Technologies de l’Information pour la Santé

10H30

Coefficient 1

Presentation of the difficulties arising in the inversion of a physical model. Presentation of the main frameworks and methods addressing the resolution of inverse problems.

• Context: case studies; difficulties arising in the inversion of an ill-posed problem (interpretation considering singular values and interpretation in the Fourier domain); information loss, necessity to regularize the problem, concept of prior information.
• Deterministic approaches: truncated singular value decomposition; estimation by minimization of a cost function.
• Overview of Bayesian statistics (Bayes’ rule, choice of an estimator, Monte Carlo methods).
• Stochastic approaches: maximum likelihood estimation – maximum a posteriori estimation – Markovian models – estimation of hyperparameters.

Laboratory session 1: deterministic methods – application to spike trains deconvolution and tomography (matlab).
Laboratory session 2: stochastic methods – application seismic exploration (matlab).

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