Things arising from electrocardiographic imaging: toward a theory of partial inverse problems.

The task of Electrocardiographic Imaging is an ill-posed inverse problem, requiring regularization. However, it has special features, firstly because it is a "non-stationary" inverse problem, and secondly because the inherent dynamical variety (e.g., epicardial breakthroughs, arrhythmias, ischemic changes) may preclude a fruitful nontrivial process model. Importantly, its structure places it in the category of "partial inverse problems" - a theory that arises from this setting. Surprising features of the resulting regularization methodology include the ability to fashion nontrivial regularization matrices in part (and sometimes entirely) from the data. There is evidence that these theoretical results can have significant practical benefits.