Wavelet, Filter Banks and Multiresolution Signal Analysis: New Techniques and Applications

小波、滤波器组和多分辨率信号分析：新技术和应用

• 批准号: 9014189
• 负责人: Martin Vetterli
• 金额: $ 15.05万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-09-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9014189&HistoricalAwards=false
• 关键词: Wavelet; Filter; Banks; Multiresolution; Signal

Techniques for handling non-stationarity in signals and images have been explored in different areas; wavelet analysis in applied mathematics, multi-rate filter bank techniques in digital signal processing and multi-resolution analysis in computer vision. Recent developments have indicated the connection between these various techniques. A goal of this work is to make a thorough exploration of the connections between these three areas and present a unified view of existing problems, techniques and applications. Further, design of new regular wavelets, examination of associated computational structures and a study of the complexity of the wavelet transform are also pursued. Finally, design of non-separable multi-dimensional wavelets, new wavelet- based-sampling methods and application to image coding are attempted.

人们在不同的领域探索了处理信号和图像中非平稳性的技术：应用数学中的小波分析，数字信号处理中的多速率滤波器组技术，以及计算机视觉中的多分辨率分析。最近的发展表明了这些不同技术之间的联系。这项工作的一个目标是彻底探索这三个领域之间的联系，并对存在的问题、技术和应用提出统一的看法。此外，还进行了新的正则小波的设计、相关计算结构的检查以及对小波变换的复杂性的研究。最后，对不可分多维小波的设计、基于小波的新采样方法及其在图像编码中的应用进行了尝试。