Efficient Early Stopping algorithm for Quantitative Susceptibility Mapping (QSM)

摘要

Introduction: Susceptibility maps are calculated from local magnetic field maps estimated from the phase of Gradient Echo MRI acquisitions by solving an ill-posed inverse problem. Most inversion methods rely on minimizing a functional until it converges1. This is time-consuming and requires fine-tuning of one or more parameters by performing the inversion many times. A recent nonlinear gradient descent (GD) algorithm2 may lead to results comparable to state-ofthe- art MEDI3 and FANSI4 by stopping the algorithm before it diverges from the true solution2. The algorithm was stabilized by a Tikhonov term largely independent of its weight. In this new framework, the number of iterations becomes the main parameter that controls the results. Nevertheless, GD algorithms typically require hundreds of iterations (albeit fast) to achieve optimal results, and manual supervision is needed as there are no available automatic methods to reliably stop these algorithms. Here, we propose an efficient nonlinear conjugate gradient method to achieve optimal results in significantly fewer iterations than other GD methods.