Amir Averbuch

Introduction to Wavelets

Outline | Lectures | Problems and solutions | Textbooks | Papers |

Course Outline:

  1. Introduction: formulating the problem
  2. Fourier analysis
  3. The continuous wavelet transform
  4. Discrete wavelet trasnforms: Frames
  5. Multiresolution analysis
  6. Orthonormal wavelets with compact support
  7. Applications

Lectures' slides and notes:

  • Slides

    Problems and solutions:

  • Problems and solutions

    Textbooks:

    1. Fourier and Wavelet Signal Processing, M. Vetterli, J. Kovacevic, V.K. Goyal (Under the Creative Commons licensing, you are free to distribute/use the book, but you cannot use it for commercial purposes or generate derivative works )
    2. I. Daubechies, Ten lectures on wavelets, SIAM 1992.
    3. S. Mallat, A wavelet tour of signal processing, Academic Press, second edition, 1999.
    4. M. Vetterli, J. Kovacevic, Wavelets and subband coding, Prentice-Hall, 1995.
    5. S. Jaffard, Y. Meyer, R.D. Ryan, Wavelets: tools for science & technology, SIAM, 2001. Review of the book.
    6. D.F. Walnut, , Wavelets Analysis, Birkhauser, 2002
    7. Mladen Victor Wickerhauser, Adapted Wavelet Analysis: from theory to software, A.K. Peters. The assocuated software with this book is free.

    Papers:

    1. Ingrid Daubechies, Where do wavelets come from ? - A personal point of view (appeared in Proceedings of the IEEE, vol. 84, no. 4, pp. 510-513, April 1996)
    2. Construction of wavelets, Jan-Olov Stromberg (IPAM, MGA Tutorial)
    3. W. Sweldens, P. Schroder, Buidling your own wavelets at home (appeared in SIGGRAPH 96)
    4. A. Cohen, J. Kovaceviv, Wavelets: The mathematical background (appeared in Proceedings of IEEE, April 1996).
    5. B. Jawerth, W. Sweldens, An introduction of wavelet based multiresolution analyses (appeared in SIAM).
    6. M. Vetterli, Wavelets, Approximation, and Compression (appeared in IEEE Signal Processing Magazine, pp. 59-73, Sept. 2001)
    7. A. Graps, An introduction to wavelets (appeared in IEEE, 1995).
    8. C. Heil, D. Walnut, Continuous and Discrete wavelet transforms (appeared in SIAM Review, vol. 31, no. 4, pp. 628-666, Dec. 1989.
    9. R.J. Duffin, A.C. Schaeffer, A class of nonharmonic Fourier series (appeared in Trans. of the American Mathematical Society, Vol. 72. no. 2, 341-366, 1952).
    10. T.Q. Nguyen, A tutorial on filter banks and wavelets .
    11. R. DeVore, B. Lucier, Wavelets. Very theoretical.
    12. B. Usevitch, A tutorial on modern lossy wavelet image compression: Foundations of JPEG 2000 (appeared in IEEE Signal Processing Magazine, pp. 22-35, Sept. 2001). Interesting application of the wavelet transform for still image compression.
    13. Wavelet Radiosity: Wavelet Methods for Integral Equations. Interesting application of the wavelet transform in graphics.
    14. Wavelets and their Applications in Computer Graphics (appeared in SIGGRAPH ’95 Course Notes).
    15. W. Sweldens, Wavelets: what next ?

        Software:

      1. Wavelet Software in Matlab. Excellent package. Well documented.