Syllabus
* General theory of inverse problems
Model and data spaces. State of information (probability density, conjuction of probabilities, non-informative state). Information from physical theory. Apriori information and data information. Combining the probabilities. Definition of the solution. Aposteriori information on the model space. Error analysis, resolution and stability. Special cases: Gaussian hypothesis.
* Stochastic methods
Trial and error method. Monte Carlo. Integration by a Monte-Carlo method. Metropolis-Hastings rule and sampling methods. Simulated annealing and parallel tempering. Genetic algorithms.
* Least-squares criterion
Methods and formulas. Analytical solution. Steepest descent method, Newton method. Nonlinear inverse problem. Linearisation. Conjugated gradients and variable metrics.
Backus method. Introduction to inverse problems on infinitely dimensional (functional) spaces.
Annotation
Model space and data space. State of information.
Information obtained from physical theories. Information obtained from measurements.
A priori information. Combination of experimental, a priori and theoretical information.
Solution of the inverse problem. Special cases: Gaussian and generalized Gaussian hypothesis.
The least-squares criterion. Trial and error method.
Stochastic metods (Monte Carlo method, simulated annealing, genetic algorithm). Analysis of error and resolution.