Quantitative susceptibility map reconstruction using annihilating filter-based low-rank Hankel matrix approach

Abstract

Purpose: 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 k-space low-rank Hankel matrix constraint, avoiding the over-smoothing problem and streaking artifacts.

Theory and methods: Based on the recent theory of annihilating filter-based low-rank Hankel matrix approach (ALOHA), QSM is formulated as deconvolution under low-rank Hankel matrix constraint in the k-space. The computational complexity and the high memory burden were reduced by successive reconstruction of 2-D planes along 3 independent axes of the 3-D phase image in Fourier domain. Feasibility of the proposed method was tested on a simulated phantom and human data and were compared with existing QSM reconstruction methods.

Results: The proposed ALOHA-QSM effectively reduced streaking artifacts and accurately estimated susceptibility values in deep gray matter structures, compared to the existing QSM methods.

Conclusions: The suggested ALOHA-QSM algorithm successfully solves the 3-dimensional QSM dipole inversion problem using k-space low rank property with no anatomical constraint. ALOHA-QSM can provide detailed brain structures and accurate susceptibility values with no streaking artifacts.

Keywords: dipole inversion; low-rank Hankel matrix completion; quantitative susceptibility mapping.