Fast magnetic susceptibility reconstruction using L0 norm of gradient

Abstract

There is a growing interest in quantifying tissue susceptibility in MRI. However, the zeros in the dipole kernel makes the calculation of the magnetic susceptibility from the measured field to be an ill-posed problem. Recently, Bayesian regularization approaches have been utilized to enable accurate quantitative susceptibility mapping(QSM), such as L2 norm gradient minimization and TV. In this work, we propose an efficient QSM method by using a sparsity promoting regularization which called L0 norm of gradient to reconstruct susceptibility map. The use of L0 norm allows us to yield high quality image and prevent penalizing salient edges. Since the L0 minimization is an NP-hard problem, a special alternating optimization strategy by introducing an auxiliary variable is adopted to solve the problem and it only takes 1-2 mins to reconstruct the whole 3D susceptibility data. Both numerical phantom simulations and human brain tests are performed to demonstrate the superior performance of the proposed method compared with previous methods.