Mondal Partha P, Rajan K
Department of Physics, Indian Institute of Science, Bangalore-560012, India.
J Opt Soc Am A Opt Image Sci Vis. 2005 Sep;22(9):1763-71. doi: 10.1364/josaa.22.001763.
Positron emission tomography (PET) and single-photon emission computed tomography have revolutionized the field of medicine and biology. Penalized iterative algorithms based on maximum a posteriori (MAP) estimation eliminate noisy artifacts by utilizing available prior information in the reconstruction process but often result in a blurring effect. MAP-based algorithms fail to determine the density class in the reconstructed image and hence penalize the pixels irrespective of the density class. Reconstruction with better edge information is often difficult because prior knowledge is not taken into account. The recently introduced median-root-prior (MRP)-based algorithm preserves the edges, but a steplike streaking effect is observed in the reconstructed image, which is undesirable. A fuzzy approach is proposed for modeling the nature of interpixel interaction in order to build an artifact-free edge-preserving reconstruction. The proposed algorithm consists of two elementary steps: (1) edge detection, in which fuzzy-rule-based derivatives are used for the detection of edges in the nearest neighborhood window (which is equivalent to recognizing nearby density classes), and (2) fuzzy smoothing, in which penalization is performed only for those pixels for which no edge is detected in the nearest neighborhood. Both of these operations are carried out iteratively until the image converges. Analysis shows that the proposed fuzzy-rule-based reconstruction algorithm is capable of producing qualitatively better reconstructed images than those reconstructed by MAP and MR P algorithms. The reconstructed images a resharper, with small features being better resolved owing to the nature of the fuzzy potential function.
正电子发射断层扫描（PET）和单光子发射计算机断层扫描彻底改变了医学和生物学领域。基于最大后验（MAP）估计的惩罚迭代算法通过在重建过程中利用可用的先验信息来消除噪声伪影，但往往会产生模糊效应。基于MAP的算法无法确定重建图像中的密度类别，因此无论密度类别如何都会对像素进行惩罚。由于没有考虑先验知识，具有更好边缘信息的重建通常很困难。最近引入的基于中值根先验（MRP）的算法保留了边缘，但在重建图像中观察到阶梯状条纹效应，这是不理想的。为了构建无伪影的边缘保留重建，提出了一种模糊方法来对像素间相互作用的性质进行建模。所提出的算法包括两个基本步骤：（1）边缘检测，其中基于模糊规则的导数用于在最近邻域窗口中检测边缘（这等同于识别附近的密度类别），以及（2）模糊平滑，其中仅对在最近邻域中未检测到边缘的那些像素进行惩罚。这两个操作都迭代进行，直到图像收敛。分析表明，所提出的基于模糊规则的重建算法能够产生比通过MAP和MRP算法重建的图像质量更好的重建图像。由于模糊势函数的性质，重建图像更清晰，小特征得到更好的分辨。
