A Variational Non-Linear Constrained Model for the Inversion of FDEM Data

Inverse problems arise in many fields of science and engineering like, e.g., astronomy, medicine, geophysics, imaging, and machine learning. We are faced with an inverse problem whenever we wish to reconstruct an unknown signal from some measured data that is generated by the first via a possibly unknown function. This function may be linear or non-linear. In either case the solution of the inverse problem is usually very sensitive to the presence of perturbations in the data. Regularization methods aim at reducing this sensitivity. For both linear and non-linear problems numerical linear algebra techniques can be used to design accurate and efficient regularization methods. Moreover, in recent years the dimension of the problems at hand has been steadily increasing. Therefore model reduction techniques, like Krylov methods, play a fundamental role in reducing the computational complexity, thus allowing the solution of extremely large problems in a reasonable amount of time. In this minisymposium we wish to provide an overview of how numerical linear algebra techniques can be exploited in the solution of linear and non-linear ill-posed inverse problems. New problems and new approaches will be presented combining classical numerical linear algebra techniques with more recent methods. Numerical experiments will show the performances of the proposed algorithms.