Total variation minimization for measure-valued images with diffusion spectrum imaging as motivation

In this paper, we present a notion of total variation for measure-valued images. Our motivation is Diffusion Spectrum Imaging (DSI) in which the diffusion at each voxel is characterized by a probability density function. We introduce a total variation denoising problem for measure-valued images. In the one-dimensional case, this problem (which involves the Monge-Kantorovich metric for measures) can be solved using cumulative distribution functions. In higher dimensions, more computationally expensive methods must be employed.