A regularized trust region method for joint reconstruction of spin magnitude, T2∗ decay, and off-resonance field map

Joint reconstruction of three parameter images - spin magnitude, T₂^* decay and off-resonance field map - is an important technique in some applications of magnetic resonance imaging (MRI). Despite its importance, the reconstruction problem is very challenging due to its nonlinearity and ill-conditioning. The standard conjugate gradient (CG) method with regularization is usually very slow for this problem. In this work, we propose a novel regularized trust region (TR) method that reconstructs the three images by solving a constrained linear sub-problem in each iteration. In particular, this method employs a change-of-variable technique, making the sub-problem linear yet keeping the convergence fast. To solve the sub-problem, we use a penalty method with preconditioned conjugate gradient (PCG) algorithm. Based on a synthesized data set, we demonstrate that our algorithm stably converges even with a poor initial guess, and the convergence rate is much higher than that of the CG algorithm.