Objective We will develop mathematical methods for scattered data approximation that can be used to implement efficient algorithms in signal processing and related areas. So far, the problem of reconstructing an unknown function from a given discrete set of sampling points has been studied in shift invariant spaces, i.e. spaces generated by translates of a function (or finitely many functions). We propose to consider the problem in spaces generated by translates of compressed copies of a function (or finitely many functions) along irregularly spaced points. We are convinced that with our model we will obtain better approximation properties, since it takes into account the structure of the sampling data. The problem will be first studied on the real line, then in the plane and finally on the sphere, where the lack of regular grids requires certainly some modifications. Both the functional analytic side and the computational aspects of the problem will be covered. The candidate has experience in the field of the proposed topic, since her research area is time-frequency analysis, frame theory, sampling theory, shift invariant spaces, etc., which constitute the background of this project. She was member of several research projects related to the topic, her master and Ph.D thesis are connected to the proposed research. The project will be carried out at the Numerical Harmonic Analysis Group (NuHAG), University of Vienna, whose key scientists are Prof. H.G. Feichtinger and Prof. K. Gröchenig. The proposed research center has a leading position in the area of sampling theory, time-frequency analysis, frame theory and wavelet analysis, which makes it the proper environment for the proposed project. The experience that NuHAG has in the mentioned areas and also in training researchers will be helpful in the developing of the professional skills of the proposer. The MC Exc. Grant EUCETIFA (2005-2009) and the cooperation with other PostDocs at NuHAG will support the project. Fields of science engineering and technologyelectrical engineering, electronic engineering, information engineeringelectronic engineeringsignal processing Keywords Mathematical sciences approximation theory frame theory irregular sampling time-frequency analysis wavelets Programme(s) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) PEOPLE-2007-2-1.IEF - Marie Curie Action: "Intra-European Fellowships for Career Development" Call for proposal FP7-PEOPLE-2007-2-1-IEF See other projects for this call Funding Scheme MC-IEF - Intra-European Fellowships (IEF) Coordinator UNIVERSITAT WIEN EU contribution € 155 986,80 Address UNIVERSITATSRING 1 1010 Wien Austria See on map Region Ostösterreich Wien Wien Activity type Higher or Secondary Education Establishments Administrative Contact Hans Georg Feichtinger (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
