title: Rapid reconstruction of quantitative susceptibility mapping via improved ℓ0norm approximation.
abstract: Quantitative susceptibility mapping (QSM) reconstruction is a well-known ill-posed problem. Various regularization techniques have been proposed for solving this problem. In this paper, a rapid method is proposed that uses ℓ0norm minimization in a gradient domain. Because ℓ0minimization is an NP-hard problem, a special alternating optimization strategy is employed to simplify the reconstruction algorithm. The proposed algorithm uses only simple point-wise multiplications and thresholding operations, and significantly speeds up the calculation. Both numerical simulations and in vivo experiments demonstrate that the proposed method can reconstruct susceptibility fast and accurately. Because morphology information weighted methods have achieved considerable success in QSM, we performed a quantitative comparison with some typical weighted methods, such as MEDI (morphology enabled dipole inversion), iLSQR (improved least squares algorithm), and wℓ1(weighted ℓ1norm minimization). The reconstructed results show that the proposed method can provide accurate results with a satisfactory speed.
authors.affiliation: Department of Communications Engineering, Xiamen University, Fujian, China. Electronic address: cbcai@xmu.edu.cn.
authors.forename: Congbo
authors.initials: C
authors.lastname: Cai
authors.affiliation: Department of Communications Engineering, Xiamen University, Fujian, China.
authors.forename: Xi
authors.initials: X
authors.lastname: Chen
authors.affiliation: Department of Communications Engineering, Xiamen University, Fujian, China.
authors.forename: Weijun
authors.initials: W
authors.lastname: Liu
authors.affiliation: Department of Electronic Science, Xiamen University, Fujian, China.
authors.forename: Shuhui
authors.initials: S
authors.lastname: Cai
authors.affiliation: Department of Communications Engineering, Xiamen University, Fujian, China.
authors.forename: Delu
authors.initials: D
authors.lastname: Zeng
authors.affiliation: Department of Communications Engineering, Xiamen University, Fujian, China.
authors.forename: Xinghao
authors.initials: X
authors.lastname: Ding
mesh_terms: D000465:Algorithms; D001921:Brain / Q000000981:diagnostic imaging; D001931:Brain Mapping / Q000379:methods*; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008297:Male
keywords: Quantitative susceptibility mapping(QSM); Rapid reconstruction; Weighting matrix; ℓ0 norm