TL;DR: In this paper, the convergence of the cascade algorithm is studied in terms of the p-norm joint spectral radius of a finite collection of transition operators determined by the sequence a restricted to a certain invariant subspace.

TL;DR: In this paper, the construction of wavelet and Gabor frames with irregular time-scale and time-frequency parameters was studied and sufficient conditions for an irregular discrete wavelet system or Gabor system to be a frame were given.

TL;DR: In this article, an adaptive wavelet method was proposed to integrate the velocity-vorticity formulation of the two-dimensional Navier-Stokes equations coupled with a penalisation technique to handle efficiently solid boundaries of arbitrary shape.

TL;DR: In this paper, a generalization of the Donoho-Johnstone denoising model for the case of the translation-invariant wavelet transform is proposed, which is not an orthogonal transformation.

TL;DR: In this paper, it is shown that it is possible to construct a continuous function with prescribed local and pointwise Holder functions outside a set of Hausdorff dimensions of dimension 0.

TL;DR: In this paper, the classical constructions of wavelets and scaling functions from conjugate mirror filters are extended to settings that lack multiresolution analyses using analogues of the classical filter conditions.

TL;DR: In this article, a new family of biorthogonal wavelet and wavelet packet transforms for discrete periodic signals and a related library of BORTHOGONAL periodic symmetric waveforms are presented.

TL;DR: In this article, the concept of projectable refinable functions was introduced and it was shown that many multivariate refinability functions are projectable, i.e., they essentially carry the tensor product structure of a function even though themselves may be nontensor product (nonseparable) refinability.

TL;DR: It is shown that the average over translations of an operator diagonal in a wavelet packet basis is a convolution, and it is argued and shown that this permits us to avoid the drawbacks of both approaches which are, respectively, the ringing and the staircasing.

TL;DR: In this article, a time-frequency representation of a one-dimensional signal is provided where the window is locally adapted to the signal, thus providing a better readability of the representation.

TL;DR: In this paper, it was shown that a convergent poly-scale subdivision process with a certain restriction on the masks converges to a continuous solution of the functional equation φ = ∑ m=1 M−1 ∑ k∈ Z d p m,k φ(2 m ·−k).

TL;DR: In this paper, the eigenvalues of an autocovariance matrix indicate directions at which the local Fourier power spectrum of a function is slowly decreasing, which provides a technique to discriminate edge-like singularities from other features in images.

TL;DR: The Weyl-Heisenberg (WH)-frame identity as discussed by the authors does not require any assumptions on ab (such as the requirement that ab ≤ 1 have a frame), and the identity holds for all bounded, compactly supported functions if and only if g ∈ L 2 (R ).

TL;DR: In this article, the wavelet transform of a step function f is defined as a function of norms, and moreover expressible to a summation form, for any given admissible function h ∈ L 2 (Q p ) satisfying (15) which is a step functions.

TL;DR: In this paper, the authors obtained necessary and sufficient conditions for the sum of two principal shift-invariant subspaces to be closed for Riesz wavelets associated with multiresolution analyses.

TL;DR: In this paper, a new class of basic wavelet packets, called highly nonstationary wavelet packet, was introduced, which generalize the class of non-stationary packet.

TL;DR: In this article, the orthogonal perturbation of coherent function systems (Gabor systems, Wilson bases, and wavelets) under convolution operators is studied in terms of spectral spread and temporal support of the prototype and the approximate design of worst-case convolution kernels.

TL;DR: In this paper, the mean size of wavelet packets in Lp was studied in terms of the p-norm joint spectral radius, which is a corollary of an asymptotic formula for the Lp norm on subdivision trees.

TL;DR: In this article, it was shown that the dimension of a band-limited wavelet ψ is bounded by n if its Fourier transform is supported in [−(2n+2/3)π, (2n + 2/3π+e] such that Dψ>n on a set of positive measure, which is the largest symmetric interval for estimating the dimension function by n.

TL;DR: In this article, a series of translates of a nonnegative summability function used in place of an orthogonal scaling function is discussed, where the coefficients in the series are taken to be sampled values of the function to be approximated.

TL;DR: In this paper, a scheme for frame decompositions that is called α-expansion is proposed, where the choice of a parameter α adequate to a given frame is a central point.

TL;DR: In this article, it was proved that all the M -band scaling functions with minimal support are asymmetric except the Haar functions, and that all these functions can be computed in a linear fashion.

TL;DR: This work tries to see whether, once the classical refinability requirement is removed, it is still possible to construct meaningful wavelet decompositions of dilates of the shift invariant space that are well suited for applications.

TL;DR: In this article, the spectral radius of the transfer operator associated with the reduced symbol of a scaling function is estimated for a certain class of rank M scaling functions, where the exponent s p ( ϕ ) is represented by a spectral radius.

TL;DR: In this paper, the authors cast some classes of fitness landscapes as problems of spectral analysis on various Cayley graphs, and show that explicit computation of the Walsh/Fourier transforms is feasible for landscapes with up to 10 8 configurations using fast Fourier transform techniques.

TL;DR: In this paper, the authors define the notion of directional spherical wavelet, i.e., wavelets on the sphere that are sensitive to directions, and present a calculation method for data given on a regular spherical grid g. This technique, which uses the FFT, is based on the invariance of g under discrete rotations around the z axis preserving the phi sampling.

TL;DR: In this article, the Balian-low theorem for Riesz bases was extended to higher dimensions, obtaining a weak form valid for all sets of time-frequency shifts which form a lattice in R 2D, and a strong form for symplectic lattices in 2D.

TL;DR: In this article, a multiscale solution method for the gravimetry problem, which is concerned with the determination of the earth's density distribution from gravitational measurements, is presented.

TL;DR: In this paper, wavelet characterizations for anisotropic Besov spaces with respect to Lp-spaces with 0