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

ITR：用于处理多尺度音频信号的基于偏微分方程的非线性算法

• 批准号: 0219004
• 负责人: Jack Xin
• 金额: $ 45.25万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-09-01 至 2006-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0219004&HistoricalAwards=false
• 关键词: ITR; PDE; Based; Nonlinear; Algorithms

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

DMS Award AbstractAward #： 0219004 PI： Xin，JackInstitution： 德克萨斯大学奥斯汀分校课程： ITR小型奖项项目经理：Catherine Mavriplis职务：ITR：基于偏微分方程的多尺度音频信号处理非线性算法本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。非线性存在于人类听觉通路中，最显著的是在耳蜗的活动基底膜（BM）和外周听觉神经元中。我们的方法是通过将耳蜗力学中的第一原理（牛顿定律）与声学响应的实验测量相结合来模拟非线性，无论是在主动BM水平还是心理声学水平。这是通过扩大从耳蜗机械原理和神经现象学导出的偏微分方程（PDE）类，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精确，鲁棒和快速的数值方法和算法求解模型偏微分方程。这些偏微分方程是非线性、非局部和色散的。数学分析也将进行适定性的偏微分方程，以及存在和多音解决方案的近似。第二阶段是为这些偏微分方程选择最佳的参数和函数形式，以进一步逼近给定的数据集。实施该项目将产生精确的基于第一原理的算法，以提高对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，特别是听力受损者在轻松使用音频信息和完成更多任务方面的表现。 日期：二○ ○二年六月二十六日