Quantitative Susceptibility Mapping (QSM) is an ill-posed inverse problem often solved by regularization: minimizing a functional until it converges. This is usually time-consuming, requiring fine-tuning of several parameters by many repetitions of the whole optimization solver. Nonlinear Dipole Inversion is a QSM method that solves a nonlinear Tikhonov-regularized functional with a gradient descent solver. We show that stopping this method early provides optimal results, largely independent of the regularization weight. Here, we propose a non-regularized nonlinear conjugate gradient solver with a new stopping criterion based on analysing susceptibility map spatial frequency coefficients to achieve fast, parameter-free and automatic QSM.
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