SPP 1114:  Mathematical Methods for Time Series Analysis and Digital Image Processing

• Subject Area: Mathematics
• Term: from 2001 to 2007
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5471034

The different research directions in signal and image processing are diverse and heterogeneous. This priority programme will focus on twotopics: - Non-linear and non-paramteric models for time series, - Local, adaptive methods in image processing. To this end, methods from the following scientific disciplines will be developed and analysed: identification of dynamical systems, non- and semiparametric models for time series, spatio-temporal dynamics, diffusion filters, stochastic methods in image processing and waveletanalysis. The scientific aims center around the development of mathematically justified algorithms and methods, the mathematical analysis of thesealgorithms and methods as well as the investigation of connections between methods from time series analysis and image processing.Moreover, the interdisciplinary comparison of these methods, which are developed by the participating scientists from numerical analysis, physics and statistics, is of particular importance for this priority programme. This comparison should be based on a common set of test problems from medicine and geophysical/enviromental sciences.

• DFG Programme: Priority Programmes

Projects

• 1Koordinatorprojekt (Applicant Maaß, Peter )
• A control problem in medical image processing (Applicant Maaß, Peter )
• An interdisciplinary evaluation of mathematical methods in signal and image processing (Applicant Maaß, Peter )
• Analyse verborgener Diffusionsprozesse (Applicant Radons, Günter )
• Analysis and postprocessing of space-time compressed flow computations (Applicant Rumpf, Martin )
• Analysis and postprocessing of space-time compressed flow computations (Applicant Turek, Stefan )
• Application of nonparametric modelling and resampling methods for statistical inference on the structure of multivariate time series (Applicant Mammen, Enno )
• Development of mathematical methods for analysing multivariate processes in the inverse setting. Development of methods for high-dimensional and spatio-temporal processes. Generalisation of the methods for point processes (Applicant Timmer, Jens )
• Edge Preserving Smoothing in Time Series and Digital Images: From Abstract Principles to Practical Applications (Applicant Winkler, Gerhard )
• Ein einheitlicher Ansatz für Entrauschungsverfahren in der Bildanalyse durch Kombination von lokaler Glättung und regularizierung (Applicant Franke, Jürgen )
• Morphological methods in 3D image fusion and sequence analysis in medical imaging (Applicant Rumpf, Martin )
• Multivariate Wavelet Analysis: Constructions and Specific Applications (Applicant Dahlke, Stephan )
• Neue mathematische Methoden zur Verknüpfung und Vervollständigung von in Raum und Zeit unregelmäßig aufgenommenen Straßenverkehrsdaten (Applicant Albeverio, Sergio )
• Neue mathematische Methoden zur Verknüpfung und Vervollständigung von in Raum und Zeit unregelmäßig aufgenommenen Straßenverkehrsdaten (Applicant Schreckenberg, Michael )
• Nichtparametrische statistische Inferenz für Zeitreihen mit unbeobachteten Komponenten (Applicant Dahlhaus, Rainer )
• Nonlinear analysis of multi-dimensional signals: local adaptive estimation of complex motion and orientation patterns (Applicant Mester, Rudolf )
• Nonlinear analysis of multi-dimensional signals: local adaptive estimation of complex motion and orientation patterns (Applicants Barth, Erhardt ;  Garbe, Christoph ;  Mester, Rudolf ;  Scharr, Hanno )
• Nonlinear analysis of multi-dimensional signals: local adaptive estimation of complex motion and orientation patterns (Applicant Barth, Erhardt )
• Nonlinear analysis of multi-dimensional signals: local adaptive estimation of complex motion and orientation patterns (Applicant Jähne, Bernd )
• Ordinale Zeitreihenanalyse (Applicant Bandt, Christoph )
• Parameter estimation in dynamical systems (Applicant Timmer, Jens )
• Recursive algorithms for locally stationary processes (Applicant Dahlhaus, Rainer )
• Rekonstruktion von erweiterten Phasenräumen und Parameterräumen aus nicht-stationären Zeitreihen (Applicant Parlitz, Ulrich )
• Relations between nonlinear filters in digital image processing (Applicant Weickert, Joachim )
• Restoration and Post Processing of Optical Flows (Applicants Garbe, Christoph ;  Preusser, Tobias ;  Rumpf, Martin )
• Semiparametrische Modellierung heteroskedastischer Zeitreihen mit fraktionellen LARCH-Prozessen (Applicant Beran, Jan )
• Signal Dynamik im Waveletphasenraum: die Wavelet Deformationsalgebra und ihre Anwendung bei der Analyse seismischer Signale (Applicant Holschneider, Matthias )
• Spatially adaptive detection of local defects in time series and stochastic processes on the integer lattice Z2 (Applicant Franke, Jürgen )
• Structural adaptive smoothing procedures with applications in imaging and time series (Applicant Spokoiny, Vladimir )
• Synchronization approach to analysis of multivariate data (Applicant Kurths, Jürgen )
• The advancement of time-variant and non-linear methods for describing directed effective connectivity in interaction networks. Applications to the investigation of EEG and fMRI signals (Applicant Leistritz, Lutz )
• Wavelet- and Frame-based treatments of variational problems with applications in geophysical data processing (in particular ocean margin analysis) (Applicant Teschke, Gerd )
• Zeitreihenanalyse von Bifurkationen elasto-plastischen Typs auf der Grundlage von extrem kurzen Beobachtungszeiten (Applicant Kantz, Holger )

• Spokesperson: Professor Dr. Peter Maaß