Truncated total least squares: a new regularization method for the solution of ECG inverse problems

Area of Science:

• Biomedical Engineering
• Computational Electrophysiology
• Medical Imaging

Background:

• Reconstructing epicardial potentials (EPs) from body surface potentials (BSPs) is an ill-posed inverse problem crucial for understanding cardiac electrical activity.
• Existing methods struggle with geometric and measurement errors inherent in the electrocardiogram (ECG) inverse problem.
• Geometric errors significantly impact the accuracy of the transfer matrix in the system equation AX = B.

Purpose of the Study:

• To introduce and evaluate the truncated total least squares (TTLS) method for reconstructing EPs from BSPs.
• To assess TTLS's performance in the presence of both geometric and measurement errors.
• To compare TTLS with conventional regularization techniques like Tikhonov and truncated single value decomposition (TSVD).

Main Methods:

• Application of the truncated total least squares (TTLS) method to solve the inverse problem.
• Utilizing a realistic heart-lung-torso model with inhomogeneous conductivities for simulations.
• Employing the h-adaptive boundary element method (h-BEM) for forward modeling.
• Comparing TTLS with Tikhonov and TSVD using zeroth-, first-, and second-order regularization.

Main Results:

• TTLS achieves comparable results to Tikhonov and TSVD when only measurement noise is present.
• TTLS demonstrates superior performance compared to Tikhonov and TSVD when geometric errors are involved.
• Zeroth-order regularization is identified as the optimal choice for the ECG inverse problem using TTLS.

Conclusions:

• The TTLS method offers a robust solution for reconstructing EPs from BSPs.
• TTLS effectively accounts for errors on both sides of the system equation, including geometric inaccuracies.
• TTLS presents a promising alternative for solving complex ECG inverse problems.