280390 VO Inverse Problems (2023W)

The course deals with the resolution of ill-posed problems, e.g. inverse problems from physics and simple problems from data science of data fitting type. More precisely, the following aspects will be covered:
-- Linear regression (and statistical aspects of least squares)
-- Discretization of continuous inverse problems
-- Rank deficiency and ill-conditioning (the SVD and the generalized inverse)
-- Tikhonov regularization
-- Iterative methods (CG and CGLS methods)
-- Nonlinear regression (Newton's method etc).

All of these topics will be complemented with exercises (Matlab or Octave).