A Riemannian Framework for Denoising Diffusion Tensor Images

Diffusion Tensor Imaging (DTI) is a relatively new imaging modality that has been extensively used to study diffusion processes in the brain and has applications ranging from diagnostic to surgical planning. However, DTI imaging systems are highly sensitive to noise, leading to reconstructed images with low SNR. Thus, there is a need for image denoising algorithms specifically designed to regularize tensor structures. Most commonly used denoising algorithms operate in the “image space”, with results prone to loss of tensor properties. This report presents an adaptation of scalar image denoising algorithms using H regularization and Total Variation (TV) regularization, to the “tensor space” via a Riemannian framework. The mathematical framework translating these algorithms to the Riemannian space is presented, followed by results on DTI images of the brain.