Research On Sparse Regularization Model And Algorithm In CT Image Reconstruction

Computed tomography(CT)is an important medical imaging technology that is widely used as an aid to diagnose diseases due to its non-invasive,high-resolution,and rapid imaging advantages.Sparse angle data acquisition can reduce X-ray radiation and shorten the scan time.However,sparse-angle data can easily lead to artifacts in the reconstructed image,which can affect the final diagnosis of the patient by the physician.Therefore,this paper addresses the problem of CT image reconstruction under sparse angles and proposes two sparse regularized image reconstruction models using iterative reconstruction algorithms combined with a priori knowledge.Based on this,efficient algorithms are designed to make the models converge to the optimal solution better according to the different characteristics of the models,respectively,as follows:We propose a new Huber-TV regularization model that combines the Total Variation(TV)and the smoothness of the Huber function to address the non-differentiability of traditional TV regularization.The Huber-TV smooth model replaces the norm in traditional TV regularization with the Huber function,which can control the function thresholds and efficiently use the linear portion of the Huber function to lightly punish high-gradient areas of the image to preserve image continuity,while heavily punishing low-gradient areas with the quadratic term to suppress discontinuous gradient jumps.The smoothing properties of the objective function of the proposed model allow us to solve the problem using gradient descent methods,which avoids the subgradient calculation in traditional TV regularization and reduces computation complexity,speeding up the iteration process.Experimental results show that the Huber-TV model improves image quality compared with the traditional TV model under sparse-angle reconstruction conditions,demonstrating its effectiveness.The TV regularization method can keep the image edges well,but step artifacts will appear in the reconstruction process.The non-convex penalty term has a good suppression effect on image artifacts,so this paper proposes a non-smooth and non-convex Log-TV model by using the non-convex penalty term of Log parametrization combined with TV regularization.The model enhances gradient sparsity while maintaining image edges and effectively eliminates artifacts.Since the penalty term in this model is nonconvex,the Alternating Direction Method Of Multipliers(ADMM)is often used to solve such problems.However,the traditional ADMM requires solving complex subproblems,which leads to a slow computing speed.We introduce the proximity term with semi-positive definite matrix in the ADMM subproblem,which makes the ADMM subproblem easy to be solved.The experimental results demonstrate that using the neighborhood ADMM to solve the Log-TV model can effectively improve the quality of the reconstructed images compared with the TV model.This paper explores the Huber-TV model and Log-TV model and their solution algorithms,and systematically evaluates their reconstruction performance.The results of the paper have theoretical significance and practical value for promoting the application of TV algorithms in CT reconstruction.