Khalidov, IldarIldarKhalidovVan De Ville, DimitriDimitriVan De VilleTHIERRY BLUUnser, MichaelMichaelUnser2024-03-082024-03-082007-12-0197808194684990277786Xhttps://scholars.lib.ntu.edu.tw/handle/123456789/640598Probably the most important property of wavelets for signal processing is their multiscale derivative-like behavior when applied to functions. In order to extend the class of problems that can profit of wavelet-based techniques, we propose to build new families of wavelets that behave like an arbitrary scale-covariant operator. Our extension is general and includes many known wavelet bases. At the same time, the method takes advantage a fast filterbank decomposition-reconstruction algorithm. We give necessary conditions for the scale-covariant operator to admit our wavelet construction, and we provide examples of new wavelets that can be obtained with our method.Continuous-time signal processing | Differential operators | Green's functions | Multiresolution analysis | Multiresolution approximation | Splines | Waveletsconference paper10.1117/12.7346062-s2.0-42149134737https://api.elsevier.com/content/abstract/scopus_id/42149134737