Signal Processing: Multiresolution Analysis

Ionut Danaila (), Pascal Joly, Sidi Mahmoud Kaber and Marie Postel
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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

Chapter Chapter 8 in An Introduction to Scientific Computing, 2023, pp 179-203 from Springer

Abstract: 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.

Date: 2023
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DOI: 10.1007/978-3-031-35032-0_8

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