The application of subspace preconditioned LSQR algorithm for solving the electrocardiography inverse problem.

Area of Science:

• Biomedical Engineering
• Computational Electrophysiology
• Medical Imaging

Background:

• Electrocardiogram (ECG) inverse problems, like computing epicardial potentials from body surface potentials, are often ill-posed.
• Regularization techniques are crucial for obtaining stable and accurate solutions to these inverse problems.
• Existing methods such as LSQR, LSQR-Tik, and Tik-LSQR have limitations in efficiency and accuracy.

Purpose of the Study:

• To investigate the efficacy of subspace preconditioned LSQR (SP-LSQR) for model-based ECG inverse problems.
• To explore and compare different subspace splitting methods for designing preconditioners.
• To evaluate the performance enhancement of SP-LSQR when optimized with genetic algorithms (GA).

Main Methods:

• Application of subspace preconditioned LSQR (SP-LSQR) to ECG inverse problems.
• Implementation of three subspace splitting schemes: Singular Value Decomposition (SVD), wavelet transform, and cosine transform for preconditioner design.
• Validation using a realistic heart-torso model simulation protocol and comparison with LSQR, LSQR-Tik, and Tik-LSQR.

Main Results:

• SP-LSQR demonstrated superior efficiency and accuracy in reconstructing epicardial potential distributions compared to LSQR, LSQR-Tik, and Tik-LSQR.
• The SVD-based preconditioner exhibited the best convergence rate and yielded the most accurate inverse solutions among the tested subspace schemes.
• Optimization using genetic algorithms (GA) further enhanced the performance of the SP-LSQR method.

Conclusions:

• SP-LSQR is a highly effective regularization technique for solving ill-posed cardiac inverse problems.
• The choice of subspace splitting method significantly impacts the performance, with SVD proving most effective.
• Genetic algorithm optimization can further improve the robustness and accuracy of SP-LSQR for ECG inverse solutions.