On epicardial potential reconstruction using regularization schemes with the L 1 - norm data term. The electrocardiographic ECG inverse problem is ill-posed and usually solved by regularization schemes. These regularization methods , such as the Tikhonov method , are often based on the L 2- norm data and constraint terms. However, L 2- norm -based methods inherently provide smoothed inverse solutions that are sensitive to measurement errors, and also lack the capability of localizing and distinguishing multiple proximal cardiac electrical sources.
This paper presents alternative regularization schemes employing the L 1 - norm data term for the reconstruction of epicardial potentials EPs from measured body surface potentials BSPs.
During numerical implementation, the iteratively reweighted norm algorithm was applied to solve the L 1 - norm -related schemes, and measurement noises were considered in the BSP data.
The proposed L 1 - norm data term-based regularization schemes with L 1 and L 2 penalty terms of the normal derivative constraint labelled as L 1 TV and L 1 L 2 were compared with the L 2- norm data terms Tikhonov with zero-order and normal derivative constraints, labelled as ZOT and FOT, and the total variation method labelled as L 2TV.
The studies demonstrated that, with averaged measurement noise, the inverse solutions provided by the L 1 L 2 and FOT algorithms have less relative error values. However, when larger noise occurred in some electrodes for example, signal lost during measurement , the L 1 TV and L 1 L 2 methods can obtain more accurate EPs in a robust manner. Therefore the L 1 - norm data term-based solutions are generally less perturbed by measurement noises, suggesting that the new regularization scheme is promising for providing practical ECG inverse solutions.
