SUPREMATIM

Recent and ongoing developments in imaging techniques and computational analysis deeply modify the way materials sciences and engineering consider their objects of research. Our project will contribute to this direction of research by developing new superresolution methods guided by high-resolution local subimages of 3D materials data. The mathematical methods of choice will be based on local and global Generalized Gaussian Mixture Models as well as Student-t Mixture Models in conjuction with variational methods. Appropriate geometrical features related to the engineering topics have to be established to provide an evaluation platform for the SR images, and to be directly involved into the Bayesian and variational models. The mathematical models will be developed, analyzed and appropriate efficient algorithms will be derived, including an examination of their convergence behavior. The models will be enlarged to multimodal images, where due to the size of the structures of interest, the HR image are taken by FIB-SEM tomography and the LR images by CT. This requires to take the special acquisition of FIB-SEM tomographic images, in particular curtaining effects and the anisotropy with respect to the third dimension into account. A numerical evaluation of the relevance and the benefit of the developed super resolution methods will be performed by comparing the effectives properties computed for reactive flow in porous media using these methods and classical mesh refinement strategies.