm can effectively improve some defects of the TV model.The NLTV constrained iterative reconstruction algorithm is a beneficial attempt to reconstruct images under the conditions of sparse sampling.