An emerging research direction considers the inverse problem of inferring electrocardiogram (ECG) from photoplethysmogram (PPG) to bring about the synergy between the easy measurability of PPG and the rich clinical knowledge of ECG to facilitate preventive healthcare. Previous reconstruction using a universal basis has limited accuracy due to the lack of rich representative power. This paper proposes a cross-domain joint dictionary learning (XDJDL) framework to maximize the expressive power for the two cross-domain signals. Building on K-SVD technique, XDJDL optimizes simultaneously the PPG and ECG signal representations and the transform between them, enabling the joint learning of a pair of signal dictionaries with a transform to characterize the relation between their sparse codes. The proposed model is evaluated with 34,000+ ECG/PPG cycle pairs containing a variety of ECG morphologies and cardiovascular diseases. Experimental results validate the accuracy and the generality of the proposed algorithm, suggesting an encouraging potential for disease screening using PPG measurement based on the proactive learned PPG-ECG relationship.