All MRI and MRF data were acquired on a 1.5T whole body scanner (Siemens Espree, Siemens Healthcare, Erlangen, Germany) with a 32 channel head receiver coil (Siemens Healthcare, Erlangen, Germany). A square field of view of 300 × 300 mm2 was covered with a matrix of 128×128 pixels. The slice thickness was 5 mm. Images from each acquisition block were reconstructed separately using non-uniform Fourier transform (NUFFT)50 . The resultant time series of images was used to determine the value for the parameters (T1, T2, M0 and off-resonance) as described above.
In vivo experiments were performed with IRB guidelines, including written informed consent. For the fully sampled spiral acquisition shown in Supplementary Movie1, 48 repetitions were acquired, each with a different interleaf of the total acquisition. A recovery time of 5 seconds was used in between various acquisitions and this was taken into account in the simulated dictionary.
For the phantom study shown in Figure 2 and 4, eight cylindrical phantoms were constructed with varying concentrations of GdCl3 (Aldrich) and agarose (Sigma) to yield different T1 and T2 values ranging from 67 to 1700 ms and 30 to 200 ms, respectively. Standard Spin Echo (SE) sequences were used to quantify T1 and T2 separately (T1 quantification: 13 TRs ranging from 50 to 5000 ms, TE = 8.5 ms, total acquisition time = 33.4 minutes; T2 quantification: Spin Echo sequences with TEs = [15 30 45 60 90 150 200 300 400] ms, TR = 10000 ms, total acquisition time = 3.2 hours.). T1 values were calculated pixel-wise using a standard three-parameter nonlinear least squares fitting routine to solve the equation: S(TR) = a + beT R/T1. T2 values were determined in a pixel-wise fashion using a two-parameter nonlinear least squares fitting routine to solve the equation S(TE) = aeT E/T2, DESPOT1 and DESPOT2 sequences using a fully sampled spiral readout were implemented based on the acquisition values from Deoni et al30 (link): DESPOT1: FA: 4° and 15°, TR:13.6 ms, DESPOT2: FA: 15° and 55°, TR=10.8 ms. The T1 and T2 values were calculated from the equations provided by Deoni et al 30 (link). A 20 s waiting period was used in between the different acquisitions. The initial 10 s of data acquisition was not used in order to ensure that the signal was in steady-state for each of the DESPOT acquisitions. In the following analysis of efficiency, only the pure time of data acquisition for the steady-state DESPOT images is used. For DESPOT1 this was 1.27 s and for DESPOT2 it was 2.29 s (which includes the time for the required DESPOT1 acquisition.)