Infimal convolution of data discrepancies for mixed noise removal

In several real-word imaging applications such as microscopy, astronomy and medical imaging, transmission and/or acquisition faults result in a combination of multiple noise statistics in the observed image. Classical data discrepancies models dealing with this scenario linearly combine standard data fidelities used for single-noise removal or consider exact log-likelihood MAP estimators which are difficult to deal with in practice. In this talk, we derive a statistically consistent variational model for combining mixed data fidelities associated to single noise distributions in a handy infimal convoution fashion by which individual noise components in the data are modelled appropriately and separated from each other after a Total Variation smoothing. Our analysis is carried out in function spaces. For the numerical solution of the resulting denoising model, we propose a semismooth Newton-type scheme and show preliminary results in the context of bilevel learning for blind mixed denoising.