Shape recognition using squared eigen-functions of the Schrödinger operator

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Project Description

A new adaptive signal/image reconstruction, analysis and denoising method has been recently developed in our group where the signal is decomposed into signal dependent functions. These functions are the L2-normalized squared eigenfunctions associated to the discrete spectrum of a Schrödinger operator, the potential of which considered to be the signal/image. These signal dependent functions provide a good approximation of the signal and exhibit interesting localization properties, and they supply new parameters that can be used to extract relevant features of signal variations. They also constitute an efficient analysis tool as the information about the signal is continuously reflected on these localized functions.In this project, the student will study the potential use of this algorithm to shape recognition where the new spectral data provided by the method will be combined with data mining approaches with a potential application to red sea marine creature recognition​​
Program - Electrical Engineering
Division - Computer, Electrical and Mathematical Sciences and Engineering
Center Affiliation - Computational Bioscience Research Center
Field of Study - ​Electrical engineering/ Applied Mathematics/Signal processing/Data mining

About the
Researcher

Taous-Meriem Laleg-Kirati

Associate Professor, Electrical and Computer Engineering

Taous-Meriem Laleg-Kirati
​Professor Laleg-Kirati's research interests encompass work across the fields of applied mathematics, control systems, and signal analysis. She works on new methods for signal analysis based on a semi-classical approach with an application to the analysis of the arterial blood pressure. Laleg-Kirati is also interested in modeling, identification, control, fault detection, inverse problems and especially seismic inversion and has expertise in solitons waves and scattering theory.

Desired Project Deliverables

​A shape recognition algorithm will be provided with Matlab or C++ implementation.-         A paper will be submitted  ​