Interactions between Harmonic Analysis, Statistical Estimation and Data Compression

谐波分析、统计估计和数据压缩之间的相互作用

• 批准号: 9978877
• 负责人: Grant Welland
• 金额: $ 2.7万
• 依托单位: University of Missouri-Saint Louis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-10-01 至 2001-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9978877&HistoricalAwards=false
• 关键词: Interactions; between; Harmonic; Analysis; Statistical

Wavelets are useful in selected applications, for example in data compression, but not for others. This lectures series deals with alternative methods when classical methods fail to meet expectations. Alternatives use transform methods with adaptive time-frequency bases, edgelets, ridgelets, and orthogonal curvelet bases to create statistical feature extractors, estimators, and denoisers. Problems characteristically suffering from the curse of dimensionality in statistics, image analysis, and neuro-computing are treated from a unified approach. In addition problems in harmonic analysis are covered including oscillatory integrals, Bochner-Riesz summability, propagation of singularities, tomography with Radon-transform tools, and nonlinear Littlewood-Paley analysis. The analysis of all problems supports fast transforms and algorithms. Finally, a concluding lecture will be devoted to open problems and directions for future research.

小波在某些应用中很有用，例如数据压缩，但不适用于其他应用。本系列讲座讨论了当经典方法无法满足期望时的替代方法。 替代方案使用具有自适应时频基、边波、脊波和正交曲波基的变换方法来创建统计特征提取器、估计器和降噪器。 统计、图像分析和神经计算中典型地遭受维数灾难的问题可以通过统一的方法来处理。此外，还涵盖了谐波分析中的问题，包括振荡积分、Bochner-Riesz 可求和性、奇点传播、使用 Radon 变换工具的断层扫描以及非线性 Littlewood-Paley 分析。 所有问题的分析都支持快速转换和算法。最后，总结讲座将专门讨论未解决的问题和未来研究的方向。