A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution

To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order derivative based total $\alpha$-order variation model, which can outperform the currently popular high order regularization models. There exist several previous works using total $\alpha$-order variations for image restoration; however first no analysis is done yet and second all tested formulations, differing from each other, utilize the zero Dirichlet boundary conditions which are not realistic (while non-zero boundary conditions violate definitions of fractional-order derivatives). This paper first reviews some results of fractional-order derivatives and then analyzes the theoretical properties of the proposed total $\alpha$-order variational model rigorously. It then develops four algorithms for solving the variational problem, one based on the variational Split-Bregman idea and three based on direct solution of the discretise-optimization problem. Numerical experiments show that, in terms of restoration quality and solution efficiency, the proposed model can produce highly competitive results, for smooth images, to two established high order models: the mean curvature and the total generalized variation.Comment: 26 page

Dublin City University at CLEF 2007: Cross-Language Speech Retrieval Experiments

The Dublin City University participation in the CLEF 2007 CL-SR English task concentrated primarily on issues of topic translation. Our retrieval system used the BM25F model and pseudo relevance feedback. Topics were translated into English using the Yahoo! BabelFish free online service combined with domain-specific translation lexicons gathered automatically from Wikipedia. We explored alternative topic translation methods using these resources. Our results indicate that extending machine translation tools using automatically generated domainspecific translation lexicons can provide improved CLIR effectiveness for this task