基于非局部广义总变分正则化的稀疏角度CT重建算法  

Sparse View CT Reconstruction Algorithm Based on Non-Local Generalized Total Variation Regularization

作　　者：蒋敏 陶红伟 程凯 JIANG Min;TAO Hongwei;CHENG Kai(College of Computer and Communication Engineer,Zhengzhou Universityof Light Industry,Zhengzhou 450000,China;Zhejiang Lab,Hangzhou 311121,China)

机构地区：[1]郑州轻工业大学计算机与通信工程学院,郑州450000 [2]之江实验室,杭州311121

出　　处：《CT理论与应用研究(中英文)》2025年第1期129-139,共11页Computerized Tomography Theory and Applications

基　　金：河南省科技攻关项目(222102210032);河南省科技攻关项目(232102210014)。

摘　　要：基于广义总变分(TGV)正则化的CT图像重建算法可以有效克服总变分(TV)正则化的阶梯效应,从而能保护重建图像过渡区域的结构特征。尽管TGV重建方法优于TV重建方法,但它仍然忽略了非局部自相似先验信息在恢复CT图像细节方面的显著作用。为了克服TGV重建方法的上述局限性,本文引入一种非局部广义总变分(NLTGV)正则项,并提出基于NLTGV正则化的稀疏角度CT重建算法。该方法不仅可以利用不同阶的非局部变分信息来保护图像结构特征,而且还可以利用非局部自相似性来恢复重建图像的细节。由于重建模型包含双非光滑项,难以直接求解,因此提出基于凸集投影的优化算法,将其分解为几个简单子问题实现有效求解。仿真和实验结果表明,与其他变分正则化重建方法相比,本文重建方法可以有效提高CT图像重建质量。CT image reconstruction algorithm based on generalized total variation(TGV)can overcome the staircase effect of total variation(TV)regularization,thereby protecting the structural features of the reconstructed image transition region.Although the TGV reconstruction method is superior to the TV reconstruction method,it still ignores the role of non-local self-similar prior information in restoring CT image details.To overcome the aforementioned limitations of TGV reconstruction method,we introduce a non-local TGV(NLTGV)regularization term and propose a sparse view CT reconstruction algorithm based on NLTGV regularization.The proposed method can not only utilize non-local variational information of different orders to protect image structural features but can also utilize non-local self-similarity to restore the details of the reconstructed image.Owing to the inclusion of dual non-smooth terms in the reconstruction model,solving it directly is difficult.Therefore,we proposed an optimization algorithm based on convex set projection,which decomposes the problem into several sub-problems to be solved.The simulation and experimental results show that the proposed NLTGV regularization reconstruction method can effectively improve the quality of reconstructed images compared with other variational reconstruction methods.

关 键 词：X射线CT 稀疏角度采样 非局部广义全变分 凸集投影算法 分裂Bregman算法 

分 类 号：P631.3[天文地球—地质矿产勘探] O242[天文地球—地质学] TP391.41[理学—计算数学]