This paper deals with multiwavelets and the different properties of approximation and smoothness associated with them. In particular, we focus on the important issue of the preservation of discrete-time polynomial signals by multifilterbanks. We introduce and detail the property of balancing for higher degree discrete-time polynomial signals and link it to a very natural factorization of the re...

Multiwavelets and multiframelets are of interest in several applications such as numerical algorithms and signal processing, due to their desirable properties such as high smoothness and vanishing moments with relatively small supports of their generating functions and masks. In order to process and represent vector-valued discrete data efficiently and sparsely by a multiwavelet transform, a mu...

Real-world flood simulators often use first-order finite volume (FV1) solvers of the shallow water equations with efficiency enhancements exploiting parallelisation on Graphical Processing Units (GPUs) and static adaptivity fixed grids. A second-order discontinuous Galerkin (DG2) solver greatly increases accuracy in predictions uniform grids, where it is comparatively costly to run, but its pra...

Interpolating scaling vectors and multiwavelets are particularly attractive for application purposes, because they provide a natural preprocessing procedure. This paper is concerned with the application of the interpolating orthonormal scaling vectors constructed in [10] to signal and image denoising. The results of several wavelets and multiwavelets for both universal and vector thresholding a...

Based on chaotic scrambling, we proposed a digital image watermarking scheme in interpolatory orthogonal multiwavelets transforming domain. At first, the logistic chaotic mapping and arnold transformating are employed to scramble the original watermarking image, then the watermark information is embedded into the middle frequency interpolatory orthogonal multiwavelets transforming coefficients ...

Various results on constructing wavelets, multiwavelets and wavelet frames for periodic functions are reviewed. The orthonormal and Riesz bases as well as frames are constructed from sequences of subspaces called multiresolution analyses. These studies employ general frequency-based approaches facilitated by functions known as orthogonal splines and polyphase splines. While the focus is on the ...

| In applications using multiwavelets, there is a necessary step of associating a given discrete signal with a function in the scaling function space V 0. This association is equivalent to including a preelter and a posttlter for the lterbank determined by the underlying multiwavelets. We give a construction for orthogonal (paraunitary) FIR pre-lters that preserve the approximation order of a g...

By using affine-invariant shape descriptors, it is possible to recognize an unknown planar object from an image taken from an arbitrary view when standard view images of candidate objects exist in a database. In a previous study, an affine-invariant function calculated from the wavelet coefficients of the object boundary has been proposed. In this work, the invariant is constructed from the mul...