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

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.