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Signal Processing: Multiresolution Analysis

In: An Introduction to Scientific Computing

Author

Listed:
  • Ionut Danaila

    (Université de Rouen Normandie, CNRS, Laboratoire de mathématiques Raphaël Salem)

  • Pascal Joly

    (Laboratoire Jacques-Louis Lions)

  • Sidi Mahmoud Kaber

    (Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions)

  • Marie Postel

    (Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions)

Abstract

This chapter is devoted to a short introduction to multiresolution analysis (MRA). It consists decomposing a function or a discrete series in a basis well adapted to capture the different scales of variation. This mathematical field has numerous theoretical and practical developments in engineering applications when used to save memory and/or computing time. Over the past three decades, wavelet functions have proven to be a very efficient tool for dealing with problems arising from data compression, and signal and image processing. We describe the main properties of three wavelets (Haar, Schauder and Daubechies) and present their application an example of image compression.

Suggested Citation

  • Ionut Danaila & Pascal Joly & Sidi Mahmoud Kaber & Marie Postel, 2023. "Signal Processing: Multiresolution Analysis," Springer Books, in: An Introduction to Scientific Computing, edition 2, chapter 0, pages 179-203, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-35032-0_8
    DOI: 10.1007/978-3-031-35032-0_8
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