Regularization

Classical regularisation of the ill-posed EIT problem: penalties that encode prior knowledge, and how to weigh them against the data.

Reading order.

1. The framework: Variational Regularization and Data Fidelity Terms.
2. Penalties: Tikhonov Regularization, Total Variation, Smoothed Total Variation, Spectral Sobolev Norms on Rectangles.
3. Regularisation without a penalty: Truncated SVD Regularization and Implicit Regularization by early stopping.
4. What is sought: Parametrizations of the Conductivity (pixels on any mesh, coarse-to-fine subspaces).
5. What the data determine: Resolution and Confidence Maps.
6. The weight: Choosing the Regularization Parameter.

Related. Priors learned from data are in Learned Priors; the connection is described in Classical and Learned Priors. Minimising the regularised functionals: Optimization.

References

1. M. Benning, M. Burger (2018). Modern regularization methods for inverse problems. Acta Numer. 27, 1–111. doi:10.1017/S0962492918000016