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.
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Notes
- 1.
In the following, \(\chi _{{[}a,b{[}}\) is the characteristic function of the interval \({}{[}a,b{[}\).
- 2.
The level j coefficient \(d^k_j\) is stored in the \((2^j+k+1)\)th component of \([d_J]\) (see (8.19)).
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Danaila, I., Joly, P., Kaber, S.M., Postel, M. (2023). Signal Processing: Multiresolution Analysis. In: An Introduction to Scientific Computing. Springer, Cham. https://doi.org/10.1007/978-3-031-35032-0_8
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DOI: https://doi.org/10.1007/978-3-031-35032-0_8
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