Application of L1-norm regularization to epicardial potential reconstruction based on gradient projection

Area of Science:

• Biomedical Engineering
• Computational Electrophysiology

Background:

• The inverse problem of electrocardiography (ECG) aims to determine epicardial potentials (EPs) reflecting myocardial activity.
• Traditional L2-norm regularization methods for this ill-posed problem cause excessive solution smoothing, hindering accurate abnormality detection.
• Direct L1-norm regularization increases computational complexity due to non-differentiability.

Purpose of the Study:

• To develop an efficient L1-norm regularization method for the ECG inverse problem.
• To reduce computational complexity and enable rapid convergence.
• To improve the accuracy of EP reconstruction compared to existing methods.

Main Methods:

• Proposed an L1-norm regularization technique utilizing variable splitting to achieve differentiability.
• Formulated the ECG inverse problem as a bound-constrained quadratic problem.
• Employed gradient projection for iterative and efficient solution.

Main Results:

• The proposed method demonstrated superior accuracy in reconstructing EPs compared to L2- and standard L1-norm methods.
• Successfully handled both measurement and geometry noise, particularly under large noise conditions.
• Achieved more precise localization of diseased regions and abnormality distinction.

Conclusions:

• The novel L1-norm regularization method offers a computationally efficient and accurate solution for the ECG inverse problem.
• This approach improves the reliability of EPs for diagnosing cardiac conditions.
• The method shows significant potential for clinical applications requiring precise myocardial activity mapping.