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Description
Magnetic Resonance Fingerprinting (MRF) allows to determine MR relaxation times quantitatively, but its performance depends on the design of acquisition schemes to enable robust parameter estimation from highly undersampled data [1]. Earlier work by Zhao et al. introduced a smoothness constraint in a Cramér-Rao lower bound-based optimization framework, motivated by the observation that smoother flip angle sequences show better performance with respect to undersampling artifacts [2]. To reduce undersampling-related artifacts, several sequence optimization approaches have been proposed [3,4]. Notably, these methods often impose an additional smoothness constraint on the flip angle sequence, even when the optimization objective already explicitly accounts for undersampling effects. In this work, we investigate the role of smoothness regularization in MRF sequence optimization. This raises a fundamental question: why is smoothness regularization still required in optimization schemes that are already designed to mitigate undersampling artifacts? To address this, we analyze the effect of different smoothness constraints on the resulting sequences and their performance in numerical simulations, phantom measurements, and in vivo experiments. Our results show that the commonly used smoothness constraint is not optimal in this setting and that alternative choices can improve performance. Furthermore, we demonstrate that omitting smoothness regularization altogether leads to a breakdown of the optimization procedure, underscoring its importance for stable and effective sequence design in MRF. Ultimately, this shows that the assumptions used to describe the functional to be minimized are overly simplistic and do not lead to improvements without additional constraints. 1 Ma D et al. Magnetic resonance fingerprinting. Nature. 2013;495:187–192. 2 Zhao B et al. Optimal experiment design for magnetic resonance fingerprinting: Cramér-Rao bound meets spin dynamics. IEEE Trans Med Imaging. 2019;38(3):844–861. 3 Heesterbeek DGJ et al. Mitigating undersampling errors in MR fingerprinting by sequence optimization. Magn Reson Med. 2023;89:2076–2087 4 Zibetti MVW et al. Optimization of 3D MR fingerprinting with Cramér-Rao lower bound and smooth signal evolutions for efficient T1, T2, and T1ρ in the knee joint. In: Proceedings of ISMRM Annual Meeting; 2025 May; Honolulu, Hawaii, USA. Abstract 1688.