Quantitative myocardial T1 mapping finds increasing applications in clinical cardiovascular magnetic resonance (CMR) imaging. For example, native myocardial T1 mapping can be used to detect myocardial edema, while T1 maps after contrast agent are helpful for the detection of fibrosis and/or storage diseases [
1,
2]. To date, developments have enabled fast cardiac T1 mapping in a clinically acceptable time, i.e., from 11 to 17 heartbeats within one breathhold. Representative techniques include modified Look-Locker inversion recovery (MOLLI) [
3], short modified Look-Locker inversion recovery (shMOLLI) [
4], saturation recovery single-shot acquisition (SASHA) [
5], and saturation pulse prepared heart rate independent inversion recovery (SAPPHIRE) [
6]. Although MOLLI and variants are the most widely used techniques [
2], they still face several challenges: (1) the occurrence of banding artifacts, in particular at high field strengths, which are due to balanced steady state free precession (bSSFP) off-resonance effects, (2) the underestimation of T1 values due to an imperfect physical modeling, and (3) a breathhold time of 11 to 17 heartbeats which may be challenging for patients. Several ideas have been proposed to overcome these limitations. For example, replacing the bSSFP readout by a fast low angle shot (FLASH) acquisition completely avoids banding artifacts [
7‐
11]. More complex physical models, which take care of the inversion efficiency or slice profile effects improve the accuracy of T1 estimation [
8,
12]. More recently, non-Cartesian acquisition schemes (mainly radial) have been employed to enable fast myocardial T1 mapping [
9‐
11]. Specifically, the combination of radial encoding with sliding window image reconstruction [
10], compressed sensing [
9] and real-time CMR [
11] has enabled high-resolution myocardial T1 mapping within a single inversion-recovery (IR) relaxation process.
Model-based reconstructions [
13‐
21] represent another strategy to accelerate quantitative parameter mapping in general. Such methods exploit inherent data redundancy by estimating parameter maps directly from an undersampled k-space for a known signal model [
14]. With respect to T1 mapping, it has been proposed to iteratively optimize model parameters by alternating between k-space and image-space [
17] with applications to the brain and heart [
22]. On the other hand, recent developments formulate T1 estimation as a nonlinear inverse problem [
19‐
21,
23]. In this way, a priori information such as sparsity constraints can be easily incorporated into the reconstruction to increase performance and in particular improve T1 accuracy and precision.
In this work, we extend a previously developed method [
20] for sparsity-constrained model-based T1 estimation to allow for cardiac applications. The data acquisition is based on a single-shot IR radial FLASH sequence and triggered to early diastole. The proposed method is validated for an experimental phantom at simulated heart rates and in vivo studies with 8 healthy subjects.