Analysis of resolution and noise properties of nonquadratically regularized image reconstruction methods for PET
Analysis of resolution and noise properties of nonquadratically regularized image reconstruction methods for PET
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DOI：
10.1109/tmi.2007.911549
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发表时间：
2008-03-01
影响因子：
10.6
通讯作者：
Leahy, Richard M.
中科院分区：
文献类型：
--
作者：
Ahn, Sangtae;Leahy, Richard M.
我们提出了准确有效的方法，用于估算非正规化图像重建的空间分辨率和噪声特性，以构建正电子发射断层扫描（PET）。众所周知，二次正则化倾向于超平滑的锋利边缘。已经提出了许多类型的边缘性非二次惩罚来克服这一问题。但是，由于其非线性，几乎没有关于非二次正则化的定量分析的研究。相比之下，四四极正规化的估计量大致是线性的，并且从分辨率和方差属性方面得到了充分的理解。我们使用泰勒扩展和剩余项来得出线性化局部扰动响应（LLPR）的新近似表达式和方差。尽管表达式是隐式的，但我们可以使用它们准确预测非二次正则化的分辨率和方差，其中基于一阶泰勒截断的常规表达式失败。他们还激励我们扩展使用基于确定的修改惩罚对非二次正则化案例的使用，以实现空间均匀的扰动响应，类似于二次正则化中均匀的空间分辨率。最后，我们开发了计算有效的方法，用于预测非正规化重建的分辨率和方差，并进行了描述这些方法有效性的仿真。
We present accurate and efficient methods for estimating the spatial resolution and noise properties of non-quadratically regularized image reconstruction for positron emission tomography (PET). It is well known that quadratic regularization tends to over-smooth sharp edges. Many types of edge-preserving nonquadratic penalties have been proposed to overcome this problem. However, there has been little research on the quantitative analysis of nonquadratic regularization due to its nonlinearity. In contrast, quadratically regularized estimators are approximately linear and are well understood in terms of resolution and variance properties. We derive new approximate expressions for the linearized local perturbation response (LLPR) and variance using the Taylor expansion with the remainder term. Although the expressions are implicit, we can use them to accurately predict resolution and variance for nonquadratic regularization where the conventional expressions based on the first-order Taylor truncation fail. They also motivate us to extend the use of a certainty-based modified penalty to nonquadratic regularization cases in order to achieve spatially uniform perturbation responses, analogous to uniform spatial resolution in quadratic regularization. Finally, we develop computationally efficient methods for predicting resolution and variance of non-quadratically regularized reconstruction and present simulations that illustrate the validity of these methods.