MR imaging reconstruction using a modified descent-type alternating direction method

In the magnetic resonance imaging (MRI) field, total variation (TV) which is the 1-norm of the gradient-magnitude images (GMI) is widely used as the regularization in the compressive sensing (CS) based reconstruction algorithm. Based on the classic augmented Lagrangian multiplier method, we propose a modified descent-type alternating direction method (ADM) for solving the TV regularized reconstruction problems in the following sense: An iteration result generated by the ADM is utilized to generate a descent direction; an appropriate step size along this descent direction is identified; and the penalty parameters are updated. The proposed algorithm effectively combines alternating direction technique with the descent-type method. Extensive results demonstrate that the proposed algorithm, is competitive with, and often outperforms, other state-of-the-art solvers in the field.