A Preconditioned ADMM Strategy for Field-Corrected Non-Cartesian MRI Reconstruction

Sparse reconstruction of non-Cartesian MRI data remains computationally challenging since multiple gridding operations must be executed at each iteration of the reconstruction. Recently, an efficient alternating-direction-method-of-multiplier (ADMM) strategy was proposed for sparse MRI reconstruction. For non-Cartesian MRI, the data fidelity sub-problem must also be solved iteratively. If off-resonance effects are accounted for, standard circulant preconditioners cannot be used to accelerate this task. In this work, we show that an algebraic reformulation of the ADMM scheme enables the use of simple but effective diagonal PCs for non-Toeplitz models, and demonstrate their practical benefit for undersampled SWIRLS 3D CE-MRA.

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