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Magnetic resonance fingerprinting (MRF) is able to estimate multiplequantitative tissue parameters from a relatively short acquisition. The maincharacteristic of an MRF sequence is the simultaneous application of (a)transient states excitation and (b) highly undersampled $k$-space. Despite thepromising empirical results obtained with MRF, no work has appeared thatformally describes the combined impact of these two aspects on thereconstruction accuracy. In this paper, a mathematical model is derived thatdirectly relates the time varying RF excitation and the $k$-space sampling tothe spatially dependent reconstruction errors. A subsequent in-depth analysisidentifies the mechanisms by which MRF sequence properties affect accuracy,providing a formal explanation of several empirically observed or intuitivelyunderstood facts. New insights are obtained which show how this analyticalframework could be used to improve the MRF protocol.

Understanding the combined effect of $k$-space undersampling and transient states excitation in MR Fingerprinting reconstructions