Yang Li^{1}, SHUAI Wang^{1}, Edward S. Hui^{2,3}, Di Cui^{2}, Hing-Chiu Chang^{2}, and Yik-Chung Wu^{1}

Magnetic resonance fingerprinting (MRF) is a novel and efficient method for the estimation of MR parameters, such as off-resonance (DB0), proton density (PD), T1 and T2. Because of the highly undersampled readout that is conventionally used, large number of dynamics (e.g. <1000) are often acquired for maintaining the fidelity of MR parameter estimations (a.k.a. dictionary matching). In this study, we propose a new algorithm, MRF reconstruction using majorization-minimization (mmMRF), such that fidelity of dictionary matching can remain similar even when significantly less number of dynamics are available.

**Materials**** ****and**** ****Methods**** **

Experiments All scans were performed on a 3T MRI scanner (Achieva, Philips Healthcare, Best) using an in-house IR-bSSFP MRF sequence with acquisition window of 5.8 ms. A variable density spiral readout trajectory with R = 24 within a radius of 25% kmax and R = 48 outside as well as zeroth moment nulling was designed using the code by Brian Hargreaves (http://www-mrsrl.stanford.edu/~brian/mintgrad/). The trajectory was sequentially rotated by after each dynamic. Other imaging parameters were: TR = 8.5 – 10.5 ms, FA = 0 – 60o, FOV = 300 mm, acquisition matrix = 128, slice thickness = 5 mm, number of dynamics = 1000. Dictionary was computed and conventional dictionary matching of MRF data were performed as previously described (1).

mmMRF To improve MRF reconstruction, a maximum likelihood estimation framework was proposed by Zhao et al (2), but it is a challenging large-scale nonconvex least square optimization problem. Zhao et al applied the alternating direction method of multipliers (ADMM), but convergence may not be guaranteed. Furthermore, since the penalties of multipliers requires adjustment and the conjugate gradient method is applied in each iteration, ADMM may not be efficient. To this end, this work proposes an accelerated majorization-minimization (MM) algorithm that guarantees convergence. In particular, MM is an iterative method where the challenging nonconvex least square optimization problem is replaced by a tight convex upper bound expanded around the last round solution (3). With the approximated problem, the algorithm is then able to support parallel computation for each voxel and the total complexity is moderate with order O(QM), where M is the number of dynamics and Q the size of dictionary. The cost function of our method is thus same as that proposed by Zhao et al (2). Our algorithm also incorporates the acceleration technique proposed by Beck et al (4) and the sparsity-induced method by Davies et al (5). Each mmMRF iteration takes 20 seconds.

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2. Zhao B, Setsompop K, Ye H, Cauley SF, Wald LL. Maximum Likelihood Reconstruction for Magnetic Resonance Fingerprinting. IEEE Trans. Med. Imaging [Internet] 2016;0:1–1. doi: 10.1109/TMI.2016.2531640.

3. Muckley MJ, Noll DC, Fessler JA. Fast parallel MR image reconstruction via B1-based, adaptive restart, iterative soft thresholding algorithms (BARISTA). IEEE Trans. Med. Imaging 2015;34:578–588. doi: 10.1109/TMI.2014.2363034.

4. Beck A, Teboulle M. A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems. SIAM J. Imaging Sci. 2009;2:183–202. doi: 10.1137/080716542.

5. Davies M, Puy G, Vandergheynst P, Wiaux Y. A Compressed Sensing Framework for Magnetic Resonance Fingerprinting. 2013:32.