This abstract presents a novel Split Bregman (SB) based approach to enable rapid minimization of the quantitative susceptibility reconstruction formulation that includes a weighted least squares fidelity constraint and a total variation (TV) penalty. The purpose of this approach is to develop a rapid minimization technique that does not need complex matrix factorization or computation of matrix preconditioners to accelerate convergence. Rapid minimization is achieved by the application of two variable substitutions, one to the weighted fidelity constraint and the other to the total variation term. Minimization of the cost functional is achieved by the novel combination of FISTA based iterative re-weighting and soft thresholding.
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