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, sk), 1 ≤ k ≤ K, at a given voxel location x may be considered as samplings of a measure supported on the unit sphere S2∈R3 at locations sk=(θk,ϕk)∈S2 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.
Denoising of diffusion magnetic resonance images using a modified and differentiable Monge–Kantorovich distance for measure-valued functions / D. La Torre, J. Marcoux, F. Mendivil, E.R. Vrscay. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - 91:(2020), pp. 105456.1-105456.9. [10.1016/j.cnsns.2020.105456]
Denoising of diffusion magnetic resonance images using a modified and differentiable Monge–Kantorovich distance for measure-valued functions
D. La TorrePrimo
;
2020
Abstract
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, sk), 1 ≤ k ≤ K, at a given voxel location x may be considered as samplings of a measure supported on the unit sphere S2∈R3 at locations sk=(θk,ϕk)∈S2 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.Pubblicazioni consigliate
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