The sparsity principle, which consists of representing some phenomena with as few variables as possible, has been recently exploited with success in variational image processing. Most of the activities in this context have been dedicated to two (overlapping) research areas. The first includes works pursuing the design of new sparsity-promoting priors both in synthesis-based, analysis-based, and hybrid models. The second deals with devising efficient and robust algorithms for solving the typically large scale and possibly non-smooth non-convex optimization problems raised by sparsity-constrained regularization. This mini-symposium addresses theoretical and numerical issues which arise from designing sparsity-promoting techniques in variational image processing.

Sparsity-inducing Non-convex Regularization for Convex Image Processing

Ivan Selesnick (New York University)

Class-adapted and Scene-Adapted Regularization for Imaging Inverse Problems

Mário Figueiredo (Instituto de Telecomunicações and IST, University of Lisboa)

Nonconvex regularization of numerical differentiation of noisy images

Rick Chartrand (Descartes Labs)

Robust and stable region-of-interest tomographic reconstruction by sparsity-inducing convex optimization

Demetrio Labate (University of Houston)

Convex Envelopes for Least Squares Low Rank Approximation

Carl Olsson (Chalmers University of Technology)

Exact continuous relaxations for the l0-regularized least-squares criteria

Emmanuel Soubies (EPFL, Biomedical Imaging Group, Lausanne VD)

On regularization/convexification of functionals including an l2-misfit term

Marcus Carlsson (Lund University)

Alternating structure-adapted proximal gradient descent (ASAP) for nonconvex nonsmooth regularised problems with smooth coupling terms. Applications in imaging problems

Pauline Tan (CMLA, École normale supérieure Paris-Saclay)

Organizers:

Alessandro Lanza (Dept. Mathematics, University of Bologna)

Serena Morigi (Dept. Mathematics, University of Bologna)

Ivan Selesnick (New York University)

Keywords:

image deblurring, image reconstruction, image representation, inverse problems, sparsity-promoting regularization