Myocardial perfusion imaging (MPI) using rest/stress single photon emission computed tomography (SPECT) allows non-invasive assessment of reversible cardiac perfusion defects. Conventionally, reversible defects are identified using a difference image, called reversible map, obtained by subtracting the stress image from the rest image after registration and normalization of the two images. The identification of reversible defects using the conventional subtraction method is however limited by noise. We propose to jointly reconstruct rest and stress projection data to directly obtain the reversible map in a single reconstruction framework to improve the detectability of reversible defects. To evaluate the performance of the proposed method, we performed phantom studies to mimic reversible defects with different levels of severity and doses. As compared to the conventional subtraction method, the joint method yielded reversible maps with much lower noise and improved defect detectability. At a normal clinical dose level, the joint method improved the signal to noise ratio (SNR) of defect contrast in reversible maps from 13.2 to 66.4, 9.7 to 35.0, 6.1 to 13.2, and 3.1 to 6.5, for defect to normal myocardium concentration ratios of 0%, 25%, 50%, and 75%, respectively. The SNRs obtained using the joint method were improved from 6.1 to 13.2, 3.9 to 9.4, 3.0 to 8.0, and 2.1 to 7.1, for 100%, 75%, 50%, and 25% of the normal clinical dose as compared to the conventional subtraction method. To access clinical feasibility, we applied the joint method to a rest/stress SPECT MPI patient study. The joint method yielded a reversible map with much lower noise, translating into a much higher defect detectability as compared to the conventional subtraction method. Our results indicate that the joint method has the potential to improve radiologists' performance for assessing defects in rest/stress SPECT MPI. In addition, the joint method can be used to reduce dose or imaging time.