2. Denoising or noise reduction

2.1 Problem position

The flagship applications of multi-resolution analysis have focused on three major generic themes: analysis, denoising and compression.

• In what follows, our focus will be on filtering or denoising, which necessarily involves multi-resolution analysis in order to extract relevant information. The observed signal is analyzed using wavelets, scale by scale, in the manner of a microscope or digital zoom. The signal is then examined at different resolutions, and the resulting coefficients (of the wavelet transform) encode the information within the wavelet's field of action. These coefficients may be sufficient to "read" the relevant information, or they may need to be transformed. Some of them can be moved, rearranged...