Engineering Applications of Fixed Point Theory

Prof. Danilo P. Mandic

Department of Electrical and Electronic Engineering
Imperial College
Exhibition Road
London, UK

Friday, May 10th, 3:00 PM, ENS 637

mandic@sys.uea.ac.uk

Abstract

There are numerous problems in adaptive systems where convergence, optimal performance and stability are key issues. This talk first introduces contraction mapping and fixed point iteration and then provides case studies with engineering applications, such as in linear and nonlinear filters, image restoration and image retrieval, and other where this theory helps to describe or understand the phenomenon. The talk is structured as follows. A historical perspective of fixed point iteration and the underlying contraction mapping is first provided. Special emphasis is given on fixed point theorems and convergence of such mappings.

Then relaxation in linear systems, and relaxation and stability in neural networks are analyzed in this light. An example is provided for a posteriori and normalized learning algorithms for adaptive filters for monophonic and stereophonic echo cancellation. Further, application of fixed point theory in image processing (restoration) is analyzed. It is shown that convergent iterative algorithms for image restoration can be considered within the class of fixed point algorithms. Next, application of the theory in processing of color images (object recognition) is provided and the benefits of using such an approach are summarized. It is shown that using the fixed point iteration, image retrieval exhibits much better accuracy.

Finally, connections with the case of complex adaptive structures and corresponding attractor geometry and domains of attraction are given. Examples are provided on modeling of air pollutants.

Biography

Danilo P. Mandic received his BSc (Hons.) degree in Electronic Engineering (Automatic Control) and his MSc degree in Signal Processing from University of Banja Luka, Bosnia--Herzegovina. He received his PhD Degree in Nonlinear Adaptive Signal Processing from Imperial College, London, U.K. He was a Lecturer and then a Senior Lecturer in Computer Science in the School of Information Systems, University of East Anglia, Norwich, U.K. He is currently a Senior Lecturer in Signal Processing in Department of Electrical and Electronic Engineering, Imperial College, London, UK. He has authored a book "Recurrent Neural Networks for Prediction", Wiley 2001, and about 100 technical papers. His professional duties include an Associate Editorship for IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, and in International Journal of Mathematical Modeling and Algorithms (Kluwer).

Dr Mandic has received awards for his collaboration with industry and was also awarded a Nikola Tesla medal for his innovative work. His areas of interest are linear and nonlinear adaptive signal processing, neural networks, biomedical signal and image processing, system identification, stability theory, and computer vision.

A list of Telecommunications and Signal Processing Seminars is available at from the ECE department Web pages under "Seminars". The Web address for the Telecommunications and Signal Processing Seminars is http://signal.ece.utexas.edu/seminars