Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995 · 744 citations · 0 references
Natural SciencesMathematicsBiomedical ImagingBiomedical Signal ProcessingComputer VisionDigital Signal ProcessingFourier AnalysisSignal ProcessingBasis FunctionsFourier TransformWavelet AnalysisWavelet Transform
Wavelets on the sphere illustrate the class of second‑generation wavelets that are not simple translates and dilates of a single function. The paper presents the basic idea behind the lifting scheme, a new construction of biorthogonal wavelets that does not rely on the Fourier transform. The authors introduce lifting directly from a wavelet‑transform viewpoint, postponing basis‑function considerations, and show it can generate second‑generation wavelets that need not be simple translates or dilates. Lifting yields a faster, fully in‑plane implementation of the wavelet transform.
In this paper we present the basic idea behind the lifting scheme, a new construction of biorthogonal wavelets which does not use the Fourier transform. In contrast with earlier papers we introduce lifting purely from a wavelet transform point of view and only consider the wavelet basis functions in a later stage. We show how lifting leads to a faster, fully in- plane implementation of the wavelet transform. Moreover, it can be used in the construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one function. A typical example of the latter are wavelets on the sphere.