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

获奖摘要获奖编号：0219004PI: Xin， JackInstitution: the University of Texas， austin项目：ITR Small prizes项目经理：Catherine mavriplis标题：ITR：基于偏微分方程的非线性多尺度音频信号处理算法该项目的目的是开发用于处理多尺度音频信号的非线性偏微分方程模型和算法。非线性存在于人的听觉通路中，尤其是在耳蜗的活跃基底膜（BM）和周围听觉神经元中。我们的方法是通过将耳蜗力学的第一原理（牛顿定律）与声学响应的实验测量相结合，在主动BM水平或心理声学水平上对非线性进行建模。这是通过扩大从耳蜗力学原理和神经现象学推导的偏微分方程（PDEs）的类别，然后针对给定的目标数据集优化解决方案来实现的。研究的第一阶段是开发准确、鲁棒和快速的求解模型偏微分方程的数值方法和算法。这些偏微分方程是非线性的、非局部的和色散的。对偏微分方程的适定性以及多音解的存在性和逼近性进行数学分析。第二阶段是为这些偏微分方程选择最优参数和函数形式，以进一步逼近给定的数据集。实施该项目将生成准确的基于第一性原理的算法，以增强对现有人类听觉实验数据的评估，并加强我们对人类听觉系统计算作用的理解。研究结果将对数字助听器设计、听力损失建模和音频压缩产生广泛影响。该项目将直接有助于增强人类的感官能力，提高人类，特别是听障人士轻松使用音频信息和完成更多任务的能力。日期：2002年6月26日

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