Related papers: Continous linear canonical Dunkl wavelet transform…
In this paper, we generalize finite depth wavelet scattering transforms, which we formulate as $\Lb^q(\mathbb{R}^n)$ norms of a cascade of continuous wavelet transforms (or dyadic wavelet transforms) and contractive nonlinearities. We then…
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…
We describe a new viewpoint on canonical quantization of linear fields on a general curved background that encompasses and generalizes the standard treatment of canonical QFT given in textbooks. Our method permits the construction of pure…
The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a general convolution operator in the graph domain is challenging due to the lack of canonical…
To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already…
Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources. This opens up a new avenue…
We revisit the properties of qubits under Lorentz transformations and, by considering Lorentz invariant quantum states in the Heisenberg formulation, clarify some misleading notation that has appeared in the literature on relativistic…
Discrete transforms, such as the discrete Fourier transform, are widely used in machine learning to improve model performance by extracting meaningful features. However, with numerous transforms available, selecting an appropriate one often…
This paper presents a multiscale decomposition algorithm. Unlike standard wavelet transforms, the proposed operator is both linear and shift invariant. The central idea is to obtain shift invariance by averaging the aligned wavelet…
We propose a generalization of convolutional neural networks (CNNs) to irregular domains, through the use of a translation operator on a graph structure. In regular settings such as images, convolutional layers are designed by translating a…
The spherical Radon-Dunkl transform $R_\kappa$, associated to weight functions invariant under a finite reflection group, is introduced, and some elementary properties are obtained in terms of $h$-harmonics. Several inversion formulas of…
Hypercomplex Fourier transforms are increasingly used in signal processing for the analysis of higher-dimensional signals such as color images. A main stumbling block for further applications, in particular concerning filter design in the…
A recently developed new approach, called ``Empirical Wavelet Transform'', aims to build 1D adaptive wavelet frames accordingly to the analyzed signal. In this paper, we present several extensions of this approach to 2D signals (images). We…
This work introduces a new unsupervised representation learning technique called Deep Convolutional Transform Learning (DCTL). By stacking convolutional transforms, our approach is able to learn a set of independent kernels at different…
We investigate basic features of Bianchi's B\"acklund transformation of quadrics to see if it can be obtained under weaker assumptions and if it can be generalized to deformations of other surfaces.
We will introduce formal frames of manifolds, which are a generalization of ordinary frames. Their fundamental properties are discussed. In particular, canonical forms are introduced, and torsions are defined in terms of them as a…
Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations…
Vanilla convolutional neural networks are known to provide superior performance not only in image recognition tasks but also in natural language processing and time series analysis. One of the strengths of convolutional layers is the…
A general theorem on the GBDT version of the B\"acklund-Darboux transformation for systems rationally depending on the spectral parameter is treated and its applications to nonlinear equations are given. Explicit solutions of direct and…
Quantum canonical transformations are defined algebraically outside of a Hilbert space context. This generalizes the quantum canonical transformations of Weyl and Dirac to include non-unitary transformations. The importance of non-unitary…