Related papers: Super-wavelets on local fields of positive charact…
We identify the result of the continuous wavelet transform with the difference of solutions of two hyperbolic partial differential equations, for which wavelet's shift and scale are considered as independent variables on 2D plane. The…
We present an algorithm for construction step wavelets on local fields of positive characteristic.
We present a Parseval tight wavelet frame for the representation and analysis of velocity vector fields of incompressible fluids. Our wavelets have closed form expressions in the frequency and spatial domains, are divergence free in the…
In this paper we develop the foundations for microlocal analysis on supermanifolds. Making use of pseudodifferential operators on supermanifolds as introduced by Rempel and Schmitt, we define a suitable notion of super wavefront set for…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
In this paper, we provide the characterization of nonhomogeneous wavelet bi-frames. First of all we introduce the reducing subspaces of Sobolev spaces over local fields of prime characteristics and then characterize the nonhomogeneous…
Continuing our recent work we study polynomial masks of multivariate tight wavelet frames from two additional and complementary points of view: convexity and system theory. We consider such polynomial masks that are derived by means of the…
Recent works emphasized the interest of numerical solution of PDE's with wavelets. In their works, A.Cohen, W.Dahmen and R.DeVore focussed on the non linear approximation aspect of the wavelet approximation of PDE's to prove the relevance…
Wavelet (Besov) priors are a promising way of reconstructing indirectly measured fields in a regularized manner. We demonstrate how wavelets can be used as a localized basis for reconstructing permeability fields with sharp interfaces from…
A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et al. but extend the analysis to a more…
Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…
A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for…
A supersymmetric field theory of light diffusion in semi-infinite disordered media is presented. With the help of this technique we justify--at the perturbative level--the local light diffusion proposed by Tiggelen, Lagendijk, and Wiersma…
We show the analogue of the Serre-Swan theorem in a context of supergeometry. This theorem gives an equivalence of the category of locally free supersheaves of bounded rank over locally ringed superspace with the category of finitely…
Superoscillations are band-limited functions with the peculiar characteristic that they can oscillate with a frequency arbitrarily faster than their fastest Fourier component. First anticipated in different contexts, such as optics or radar…
The main objective of this paper is to define the mother wavelet on local fields and study the continuous wavelet transform (CWT) and some of their basic properties. its inversion formula, the Parseval relation and associated convolution…
We show that the second oversampling theorem for affine systems generates super-wavelets. These are frames generated by an affine structure on the space $L^2(\br)\oplus...\oplus L^2(\br)$.
We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper…
Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called…
An explicit description of all Walsh polynomials generating tight wavelet frames is given. An algorithm for finding the corresponding wavelet functions is suggested, and a general form for all wavelet frames generated by an appropriate…