Geometric kernel smoothing of tensor fields

TL;DR

This paper investigates kernel smoothing techniques for denoising tensor fields, analyzing the impact of noise and tensor structure using simulations and theory, and compares estimators under different metrics and noise models.

Contribution

It provides a comprehensive analysis of tensor smoothing methods, comparing Euclidean, log-Euclidean, and affine invariant metrics, and evaluates estimators under Rician noise.

Findings

Different metrics affect smoothing performance.

Theoretical insights into noise effects on tensor denoising.

Comparison of regression estimators under Rician noise.

Abstract

In this paper, we study a kernel smoothing approach for denoising a tensor field. Particularly, both simulation studies and theoretical analysis are conducted to understand the effects of the noise structure and the structure of the tensor field on the performance of different smoothers arising from using different metrics, viz., Euclidean, log-Euclidean and affine invariant metrics. We also study the Rician noise model and compare two regression estimators of diffusion tensors based on raw diffusion weighted imaging data at each voxel.