A wavelet filter criterion for an a-priori evaluation of wavelet coding and denoising performances

Wavelet transforms are used in number of important signal and image processing tasks including image coding. The choice of the filter bank is very important and is directly linked to the efficiency of the compression. An objective criterion to guide the choice of the wavelet filters is pro- posed. It is composed of two indexes. The first one is a frequency index computed from the aliasing of the filters. The second is a spatial index computed from the spread of the coefficients in spatial domain. The quality of a filter is a trade-off between frequency and spatial quality. From these indexes a filter set can be represented by a point in a plan. The abscissa is given by the frequency index and the ordinate by the spatial index. The criterion is computed for various filters that are represented in the defined plan. This gives a tool for comparing wavelet filters. In a second time the coding performances of the filters are estimated. The denoising performances are also estimated. The results shows that the two proposed indexes allow a good estimation of the coding and denoising performances of the wavelet filters.