郑州大学学报（理学版）2026，Vol.58Issue(3)：50-58,85,10.DOI:10.13705/j.issn.1671-6841.2024190
FGBK在医学断层图像重构仿真中的应用与改进
The Application and Improvement of FGBK in Medical Tomographic Image Reconstruction Simulation
摘要
Abstract
The Kaczmarz algorithm,a cornerstone in medical tomographic image reconstruction,was en-cumbered by inherent challenges pertaining to high computational complexity and prolonged processing times.To circumvent these issues,a novel row index set selection method,free scale greedy block Kacz-marz(FSGBK),was meticulously designed based on the maximum residual principle.This approach could demonstrably enhances the algorithm's convergence velocity,yet it concurrently introduced a po-tential drawback:the selected index sets might exhibit pronounced correlations,resulting in amplified in-ternal structural errors within the reconstructed image.To address this specific shortcoming and enhance the overall reconstruction fidelity,the K-means FGBK(KFGBK)algorithm was proposed.By this ap-proach,a meticulously chosen subset of linearly independent rows from the coefficient matrix served as the foundation for K-means clustering.These rows functioned as initial centroids,guiding the clustering process to effectively partition the data and construct multiple,largely linearly independent sets.The ulti-mate index set was then judiciously selected from these meticulously crafted subsets.Building upon these advancements,a core algorithm integrating the strengths of both FSGBK and KFGBK,namely K-means FSGBK(KFSGBK),was introduced.Empirical results derived from a comprehensive suite of experi-ments unequivocally demonstrated that this integrated algorithm struck a superior balance between conver-gence speed and the accurate reconstruction of internal structural details.Furthermore,its performance consistently surpassed that of mainstream algorithms,including the conventional FGBK,attesting to its en-hanced efficacy and potential for practical application in medical image reconstruction.This research there-fore brought a significant contribution to improve medical image reconstruction methods.关键词
图像重构/K-means/Kaczmarz/FGBKKey words
image reconstruction/K-means/Kaczmarz/FGBK分类
数理科学引用本文复制引用
时文雅,蔡盼煜,孙思超,郇战..FGBK在医学断层图像重构仿真中的应用与改进[J].郑州大学学报（理学版）,2026,58(3):50-58,85,10.基金项目
国家自然科学基金项目(12201075) （12201075）
江苏省研究生科研创新计划项目(KYCX23-3072) （KYCX23-3072）
