Related papers: Comparison of Discrete and Continuous Wavelet Tran…
We revisit the fundamental notion of continuity in representation theory, with special attention to the study of quantum physics. After studying the main theorem in the context of representation theory, we draw attention to the significant…
Over the past years, various representation systems which sparsely approximate functions governed by anisotropic features such as edges in images have been proposed. We exemplarily mention the systems of contourlets, curvelets, and…
In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in…
It is shown that multiple representations (such as replicas or Hilbert transforms) of a random waveform can interfere constructively to form a compact pattern, akin to a wave packet, when the representations are created in synchrony with…
Like the continous shearlet transform and their relatives, discrete transformations based on the interplay between several filterbanks with anisotropic dilations provide a high potential to recover directed features in two and more…
Over the past years, various representation systems which sparsely approximate functions governed by anisotropic features such as edges in images have been proposed. We exemplarily mention the systems of contourlets, curvelets, and…
Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics…
The dual-tree complex wavelet transform (DT-CWT) is known to exhibit better shift-invariance than the conventional discrete wavelet transform. We propose an amplitude-phase representation of the DT-CWT which, among other things, offers a…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
A traditional wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a system of unitary operators defined in terms of translation and dilation operations. A Coxeter/fractal-surface…
The Continuous Boostlet Transform (CBT) is introduced as a powerful tool for analyzing spatiotemporal signals, particularly acoustic wavefields. Overcoming the limitations of classical wavelets, the CBT leverages the Poincar\'e group and…
We show that continuous transform with the complex Morlet wavelet is easily performed if we replace the integration of the fast-oscillation function by the solution of the diffusion differential equations. The most important advantage of…
This paper introduces the synchrosqueezed curvelet transform as an optimal tool for 2D mode decomposition of wavefronts or banded wave-like components. The synchrosqueezed curvelet transform consists of a generalized curvelet transform with…
Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generator with parabolic scaling, shearing, and translation…
We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differential equations. In particular, we study the correspondence…
A scattering transform defines a locally translation invariant representation which is stable to time-warping deformations. It extends MFCC representations by computing modulation spectrum coefficients of multiple orders, through cascades…
We describe local and global properties of wavelet transforms of ultradifferentiable functions. The results are given in the form of continuity properties of the wavelet transform on Gelfand-Shilov type spaces and their duals. In…
We show that the centered discrete Hilbert transform on integers applied to a function can be written as the conditional expectation of a transform of stochastic integrals, where the stochastic processes considered have jump components. The…
This paper presents a wavelet representation using baseband signals, by exploiting Kotel'nikov results. Details of how to obtain the processes of envelope and phase at low frequency are shown. The archetypal interpretation of wavelets as an…
We consider the problem of characterizing the Sobolev wavefront set of a tempered distribution $u\in\mathcal{S}'(\mathbb{R}^{d})$ in terms of its continuous wavelet transform, with the latter being defined with respect to a suitably chosen…