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Improving Tikhonov regularization with linearly constrained optimization: application to the inverse epicardial
1Institute of Biomedical Engineering, University of Montreal, Quebec, Canada.
Mathematical Biosciences
|November 1, 1992
Summary
New methods enhance Tikhonov regularization for ill-posed problems without prior knowledge. These techniques improve accuracy and provide qualitative insights for inverse problems like electrocardiography.
Area of Science:
- Computational mathematics
- Biomedical engineering
- Inverse problems
Background:
- Tikhonov regularization is a standard method for solving ill-posed inverse problems.
- Existing methods often require prior knowledge of the solution or error characteristics.
- Improving accuracy and qualitative information retrieval remains a challenge.
Purpose of the Study:
- To present two novel methods for enhancing Tikhonov regularization accuracy.
- To apply these methods to the inverse problem of electrocardiography.
- To demonstrate improved solution recovery without a priori assumptions.
Main Methods:
- Development of two Tikhonov regularization improvement techniques.
- Exploitation of overregularized and underregularized Tikhonov solutions.
- Application to a spherical heart-torso model with simulated potential distributions.
Main Results:
- The proposed methods yield more accurate epicardial solutions than the optimal Tikhonov solution.
- Qualitative information, such as correct extrema positioning, is obtained.
- These improvements are achieved without prior knowledge of solution or error properties.
Conclusions:
- The novel methods offer significant improvements over standard Tikhonov regularization for inverse problems.
- Accurate and qualitatively informative solutions can be recovered using these techniques.
- A heuristic approach for selecting regularization parameters is discussed.