Estimating fiber orientation distribution from diffusion MRI with spherical needlets

TL;DR

This paper introduces a new spherical needlet-based method for estimating fiber orientation distributions from diffusion MRI data, improving accuracy and feature preservation over existing techniques.

Contribution

The paper presents a novel FOD estimation approach using spherical needlets and $l_1$-penalized regression, enhancing resolution of crossing fibers and noise robustness.

Findings

Accurately resolves small-angle fiber crossings

Automatically detects isotropic diffusion regions

Produces realistic crossing fiber maps in real data

Abstract

We present a novel method for estimation of the fiber orientation distribution (FOD) function based on diffusion-weighted Magnetic Resonance Imaging (D-MRI) data. We formulate the problem of FOD estimation as a regression problem through spherical deconvolution and a sparse representation of the FOD by a spherical needlets basis that form a multi-resolution tight frame for spherical functions. This sparse representation allows us to estimate FOD by an $l_1$-penalized regression under a non-negativity constraint. The resulting convex optimization problem is solved by an alternating direction method of multipliers (ADMM) algorithm. The proposed method leads to a reconstruction of the FODs that is accurate, has low variability and preserves sharp features. Through extensive experiments, we demonstrate the effectiveness and favorable performance of the proposed method compared with two existing methods. Particularly, we show the ability of the proposed method in successfully resolving fiber crossing at small angles and in automatically identifying isotropic diffusion. We also apply the proposed method to real 3T D-MRI data sets of healthy elderly individuals. The results show realistic descriptions of crossing fibers that are more accurate and less noisy than competing methods even with a relatively small number of gradient directions.