Chen Geng, Dong Bin, Zhang Yong, Shen Dinggang, Yap Pew-Thian
Department of Radiology and BRIC, University of North Carolina, Chapel Hill, USA.
Beijing International Center for Mathematical Research, Peking University, Beijing, China.
Med Image Comput Comput Assist Interv. 2017 Sep;10433:629-637. doi: 10.1007/978-3-319-66182-7_72. Epub 2017 Sep 4.
In this paper, we introduce a strategy for performing neighborhood matching on general non-Euclidean and non-flat domains. Essentially, this involves representing the domain as a graph and then extending the concept of convolution from regular grids to graphs. Acknowledging the fact that convolutions are features of local neighborhoods, neighborhood matching is carried out using the outcome of multiple convolutions at multiple scales. All these concepts are encapsulated in a sound mathematical framework, called graph framelet transforms (GFTs), which allows signals residing on non-flat domains to be decomposed according to multiple frequency subbands for rich characterization of signal patterns. We apply GFTs to the problem of denoising of diffusion MRI data, which can reside on domains defined in very different ways, such as on a shell, on multiple shells, or on a Cartesian grid. Our non-local formulation of the problem allows information of diffusion signal profiles of drastically different orientations to be borrowed for effective denoising.
在本文中，我们介绍了一种在一般非欧几里得和非平坦域上执行邻域匹配的策略。本质上，这涉及将域表示为一个图，然后将卷积的概念从规则网格扩展到图。认识到卷积是局部邻域的特征，邻域匹配是通过在多个尺度上进行多次卷积的结果来执行的。所有这些概念都封装在一个合理的数学框架中，称为图小波变换（GFT），它允许驻留在非平坦域上的信号根据多个频率子带进行分解，以丰富地表征信号模式。我们将GFT应用于扩散磁共振成像（MRI）数据的去噪问题，这些数据可以驻留在以非常不同的方式定义的域上，例如在一个球壳上、多个球壳上或笛卡尔网格上。我们对该问题的非局部公式允许借用方向截然不同的扩散信号轮廓的信息进行有效的去噪。
