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Interest in time series analysis and image processing has been growing very rapidly in recent years. Input from different scientific disciplines and new theoretical advances are matched by an increasing demand from an expanding diversity of applications. Consequently, signal and image processing has been established as an independent research direction in such different areas as electrical engineering, theoretical physics, mathematics or computer science.
This has lead to some rather unstructured developments of theories, methods and algorithms. The authors of this book aim at merging some of these diverging directions and to develop a consistent framework, which combines these heterogeneous developments. The common core of the different chapters is the endavour to develop and analyze mathematically justified methods and algorithms. This book should serve as an overview of the state of the art research in this field with a focus on nonlinear and nonparametric models for time series as well as of local, adaptive methods in image processing.
The presented results are in its majority the outcome of the DFG-priority program SPP 1114 Mathematical methods for time series analysis and digital image processing. The starting point for this priority program was the consideration, that the next generation of algorithmic developments requires a close cooperation of researchers from different scientific backgrounds. Accordingly, this program, which was running for 6 years from 2001 to 2007, encompassed approximately 20 research teams from statistics, theoretical physics and mathematics.
The intensive cooperation between teams from different specialized disciplines is mirrored by the different chapters of this book, which were jointly written by several research teams. The theoretical findings are always tested with applications of different complexity.
We do hope and expect that this book serves as a background reference to the present state of the art and that it sparks exciting and creative new research in this rapidly developing field.
This book, which concentrates on methodologies related to identification of dynamical systems, non- and semi-parametric models for time series, stochastic methods, wavelet or multiscale analysis, diffusion filters and mathematical morphology, is organized as follows.
Multivariate Time Series Analysis
Surrogate Data – A Qualitative and Quantitative Analysis
Multiscale Approximation
Inverse Problems and Parameter Identification in Image Processing
Analysis of Bivariate Coupling by Means of Recurrence
Structural Adaptive Smoothing Procedures
Nonlinear Analysis of Multi-Dimensional Signals