基于混合正则项的稀疏角度CT图像重建  

Sparse Angle CT Image Reconstruction Based on Mixed Regular Terms

作　　者：顼健璐 白艳萍[1] 续婷[1] 程蓉 XU Jianlu;BAI Yanping;XU Ting;CHENG Rong(School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2024年第6期744-752,共9页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61774137);山西省基础研究计划资助项目(202103021224195,202103021224212,202103021223189,20210302123019)。

摘　　要：针对传统迭代算法无法保证在数据欠采样情况下重建出高质量医学CT图像的问题,提出了一种基于表面积最小化和群稀疏表示(GSR)的双正则项惩罚最小二乘的方法来用于稀疏角度CT图像重建。根据网格场中噪声图像比平滑图像表面积要大这一规律,将表面积项作为重建图像的一个先验约束,以达到平滑图像噪声的目的;再根据GSR利用非局部相似性保留图像细微结构这一特性,将GSR作为另一个先验约束,建立重建模型。采用交替最小化方案将重建问题解耦为求解中间图像子问题和求解字典以及稀疏表示子问题,之后利用半二次分裂法和分裂布雷格曼方法分别对两个子问题进一步求解。实验结果表明,与算法PLS-GSR、PLS-NLM、SART-GSR相比,本文算法的重建图像有良好的视觉效果,可以较清晰地辨别图像的内部结构和细节,并且FSIM值、PSNR值和MSE值均优于对比算法。To solve the problem that the traditional iterative algorithms can not guarantee the reconstruction of high-quality medical CT images in the case of data undersampling,a method of double regular term penalty least squares based on surface area minimization and Group Sparse Representation(GSR)was proposed for sparse angle CT image reconstruction.According to the rule that the surface area of the noisy image is larger than that of the smooth image in the grid field,the surface area term was used as a prior constraint on reconstructing the image to achieve the purpose of smoothing the image noise;based on the feature that GSR preserves the fine structure of the image by using non-local similarity,the reconstruction model was established by using GSR as another prior constraint.An alternate minimization scheme was used to decouple the reconstruction problem into solving the intermediate image subproblem,and solving the dictionary and sparse representation subproblem.Then,the two sub-problems were further solved by the half-quadratic splitting method and the split Bregman method respectively.The experimental results show that compared with the algorithms PLS-GSR,PLS-NLM and SART-GSR,the reconstructed image of the proposed algorithm has good visual effect,which can clearly identify the internal structure and details of the image,and the value of FSIM,PSNR and MSE are superior to the comparison algorithm.

关 键 词：群稀疏表示 表面积 图像平滑 非局部相似性 图像重建 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]