We present novel families of wavelets and associated filterbanks for the analysis and representation of functions defined on circulant graphs. In this work, we leverage the inherent vanishing moment property of the circulant graph Laplacian operator, and by extension, the e-graph Laplacian, which is established as a parameterization of the former with respect to the degree per node, for the des...

This paper presents an alternative to the semi-orthogonal spline wavelets classically used for multiresolution representation in the eld of computer aided design. This new approach involves less computation, is more modular, and is potentially more exible than the classical approach. This multiresolution scheme is presented through the use of HB-splines, a speciic subset of particular B-splines...

We build wavelet-like functions based on a parametrized family of pseudo-differential operators L~ν that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green function of L~ν , generate a family of L-spline spaces. These spaces have the approximation order equal to the order of the underlying operator. A sequenc...

We exhibit the necessary range for which functions in Sobolev spaces L p s $L^s_p$ can be represented as an unconditional sum of orthonormal spline wavelet systems, such Battle–Lemarié wavelets. also consider natural extensions to Triebel–Lizorkin spaces. This builds upon, and is a generalization of, previous work Seeger Ullrich, where analogous results were established Haar system.

Shift-orthogonal wavelets are a new type of multiresolution wavelet bases that are orthogonal with respect to translation (or shifts) within one level but not with respect to dilations across scales. In this paper, we characterize these wavelets and investigate their main properties by considering two general construction methods. In the first approach, we start by specifying the analysis and s...