Methods that minimise the regularised reconstruction functional: Newton-type methods for least squares, quasi-Newton methods, and proximal splitting for non-smooth and learned priors.
Reading order.
- Least squares: Gauss-Newton Method, Levenberg-Marquardt Method, Line Search.
- Quasi-Newton: L-BFGS, L-BFGS-B with Box Constraints on Conductivity.
- Splitting: Proximal Operator, ADMM, Chambolle-Pock Algorithm, Nested ADMM Reconstruction.
- Stochastic methods: Stochastic and Adaptive Gradient Methods.
- When to stop: Stopping Criteria, Noise-Level Stagnation Test.
A guide to the choice of method is Choosing an Optimizer.
Related. Gradients: Adjoint Gradients; regularisers: Regularization and Learned Priors.
References
- J. Nocedal, S. J. Wright (2006). Numerical Optimization, 2nd ed. Springer. doi:10.1007/978-0-387-40065-5