FGBK在医学断层图像重构仿真中的应用与改进OA

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.