A theoretical framework for the regularization of Poisson likelihood estimation problems
A theoretical framework for the regularization of Poisson likelihood estimation problems
复制标题
泊松似然估计问题正则化的理论框架
DOI：
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Johnathan M. Bardsley
中科院分区：
文献类型：
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作者：
Johnathan M. Bardsley
设z=Au+gamma是一个不适定的线性算子方程。例如，在天文学和医学成像中都会出现这样的模型，在这种情况下，$gamma$对应于背景，$u$对应于未知的真实图像，$A$对应于前向算子，$z$对应于数据。这个方程的正则解可以通过求解
$R_alpha（A，z）= argmin_{ugeq 0} {T_0（Au;z）+alpha J（u）}，$
其中$T_0（Au; z）$是泊松似然泛函的负对数，$alpha>0$和$J$分别是正则化参数和泛函。本文的目标是确定保证R_alpha$定义z=Au+gamma$正则化方案的一般条件。在这种情况下，确定正则化方案的适当定义很重要：它不仅有助于统一以前的理论论点，而且还将为未来的理论分析提供一个框架。为了说明后者，我们结束了文件的应用程序的一般框架的情况下，分析还没有做。
Let $z=Au+gamma$ be an ill-posed, linear operator equation. Such a model arises, for example, in both astronomical and medical imaging, in which case $gamma$ corresponds to background, $u$ the unknown true image, $A$ the forward operator, and $z$ the data. Regularized solutions of this equation can be obtained by solving
$R_alpha(A,z)= argmin_{ugeq 0} {T_0(Au;z)+alpha J(u)},$
where $T_0(Au;z)$ is the negative-log of the Poisson likelihood functional, and $alpha>0$ and $J$ are the regularization parameter and functional, respectively. Our goal in this paper is to determine general conditions which guarantee that $R_alpha$ defines a regularization scheme for $z=Au+gamma$. Determining the appropriate definition for regularization scheme in this context is important: not only will it serve to unify previous theoretical arguments in this direction, it will provide a framework for future theoretical analyses. To illustrate the latter, we end the paper with an application of the general framework to a case in which an analysis has not been done.
DOI：
10.1364/josaa.10.001014
发表时间：
1993-05-01
影响因子：
1.9
作者：
SNYDER, DL;HAMMOUD, AM;WHITE, RL
通讯作者：
WHITE, RL