Image restoration can be considered the basic model of inverse problems. Recent regularization approaches involve the minimization of special Tikhonov functionals, with nonlinear data fitting and/or penalty terms aimed at reducing oversmoothness and ringing effects, promoting sparsity, or dealing with specific model-dependent noise filtering. The minisymposium will focus on nonlinear regularization methods, with special emphasis to adaptive strategies such as trust region techniques, unsupervised choice of the regularization level, automatic selection of the domain where enforcing the sparsity. Ill-posed imaging problems, with Poisson and Gauss models arising in different application fields such as medical imaging and geophysics, will be discussed.

Adaptive image restoration in variable exponent Lebesgue spaces

Claudio Estatico (University of Genoa)

On an elliptical trust-region procedure for ill-posed nonlinear least squares problems

Stefania Bellavia (University of Florence)

Poisson imaging reconstruction by means of a consistent adaptive regularization method promoting (grouped) sparsity

Sabrina Guastavino (University of Genoa)

An infimal-convolution modelling for mixed image denoising problems

Luca Calatroni (CMAP, École Polytechnique CNRS)

Organizers:

Claudio Estatico (University of Genoa)

Giuseppe Rodriguez (University of Cagliari)

Keywords:

image reconstruction, inverse problems, nonlinear optimization, numerical linear algebra