The purpose of this study is to form PET image reconstruction sparse priors based on MR image learned dictionaries in Bayesian PET image reconstruction and to evaluate the performance in myocardial perfusion (MP) defect detection. A set of time activity curves representing the typical patient Rb-82 bio-distribution was applied in the analytical simulation with 2.5-min and 4.5-min cumulated activities. For each count levels, we used the 4D XCAT phantom to simulate two MP imaging datasets, one with normal MP and the other with a reduced activity region on the left ventricle. Using the SIMRI simulator, MR images were simulated with sequence specified to be 3D T1-weighted as in a clinical PET/MRI protocol. The maximum a posterior (MAP) PET image reconstruction that took dictionary-based sparse approximation of PET images as the prior was applied. Assuming that the PET and MR images can be sparsified under the same dictionary, the K-SVD algorithm was used in the dictionary learning (DL) process from the MR images. The receiver operating characteristic (ROC) analysis on the reconstructed images for perfusion defect detection was performed using a channelized Hotelling observer (CHO). The DL MAP algorithm demonstrated improved noise versus bias tradeoff compared to that from the ML algorithm and also provided better performance in the MP defect detection task.