New Orthogonal Polynomials and their Applications
We propose development and validation of novel mathematical tools which can be used for information processing for object and/or model identification and detection within decision support systems (DSS) in various decision frameworks such as situation assessment and analysis, genetic modeling and analysis, medical imaging, etc. The project will have two main novel contributions: (1) introducing new families of polynomials and (2) the discretization of old and new polynomials. Specifically, in the proposed research, symmetries of n dimensional lattices for defining families of orthogonal functions and orthogonal polynomials will be exploited in order to be used in n dimensional Fourier analysis in digital
and analog signal processing, as well as in object and pattern recognition methods. The aforementioned symmetries have been recently linked to knot symmetries and to DNA properties, [BPP]. The project aims at better in-depth understanding the of these relations which will further lead to fundamental contributions in knot theory and group theory and their various practical applications. The proposed research is of an immediate interest to the partner organization OODA Technologies Inc. since one of their principal activities is research and development of tools for DSS. Furthermore, the research pertaining to this project involves our results obtained within Pseudodifferential Operator Theory and Seismic Images (POTSI) project, [MP], in which OODA Technologies Inc. has already been involved. Together with the research conducted within another cluster project in which OODA Technologies is participating (with Laval University, DRDC and MITACS) this project answers and complements the needs not only of OODA Technologies Inc, but also of Defense Research and Development of Canada (DRDC).