Quantitative Susceptibility Map Reconstruction Using Annihilating Filter-based Low-Rank Hankel Matrix Approach

TL;DR

This paper introduces a novel QSM reconstruction method using an annihilating filter-based low-rank Hankel matrix approach, which effectively reduces streaking artifacts and improves susceptibility estimation without requiring prior anatomical information.

Contribution

The work formulates QSM reconstruction as a low-rank Hankel matrix constrained deconvolution problem in k-space, enabling artifact reduction and accurate susceptibility mapping.

Findings

Significantly reduces streaking artifacts in QSM images.

Accurately estimates susceptibility in deep gray matter.

Does not require additional anatomical priors.

Abstract

Quantitative susceptibility mapping (QSM) inevitably suffers from streaking artifacts caused by zeros on the conical surface of the dipole kernel in k-space. This work proposes a novel and accurate QSM reconstruction method based on a direct k-space interpolation approach, avoiding problems of over smoothing and streaking artifacts. Inspired by the recent theory of annihilating filter-based low-rank Hankel matrix approach (ALOHA), QSM reconstruction problem is formulated as deconvolution problem under low-rank Hankel matrix constraint in the k-space. To reduce the computational complexity and the memory requirement, the problem is formulated as successive reconstruction of 2-D planes along three independent axes of the 3-D phase image in Fourier domain. Extensive experiments were performed to verify and compare the proposed method with existing QSM reconstruction methods. The proposed ALOHA-QSM effectively reduced streaking artifacts and accurately estimated susceptibility values in deep gray matter structures, compared to the existing QSM methods. Our suggested ALOHA-QSM algorithm successfully solves the three-dimensional QSM dipole inversion problem without additional anatomical information or prior assumption and provides good image quality and quantitative accuracy.