Course No.:21601Z
Period:10
Credits:0.5
Course Category:Lecture
Primary Coverage:
Wavelet methodology has been one of the most important development in applied mathematics, engineering, and statistics in recent years. Wavelet bases offer a degree of localization both in space and in frequency and provide efficient representation for a wide range of function spaces. Wavelet methods have been widely applied in many fields including signal processing, image compression, pattern recognition, feature extraction, medical imaging, speech coding, as well as
statistical estimation. In these lectures, we address three basic questions: what, why, and how. Specifically, we will discuss the following topics:
1. Wavelets and multiresolution analysis
2. Wavelets and data compression
3. Nonparametric function estimation
4. The connection between wavelet thresholding and the
shrinkage estimation in multivariate decision theory
5. Wavelets and chemical identification
6. wavelets and functional linear model for chemical calibration
Along the way, we will also discuss some challenging problems for future research.
Author: Tianwen Cai