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Wavelets and Applications

M. Unser

Series of invited lectures, Information Engineering Department, University of Siena, Italian Republic, July 5-7, 2000.



Wavelets provide a new way of decomposing signals or images into their elementary constituents across scale (multi-resolution decomposition). They provide a one-to-one representation (orthogonal transform) in very much the same way as the Fourier transform, except that the basis functions are now localized in both time (or space) and frequency. Wavelets have many remarkable properties and are extremely versatile. During the past few years, they have being tried on many problems in different areas of applied mathematics and engineering, often with good success.

In this series of lectures, I will present the basic signal processing and mathematical principles behind wavelets. I will also introduce the students to the more advanced aspects of wavelet theory. I will discuss applications in biomedical image processing.

Course Content

  • Lecture 1: Introduction to Wavelets—The Signal Processing Perspective

  • Lecture 2: Multiresolution Analysis and Wavelet Bases of L2

  • Lecture 3: Wavelet Theory. Applications in Medicine and Biology

References


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