Inverse problems are usually ill‐conditioned, requiring the adoption of regularization techniques to obtain reliable results. The choice of the regularization method and of the related parameters represents a critical issue that must be based on the knowledge of reliable additional information on the problem. In the paper some possibilities and pitfalls for the choice of regularization strategy are presented and compared.
Electromagnetic inverse problems (EIP) are usually formulated starting from a direct problem, based on a direct operator, providing the effects (e.g. fields, fluxes) generated by known sources acting through known systems. The direct operators involved in many real world electromagnetic phenomena, due to their compactness, lead to ill posed inverse problems. Inversion procedures pursue the solution regularity through the adoption of various regularization techniques. Improper use of regularizations may unduly constrain the approximated solution and, consequently, cause significant lack of accuracy. Mathematical tools for an effective choice of the regularization technique are not available for every application, and a number of issues are still open. The paper presents a common mathematical model for most of the regularization techniques, discussing their benefits and limitations.
The paper discusses limits, applicability conditions, and impact on the performance of reconstruction procedures, of some relevant characteristics of the inversion algorithms, with particular reference to robustness against noise and inaccuracies in the system parameters.
Some criteria for an effective application of regularization are also discussed, showing in particular how proper choices, founded on a careful analysis of the direct problem, may reveal quite effective in improving the solution quality.
