通过抑制最大奇异向量上的投影来加速 Landweber 型算法。

Acceleration of Landweber-type algorithms by suppression of projection on the maximum singular vector.

机构信息

Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI.

出版信息

IEEE Trans Med Imaging. 1992;11(4):479-87. doi: 10.1109/42.192683.

DOI:10.1109/42.192683

Abstract

A procedure that speeds up convergence during the initial stage (the first 100 forward and backward projections) of Landweber-type algorithms, for iterative image reconstruction for positron emission tomography (PET), which include the Landweber, generalized Landweber, and steepest descent algorithms, is discussed. The procedure first identifies the singular vector associated with the maximum singular value of the PET system matrix, and then suppresses projection of the data on this singular vector after a single Landweber iteration. It is shown that typical PET system matrices have a significant gap between their two largest singular values; hence, this suppression allows larger gains in subsequent iterations, speeding up convergence by roughly a factor of three.

摘要

讨论了一种在正电子发射断层扫描（PET）迭代图像重建中，加速 Landweber 型算法初始阶段（前向和后向投影的前 100 次）收敛速度的方法，该算法包括 Landweber 算法、广义 Landweber 算法和最速下降算法。该方法首先识别与 PET 系统矩阵最大奇异值相关的奇异向量，然后在单次 Landweber 迭代后抑制数据在该奇异向量上的投影。结果表明，典型的 PET 系统矩阵的两个最大奇异值之间存在显著差距；因此，这种抑制可以在后续迭代中获得更大的增益，从而将收敛速度提高约三倍。