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Fast Nonconvex $T_2^*$ Mapping Using ADMM

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Document pages: 10 pages

Abstract: Magnetic resonance (MR)-$T 2^*$ mapping is widely used to study hemorrhage,calcification and iron deposition in various clinical applications, it providesa direct and precise mapping of desired contrast in the tissue. However, thelong acquisition time required by conventional 3D high-resolution $T 2^*$mapping method causes discomfort to patients and introduces motion artifacts toreconstructed images, which limits its wider applicability. In this paper weaddress this issue by performing $T 2^*$ mapping from undersampled data usingcompressive sensing (CS). We formulate the reconstruction as a nonconvexproblem that can be decomposed into two subproblems. They can be solved eitherseparately via the standard approach or jointly via the alternating directionmethod of multipliers (ADMM). Compared to previous CS-based approaches thatonly apply sparse regularization on the spin density $ boldsymbol X 0$ and therelaxation rate $ boldsymbol R 2^*$, our formulation enforces additional sparsepriors on the $T 2^*$-weighted images at multiple echoes to improve thereconstruction performance. We performed convergence analysis of the proposedalgorithm, evaluated its performance on in vivo data, and studied the effectsof different sampling schemes. Experimental results showed that the proposedjoint-recovery approach generally outperforms the state-of-the-art method,especially in the low-sampling rate regime, making it a preferred choice toperform fast 3D $T 2^*$ mapping in practice. The framework adopted in this workcan be easily extended to other problems arising from MR or other imagingmodalities with non-linearly coupled variables.

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