Statistics and Its Interface

Volume 17 (2024)

Number 3

Spatially robust adaptive ensemble average propagator reconstruction via spherical polar Fourier imaging

Pages: 451 – 468

DOI: https://dx.doi.org/10.4310/23-SII791

Authors

Xifeng Wang (Department of Biostatistics, University of North Carolina Chapel Hill)

Shangbang Rao (Department of Biostatistics, University of North Carolina Chapel Hill)

Jian Cheng (School of Computer Science and Engineering, Beihang University)

Ye Wu (Department of Radiology, and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill)

Pew-Thian Yap (Department of Radiology, and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill)

Joseph Ibrahim (Department of Biostatistics, University of North Carolina Chapel Hill)

Hongtu Zhu (Department of Biostatistics, University of North Carolina Chapel Hill)

Abstract

The aim of this paper is to propose a robust multi-scale adaptive and sequential smoothing (MASS) method framework to spatially and adaptively infer the ensemble average propagator (EAP) of water diffusion in brain regions with complex fiber configurations. We consider Spherical Polar Fourier Imaging (SPFI), which is a model-free and fast analytical high angular resolution diffusion imaging (HARDI) technique, for EAP reconstruction. SPFI uses the combination of angular and radial elementary functions expressed in a spherical coordinate system, making it less reliant on data assumptions and sampling requirements than other HARDI techniques. We reformulate the EAP reconstruction as a robust regression problem using Huber’s loss function with Spherical Polar Fourier (SPF) basis as covariates. Similarity and distance weights are introduced to account for spatial smoothness of HARDI, while preserving the unknown discontinuities (e.g., edges between white matter and grey matter). Experimental results indicate that MASS can reduce the angle detection errors in fiber crossing area and provides more accurate reconstructions than standard voxel-wise methods under the presence of outliers.

Keywords

ensemble average propagator, high angular resolution diffusion imaging, multi-scale adaptive and sequential smoothing, propagation-separation, robust

Full Text (PDF format)

Received 1 December 2022

Accepted 15 March 2023

Published 19 July 2024