Improved Harmonic Incompatibility Removal for Susceptibility Mapping via Reduction of Basis Mismatch (Journal of Computational Mathematics, 2022)
In quantitative susceptibility mapping (QSM), the background field removal is an essential data acquisition step because it has a significant effect on the restoration quality by generating a harmonic incompatibility in the measured local field data. Even though the sparsity based first generation harmonic incompatibility removal (1GHIRE) model has achieved the performance gain over the traditional approaches, the 1GHIRE model has to be further improved as there is a basis mismatch underlying in numerically solving Poisson’s equation for the background removal. In this paper, we propose the second generation harmonic incompatibility removal (2GHIRE) model to reduce a basis mismatch, inspired by the balanced approach in the tight frame based image restoration. Experimental results shows the superiority of the proposed 2GHIRE model both in the restoration qualities and the computational efficiency.
Keywords: Quantitative susceptibility mapping; Magnetic resonance imaging; Deconvolution; Partial differential equation; Harmonic incompatibility removal; (tight) wavelet frames; sparse approximation.