This paper aims to identify approaches that generate appropriate synthetic data (computer generated) for cardiac phase-resolved blood-oxygen-level-dependent (CP-BOLD) MRI. CP-BOLD MRI is a new contrast agent- and stress-free approach for examining changes in myocardial oxygenation in response to coronary artery disease. However, since signal intensity changes are subtle, rapid visualization is not possible with the naked eye. Quantifying and visualizing the extent of disease relies on myocardial segmentation and registration to isolate the myocardium and establish temporal correspondences and ischemia detection algorithms to identify temporal differences in BOLD signal intensity patterns. If transmurality of the defect is of interest pixel-level analysis is necessary and thus a higher precision in registration is required. Such precision is currently not available affecting the design and performance of the ischemia detection algorithms. In this work, to enable algorithmic developments of ischemia detection irrespective to registration accuracy, we propose an approach that generates synthetic pixel-level myocardial time series. We do this by 1) modeling the temporal changes in BOLD signal intensity based on sparse multi-component dictionary learning, whereby segmentally derived myocardial time series are extracted from canine experimental data to learn the model; and 2) demonstrating the resemblance between real and synthetic time series for validation purposes. We envision that the proposed approach has the capacity to accelerate development of tools for ischemia detection while markedly reducing experimental costs so that cardiac BOLD MRI can be rapidly translated into the clinical arena for the noninvasive assessment of ischemic heart disease.