Generalized row-action methods for tomographic imaging
Generalized row-action methods for tomographic imaging
复制标题
DOI：
10.1007/s11075-013-9778-8
复制
发表时间：
2014-09-01
影响因子：
2.1
通讯作者：
Hansen, Per Christian
中科院分区：
文献类型：
--
作者：
Andersen, Martin S.;Hansen, Per Christian
行动作方法在层析图像重建中起着重要的作用。许多这样的方法可以被视为最小化大量凸函数和的增量梯度方法，尽管它们的全局收敛速度相对较差，但这些方法通常表现出快速的初始收敛，这在低精度解可以接受的应用中是可取的。在这篇文章中，我们提出了一类增量近端梯度法的松弛变体，这些变体推广了许多现有的用于层析成像的行-作用法。此外，它们允许我们通过正则化得到新的用于层析成像的增量算法，该算法融合了不同类型的先验信息。通过数值算例验证了该方法的有效性。
Row-action methods play an important role in tomographic image reconstruction. Many such methods can be viewed as incremental gradient methods for minimizing a sum of a large number of convex functions, and despite their relatively poor global rate of convergence, these methods often exhibit fast initial convergence which is desirable in applications where a low-accuracy solution is acceptable. In this paper, we propose relaxed variants of a class of incremental proximal gradient methods, and these variants generalize many existing row-action methods for tomographic imaging. Moreover, they allow us to derive new incremental algorithms for tomographic imaging that incorporate different types of prior information via regularization. We demonstrate the efficacy of the approach with some numerical examples.