Forschung

HASSIP: Harmonic Analysis and Statistics for Signal and Image Processing

Basic Description

HASSIP is a Research Training Network funded by the European Commission within the Improving the Human Potential program. The aim of the HASSIP network is to develop research activities and systematic interactions in mathematical analysis and statistics that are directly connected to signal and image processing. Although the Acoustics Research Institute was not initially a partner of this network, P. Balazs became a fellow of this network through cooperation with the group NuHAG.

Partners

  • NuHAG, Faculty of Mathematics, University of Vienna
  • Groupe de Traitement du Signal, Laboratoire d'Analyse Topologie et Probabilités, LATP/ CMI, Université de Provence, Marseille
  • Modélisation, Synthèse et Contrôle des Signaux Sonores et Musicaux des LMA / CRNS Marseille
  • Unité de physique théorique et de physique mathématique – FYMA

Subprojects

  • Basic Properties of Bessel and Frame Multipliers: For Bessel sequences, the investigation of operators M = ∑ mk < f , ψk > is very natural and useful. The above M are Bessel multipliers. The goal of this project is to set the mathematical basis for this kind of operator.
  • Best Approximation of Matrices by Frame Multipliers: Finding the best approximation by multipliers of matrices that represent time-variant systems gives a way to find efficient algorithms to implement such operators. 

Publications

  • P. Balazs, "Hilbert-Schmidt Operators and Frames - Classification, Approximation by Multipliers and Algorithms" , International Journal of Wavelets, Multiresolution and Information Processing, Vol. 6, No. 2, pp. 315 - 330, March 2008, preprint, Codes and Pictures: here
  • P. Balazs, "Basic Definition and Properties of Bessel Multipliers", Journal of Mathematical Analysis and Applications, 325, 1: 571--585. (2007) doi:10.1016/j.jmaa.2006.02.012, preprint

Project-completion

This project ended on 01.01.2009. Its completion allowed the sucessfull application for a 'High Potential'-Project of the WWTF, see MULAC.