Related papers: Comparison of Discrete and Continuous Wavelet Tran…
In this paper, we exploit the theory of convolution of index Whittaker transform for study of continuous and discrete Index Whittaker wavelet transform and discuss some of its basic properties. Certain boundedness, Plancherel as well as…
The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…
The continuous wavelet transform has become a widely used tool in applied science during the last decade. In this article we discuss some generalizations coming from actions of closed subgroups of $\mathrm{GL}(n,\mathbb{R})$ acting on…
In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…
This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
This article consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. Also an efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet.…
By analogy with the real and complex affine groups, whose unitary irreducible representations are used to define the one and two-dimensional continuous wavelet transforms, we study here the quaternionic affine group and construct its…
The empirical wavelet transform is a data-driven time-scale representation consisting of an adaptive filter bank. Its robustness to data has made it the subject of intense developments and an increasing number of applications in the last…
This paper reviews two different uses of the continuous wavelet transform for modal identification purposes. The properties of the wavelet transform, mainly energetic, allow to emphasize or filter the main information within measured…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from…
A formally exact discrete multi-resolution representation of quantum field theory on a light front is presented. The formulation uses an orthonormal basis of compactly supported wavelets to expand the fields restricted to a light front. The…
The group $G_2$ of invertible affine transformations of $\mathbb{R}^2$ has, up to equivalence, one square--integrable representation. Two new realizations of this representation are presented and novel continuous wavelet transforms, acting…
The representation of discrete, compact wavelet transformations (WTs) as circuits of local unitary gates is discussed. We employ a similar formalism as used in the multi-scale representation of quantum many-body wavefunctions using unitary…
This paper presents a new approach for 3D shape generation, inversion, and manipulation, through a direct generative modeling on a continuous implicit representation in wavelet domain. Specifically, we propose a compact wavelet…
As a main research area in applied and computational harmonic analysis, the theory and applications of framelets have been extensively investigated. Most existing literature is devoted to framelet systems that only use one dilation matrix…
We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in…
In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…
Transformer-based architectures have advanced medical image analysis by effectively modeling long-range dependencies, yet they often struggle in 3D settings due to substantial memory overhead and insufficient capture of fine-grained local…