Continuous wavelet transform and continuous multiscale analysis

AbstractWe study a generalization to the continuous wavelet transform of the concept of dyadic multiscale analysis, useful in the analysis and application of orthonormal wavelet decompositions. The resulting notion of scaling and its limitation is discussed and a possible modification is introduced. With this modified notion of scaling the “information loss” which occurs, when analyzing a signal with orthonormal wavelets (i.e., using a discrete subset of the shift dilation plane only) instead of performing the same analysis with continuously varying scale factors and translations, is illustrated by analyzing an example signal