La Rivière P J, Pan X
Department of Radiology, The University of Chicago, IL 60637, USA.
IEEE Trans Med Imaging. 2000 Aug;19(8):773-86. doi: 10.1109/42.876303.
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.
我们开发并研究了一种断层图像重建方法，其中在通过未加窗滤波反投影（FBP）进行重建之前，使用基于粗糙度惩罚泊松似然目标函数的非参数回归对每个投影进行独立平滑处理。作为进一步的推广，粗糙度惩罚是根据投影的单调变换（称为链接函数）来表示的。通过使用汉宁窗，将该方法与平移不变投影滤波进行比较，并与一种相关的非参数回归方法进行比较，后者使用基于加权最小二乘（WLS）而非泊松似然的目标函数。结果发现，该方法在分辨率 - 噪声权衡方面比汉宁滤波器以及WLS方法都有改进。我们还研究了三种不同链接函数（恒等、平方根和对数链接）的分辨率和噪声效应。发现链接函数的选择会影响重建图像的分辨率均匀性和各向同性特性。特别是，在具有本质上均匀且各向同性分辨率的理想化成像系统中，选择平方根链接函数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，其噪声性能仍优于汉宁滤波器以及WLS方法。
