Spatial sparse constraint in the transmembrane potential based ECG inverse problem

The aim of Electrocardiographic (ECG) inverse problem is to use the measured ECG signals on the body surface to noninvasively reconstruct the activity of heart. Due to the ill-posedness, the solution of ECG inverse problem needs employ as much prior information about the cardiac activities as possible. In this study, the spatial sparse performance of the transmembrane potential (TMP) was investigated as a priori constraint to tackle the TMP based ECG inverse problem for the first time. The existence of the spatial sparseness was detailed analyzed and a novel spatial variation operator in terms of the spatial connection relationship of the heart mesh was proposed to describe it, and combined as a L1 norm penalty term into the solution of the TMP based ECG inverse problem. The iteratively reweighted norm (IRN) algorithm was used to solve the L1 norm based problem. With the simulation study based on the virtual heart and realistic volume conductor model, the proposed method was compared to the common Tikhonov method with zero order and spatial Laplacian operators to reconstruct the TMP on the cardiac surface. The results demonstrated that the spatial sparseness constraint is successfully combined into the ECG inverse problem and more accurate TMP distribution can be obtained.