A coupling model and ADMM algorithm based on TGV and shearlet regularization term for MRI reconstruction

Motivated by the ideas from two step model and its deformation, we propose a coupling model for MR image reconstruction, based on the advantages of TGV and shearlet regularization terms. By using variable splitting technique, splitting Bregman iteration scheme and alternating minimization method, the proposed model can be decomposed into several subproblems to avoid solving high-order PDEs. The u subproblem can be solved by Cramer’s rule and the diagonalization technique of the Fourier transform. The other subproblems can be solved simply by some shrinkage formulas. We also use the Barzilai-Borwein step selection scheme to accelerate these subproblem’s solutions. Finally, an ADMM algorithm is proposed to solve the coupling model. The numerical results show that the proposed coupling model and algorithm are feasible and effective.