Conclusion

Wavelets were introduced in the early 1980s, in the context of signal analysis and oil exploration. At the time, the aim was to represent signals in such a way as to simultaneously display temporal information (location in time and therefore in space, duration) and frequency information, thereby facilitating the identification of the physical characteristics of the subsurface.

The current boom in wavelet transforms and wavelet packets is mainly due to two specific properties resulting from decompositions on orthogonal wavelet bases: representation sparsity and the tendency to transform a stationary random process into decorrelated Gaussian sequences.

In the context of noise reduction, more commonly known as "denoising", the success of wavelet-based multiresolution analysis is precisely ensured by its decorrelation capability (separation...