The IDEAL signal model for hyperpolarized metabolic imaging is extended and spatiotemporal regularization and b0-map recalibration is included. The approach is tested on simulated data and in-vivo metabolic imaging data of the heart. Allowing variable b0-fields and including sparsity regularization signal leakage and ghosting can be significantly reduced (average reduction of root-mean-square error (RMSE) by 16% and 30%). Spatial and temporal regularization of the metabolite intensities considerably improved accuracy of the estimate in terms of RMSE with additional reductions by 68% and 20%, respectively. Thus, the metabolic conversion of [1-13C]pyruvate into [1-13C]lactate and 13C-bicarbonate can be measured with improved accuracy.