We report on the implementation of a novel total-variation denoising method for diffusion spectrum images (DSI). Our method works on the raw signal obtained from dMRI. From the Stejskal-Tanner equation [6], the signals S(x, s_k), 1 ≤ k ≤ K, at a given voxel location x may be considered as samplings of a measure supported on the unit sphere ${\mathbb{S}}^2\in {\mathbb{R}}^3$ at locations $s_k=({\theta }_k,{\varphi }_k)\in {\mathbb{S}}^2$ which quantify the ease/difficulty of diffusion in these directions. We consider the entire signal S as a measure-valued function in a complete metric space which employs the Monge–Kantorovich (MK) metric. A total variation (TV) for measures and measure-valued functions is also defined. A major advance in this paper is the use of a modification of the standard MK distance which permits rapid computation in higher dimensions. An added bonus is that this modified metric is differentiable. The resulting TV-based denoising problem is a convex optimization problem.

我们报告了一种新型的全光谱降噪方法，用于扩散光谱图像（DSI）。我们的方法适用于从dMRI获得的原始信号。从Stejskal-唐纳方程[6]，信号小号（X，S _ķ），1≤  ķ  ≤  ķ，在给定体素的位置X可被认为是支撑在单位球面上的度量的采样${\mathbb{小号}}^2\in {\mathbb{[R}}^3$ 在地点 $s_{ķ}=（{\theta }_{ķ}，{\varphi }_{ķ}）\in {\mathbb{小号}}^2$量化了在这些方向上扩散的难易程度。我们认为整个信号S是采用Monge–Kantorovich（MK）度量的完整度量空间中的度量值函数。还定义了度量和度量值函数的总变化量（TV）。本文的主要进步是使用了标准MK距离的修改，该修改允许在更高维度上进行快速计算。另外一个好处是，此修改后的指标是可区分的。产生的基于电视的降噪问题是凸优化问题。