We develop and investigate an approach to tomographic image reconstruction in which nonparametric regression using a roughness-penalized Poisson likelihood objective function is used to smooth each projection independently prior to reconstruction by unapodized filtered backprojection (FBP). As an added generalization, the roughness penalty is expressed in terms of a monotonic transform, known as the link function, of the projections. The approach is compared to shift-invariant projection filtering through the use of a Hanning window as well as to a related nonparametric regression approach that makes use of an objective function based on weighted least squares (WLS) rather than the Poisson likelihood. The approach is found to lead to improvements in resolution-noise tradeoffs over the Hanning filter as well as over the WLS approach. We also investigate the resolution and noise effects of three different link functions: the identity, square root, and logarithm links. The choice of link function is found to influence the resolution uniformity and isotropy properties of the reconstructed images. In particular, in the case of an idealized imaging system with intrinsically uniform and isotropic resolution, the choice of a square root link function yields the desirable outcome of essentially uniform and isotropic resolution in reconstructed images, with noise performance still superior to that of the Hanning filter as well as that of the WLS approach.

译文

:我们开发并研究了一种断层图像重建方法,其中在使用非变迹滤波反投影(FBP)进行重建之前,使用使用粗糙度惩罚化的泊松似然目标函数的非参数回归来独立平滑每个投影。作为附加的概括,粗糙度损失用投影的单调变换(称为链接函数)表示。通过使用Hanning窗口,将该方法与不变位移投影滤波以及使用基于加权最小二乘(WLS)而不是泊松似然性的目标函数的相关非参数回归方法进行了比较。发现该方法导致在汉宁滤波器和WLS方法上的分辨率-噪声折衷方面的改进。我们还将研究三种不同链接功能的分辨率和噪声影响:标识,平方根和对数链接。发现链接函数的选择会影响重构图像的分辨率均匀性和各向同性。特别是,在具有本质上均匀且各向同性分辨率的理想成像系统的情况下,平方根链接函数的选择会在重建图像中产生基本均匀且各向同性分辨率的理想结果,而噪声性能仍然优于汉宁过滤器以及WLS方法的过滤器。

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