Solving the Electrocardiography Inverse Problem by Using an Optimal Algorithm Based on the Total Least Squares Theory

The inverse problem of electrocardiography (ECG) is to estimate the activity of the heart from the measured body surface potentials (BSPs) using the numerical methods. Since it is ill-posed, it needs the dedicated numerical regularization process. The common regularization methods used in the ECG inverse problem, like Tikhonov regularization and Truncated Singular Decomposition (TSVD), are based on the linear least square, in which only the measurement noise in the right hand side BSP data is considered. In the paper, we attempt to investigate the ECG inverse problem with a full consideration of noises/errors appearing on both sides of the linear system equation Ax=b. Here, we solve the ECG inverse problem that reconstructs epicardial potentials (EPs) from BSPs by using an optimal algorithm based on the Total Least Squares (TLS) theory - Regularized TLS (RTLS), which has not been investigated in the bioelectromagnetic inverse problems. The algorithm is tested by using a realistic shaped heart-lung-torso model with inhomogeneous conductivities. The performance of the RTLS is compared with other conventional approaches like Tikhonov and TSVD. In the numerical experiments, the EPs are reconstructed with a combination of measurement noise and/or geometry errors. The simulation results demonstrate that, in most cases, RTLS performs better than Tikhonov and TSVD. With proper physiological constraints, RTLS is able to robustly reconstruct EPs from BSPs, and therefore is a promising, feasible alternative for the ECG inverse problem.