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Lectures on Splines and Wavelets

M. Unser

Series of invited lectures, Information Engineering Department, University of Siena, Italian Republic, July 14-18, 2003.



Our intent with this series of lectures is to provide a general introduction to splines and wavelets. Our main point will be to show that these two topics, which are traditionally treated as separate, are closely related. We will first describe the use of splines in the context of signal and image processing and discuss some recent algorithms that are based on digital filtering. Next, we will consider the possibility of coarsening the spline grid and introduce the important concept of multiresolution analysis. This will lead us quite naturally to the study of wavelet bases which provide a powerful way of decomposing signals into their elementary constituents across scale (multi-resolution decomposition). Finally, we will look at some advanced aspects of wavelet theory and present a new formulation, which uses fractional splines, that makes the matter much more transparent.

Course Content

  • July 14, Lecture 1: Splines and Interpolation

  • July 15, Lecture 2: From Splines to Wavelets

  • July 16, Lecture 3: Wavelet Theory Demystified

  • July 17, Final Test

References

Additional Reading

  • M. Unser, M. Unser, "Wavelet Games," Wavelet Digest, vol. 11, no. 4, April 1, 2003.


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