Compared to the clinical 12-lead electrocardiogram, the ECG imaging (ECGI) provides a unique way to study the electric activity of the heart using body surface potential mapping (BSPM), which consists of hundreds of electrodes on the torso surface. This essentially presents an inverse problem, and the associated ill-posedness has posed a tremendous challenge to monitor the variation of epicardial potential via the BSPM: the solution is vulnerable to measurement noise and highly sensitive to the variation of mesh resolution in boundary element method framework. While regularization has been introduced to constrain the solution space, including the Tikhonov regularization and truncated singular value decomposition (TSVD) methods, they mostly ignore the spatiotemporal correlation of the electrical potential distribution on the epicardial surface and the heart potential is typically reconstructed at each time stamp independently. This has crimped the effectiveness of most existing approaches. In this present study, we aim to recover the epicardial potential in a certain time span simultaneously, capitalizing on the inherent spatiotemporal correlation. Specifically, we propose a novel low-rank and joint-sparse decomposition (LJSD) and optimization to solve the inverse problem. This iterative optimization problem is easy to solve and the numerical result suggests that it outperforms those conventional regularization approaches.