基于包络引导共轭梯度的 PET 正则化。

PET regularization by envelope guided conjugate gradients.

机构信息

Lucent Technol., AT&T Bell Labs., Murray Hill, NJ.

出版信息

IEEE Trans Med Imaging. 1996;15(3):385-9. doi: 10.1109/42.500147.

Abstract

The authors propose a new way to iteratively solve large scale ill-posed problems and in particular the image reconstruction problem in positron emission tomography by exploiting the relation between Tikhonov regularization and multiobjective optimization to obtain iteratively approximations to the Tikhonov L-curve and its corner. Monitoring the change of the approximate L-curves allows the authors to adjust the regularization parameter adaptively during a preconditioned conjugate gradient iteration, so that the desired solution can be reconstructed with a small number of iterations.

摘要

作者提出了一种新的迭代方法来解决大规模不适定问题，特别是通过利用 Tikhonov 正则化和多目标优化之间的关系来获得 Tikhonov L 曲线及其角的迭代逼近，从而解决正电子发射断层扫描中的图像重建问题。监测近似 L 曲线的变化可以使作者在预处理共轭梯度迭代过程中自适应地调整正则化参数，从而可以用较少的迭代次数重建所需的解。