"第十四讲：小波域图像处理中的几何小波介绍与分析"

The fourteenth lecture on geometric wavelets introduces the concept of curvelets in image processing. Curvelets, first introduced by Si Long Peng in July 2007, are a type of geometric wavelet that offer a powerful tool for representing and analyzing images. The lecture covers three main topics: Curvel et, Bandel et, and Cont ourl et. The Curvel et transform is a method for decomposing an image into curve-like structures, while the Bandel et transform focuses on capturing edges and fine details in an image. The Cont ourl et transform is used to extract contours and shapes from an image. Francisco Blanco-Silva, from the Department of Mathematics at Purdue University, provides an in-depth analysis of curvelets and their applications in image processing. The lecture highlights the mathematical foundations of curvelet transforms, including the continuous and discrete curvelet transforms. The use of curvelets in image processing offers several advantages, such as improved representation of image features, better localization of image structures, and enhanced compression capabilities. Curvelets have found applications in a wide range of fields, including medical imaging, remote sensing, and computer vision. Overall, the lecture on geometric wavelets and curvelets provides a comprehensive overview of this cutting-edge technology and its potential impact on image processing. Through a combination of theory and practical applications, students gain a deeper understanding of curvelets and their role in modern imaging techniques.