Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In the magnetic resonance imaging MRI field, total variation TV which is the i¾?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,  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.
['Hao Chen', 'Jinxu Tao', 'Yuli Sun', 'Bensheng Qiu', 'Zhongfu Ye']
I am writing a research paper on a idea MR imaging reconstruction using a modified descent-type alternating direction method
[{"from": "human", "value": "I am writing a research paper on a idea MR imaging reconstruction using a modified descent-type alternating direction method"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In the magnetic resonance imaging MRI field, total variation TV which is the i\u00be?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,  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."}]