ITR: PDE Based Nonlinear Algorithms for Processing Multi-Scale AudioSignals

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DMS Award AbstractAward #: 0219004PI: Xin, JackInstitution: University of Texas, AustinProgram: ITR Small AwardsProgram Manager: Catherine MavriplisTitle: ITR: Partial Differential Equation Based Nonlinear Algorithms for Processing Multi-Scale Audio SignalsThe aim of the project is to develop nonlinear partial differential equation models and algorithms for processing multi-scale audio signals. Nonlinearities are present in human auditory pathways, most notably in active basilar membranes (BM) of cochleas and peripheral auditory neurons. Our approach is to model the nonlinearities by combining first principles (Newton's Laws) in cochlear mechanics with experimental measurements of acoustic responses, at either the active BM level or the psycho-acoustic level. This is achieved by enlarging the class of partial differential equations (PDEs) derived from cochlear mechanical principles and neural phenomenology, then optimizing solutions towards the given set of target data. The first phase of research is to develop accurate, robust and fast numerical methods and algorithms for solving model PDEs. These PDEs are nonlinear, nonlocal and dispersive. Mathematical analysis will also be performed on the well-posedness of the PDEs, as well as existence and approximation of multi-tone solutions. The second phase is to select the optimal parameters and functional forms for these PDEs to further approximate the given data set.Carrying out the project will generate accurate first principle based algorithms to enhance the evaluation of available experimental data on human audition, and strengthen our understanding of the computational role of human auditory systems. The results will have broad impact on digital hearing aid design, modeling of hearing loss, and audio compression. The project shall directly contribute to amplifying human sensory abilities, enhancing the performance of human beings, especially the hearing-impaired, in using audio information with ease and for more tasks. Date: June 26, 2002