A persistent challenge in solving inverse problems in electrocardiography is the application of suitable constraints to the calculation of cardiac sources. Whether one formulates the inverse problem in terms of epicardial potentials or activation wavefronts, the problem is physically ill-posed and hence results in numerically unstable computations. Suitable physiological constraints applied with appropriate weighting can recover useful inverse solutions. However, it is often difficult to determine the best possible constraints and their optimal weighting. We have recently begun to use multi-electrode catheters as a means of mapping epicardial signals in animal models. To accommodate the sparse sampling of this venous catheter based approach, we have applied statistical signal processing methods to estimate complete epicardial maps of activation time and epicardial potentials. Such measurements-and the estimated maps from them-also have the potential to provide high quality constraints for electrocardiographic inverse problems because they provide direct-albeit sparse-access to the desired solution. In this presentation we describe several approaches we have applied to extract useful constraints from sparsely sampled epicardial signals as well as a training set of epicardial maps, and use them to improve the quality of computed inverse solutions. Results suggest that combining various information sources provides valuable constraint information. Such a multimodal approach to cardiac mapping is clinically and technically viable and offers a possible means to overcome a major remaining limitation of inverse electrocardiography.