Some convex and nonconvex variational principles for image processing

In the talk we give a statistical motivation for variational denoising techniques in image processing. The convex techniques derived in such a way are well-known and established and rely on statistical priors and intensity errors. Correcting for sampling errors results in nonconvex variational principles which can be solved by convexification. For highdimensional data, such as medical MRI data, there is a theory based on quasi-convexification for the proposed variational problems for correcting for sampling errors. However, the existence of a quasi-convex envelope does not provide a way to numerically solve the problem.