Zeng Gengsheng L, Li Ya
IEEE Trans Radiat Plasma Med Sci. 2017 Nov;1(6):511-516. doi: 10.1109/TRPMS.2017.2722863. Epub 2017 Jul 3.
This paper proposes a novel method of using the frequency-domain transfer function to investigate the property of an iterative algorithm for minimizing a quadratic objective function. This paper focuses on a two-dimensional (2D) tomography problem, which can be X-ray computed tomography (CT), positron emission tomography (PET), and single photon emission computed tomography (SPECT). Two questions regarding to the linear iterative Landweber algorithm are considered. The first question is whether stopping early is equivalent to getting a minimum-norm solution. The second question is whether the low frequency components always converge first. Our answers to these two questions are No.
本文提出了一种利用频域传递函数来研究用于最小化二次目标函数的迭代算法性质的新方法。本文聚焦于二维（2D）断层扫描问题，其可以是X射线计算机断层扫描（CT）、正电子发射断层扫描（PET）和单光子发射计算机断层扫描（SPECT）。考虑了关于线性迭代Landweber算法的两个问题。第一个问题是提前停止是否等同于获得最小范数解。第二个问题是低频分量是否总是先收敛。我们对这两个问题的答案都是否定的。
