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The authors present a new method for regularizing the ill-posed problem of computing epicardial potentials from body surface potentials. The method simultaneously regularizes the equations associated with all time points, and relies on a new theorem which states that a solution based on optimal regularization of each integral equation associated with each principal component of the data will be more accurate than a solution based on optimal regularization of each integral equation associated with each time point. The theorem is illustrated with simulations mimicking the complexity of the inverse electrocardiography problem. As must be expected from a method which imposes no additional a priori constraints, the new approach addresses uncorrelated noise only, and in the presence of dominating correlated noise it is only successful in producing a "cleaner" version of a necessarily compromised solution. Nevertheless, in principle, the new method is always preferred to the standard approach, since it (without penalty) eliminates pure noise that would otherwise be present in the solution estimate.