Multiscale Modeling and Approximation in Novel Geometric and Nonlinear Settings

Drexel University, Philadelphia PA

Investigators

Abstract

Multiscale data representation has been proven to be one of the most effective methods for representing data. Such methods are of major current interests not only in applied mathematics but also in computer science and engineering (especially the computer graphics and scientific simulation communities), and it is the job of applied mathematicians to answer (interrelated) questions such as: When do these methods work? How to fix them when they break? How to bring these methods to novel settings ? etc.. The proposed projects develop various multiscale representations of data in novel geometric and nonlinear settings; such representations do for such data what wavelets were able to do for images and signals. The resulted multiscale representations are the key to data compression, feature extraction, noise removal and a number of other signal processing tasks that are key to informational technologies (computer graphics, computer-aided design, wireless communication, etc..), medical imaging technology (MRI and other kinds of radiology), military signal processing(sonar and radar etc.) Our goal of analysis and synthesis of many new types of data fits right into the broad and fundamental goal of finding efficient ways to organize and manipulate enormous and complex volumes of high-dimensional data. Such data analysis problems have gotten so ubiquitous and sophisticated throughout science, medicine, engineering that the need of applying abstract mathematical techniques becomes fruitful and inevitable. The project provides interdisciplinary research and training opportunities for graduate students, and stimulates collaboration among computational mathematicians, engineers and scientists.