Related papers: Evolution Equations on Gabor Transforms and their …
Gabor transform is one of the performed tools for time-frequency signal analysis. The principal aim of this paper is to generalize the Gabor Fourier transform to the quaternion linear canonical transform. Actually, this transform gives us…
In this paper we present the latent signal analysis problem as a recasting of the complex extension problem. Almost universally, the approach has been to use the Hilbert Transform (HT) to construct Gabor's analytic signal. This approach…
The article describes a system for image recognition using deep convolutional neural networks. Modified network architecture is proposed that focuses on improving convergence and reducing training complexity. The filters in the first layer…
Let $G$ be a locally compact abelian group with a Haar measure, and $Y$ be a measure space. Suppose that $H$ is a reproducing kernel Hilbert space of functions on $G\times Y$, such that $H$ is naturally embedded into $L^2(G\times Y)$ and is…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
Here we propose an evolutionary algorithm that self modifies its operators at the same time that candidate solutions are evolved. This tackles convergence and lack of diversity issues, leading to better solutions. Operators are represented…
The translation of an operator is defined by using conjugation with time-frequency shifts. Thus, one can define $\Lambda$-shift-invariant subspaces of Hilbert-Schmidt operators, finitely generated, with respect to a lattice $\Lambda$ in…
Representations of the celebrated Heisenberg commutation relations in quantum mechanics and their exponentiated versions form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric…
In this paper Gabor system of certain type based on the unitary dual of the Heisenberg group $\mathbb{H}^n$ is introduced and a sufficient condition is obtained for the Gabor system to be a Bessel sequence for…
For the Weyl-Heisenberg group, convolutions between functions and operators were defined by Werner as a part of a framework called quantum harmonic analysis. We show how recent results by Feichtinger can be used to extend this definition to…
We define the harmonic evolution of states of a graph by iterative application of the harmonic operator (Laplacian over $Z_2$). This provides graphs with a new geometric context and leads to a new tool to analyze them. The digraphs of…
In this paper we show how to construct a certain class of orthonormal bases in $L^2({\bf R}^d)$ starting from one or more Gabor orthonormal bases in $L^2({\bf R})$. Each such basis can be obtained acting on a single function…
In this paper we consider the problem of defining transforms for signals on directed graphs, with a specific focus on defective graphs where the corresponding graph operator cannot be diagonalized. Our proposed method is based on the Schur…
A new model for evolving Evolutionary Algorithms is proposed in this paper. The model is based on the Linear Genetic Programming (LGP) technique. Every LGP chromosome encodes an EA which is used for solving a particular problem. Several…
Evolutionary optimization algorithms are often derived from loose biological analogies and struggle to leverage information obtained during the sequential course of optimization. An alternative promising approach is to leverage data and…
We study the phase reconstruction of signals $f$ belonging to complex Gaussian shift-invariant spaces $V^\infty(\varphi)$ from spectrogram measurements $|\mathcal{G} f(X)|$ where $\mathcal{G}$ is the Gabor transform and $X \subseteq…
Deep Convolutional Neural Networks (DCNNs) are capable of obtaining powerful image representations, which have attracted great attentions in image recognition. However, they are limited in modeling orientation transformation by the internal…
We provide a construction of Gabor frames that encode local linearizations of a signal detected on a curved smooth manifold of arbitrary dimension, with Gabor filters that can detect the presence of higher-dimensional boundaries in the…
We present an algorithm using transformation groups and their irreducible representations to generate an orthogonal basis for a signal in the vector space of the signal. It is shown that multiresolution analysis can be done with amplitudes…
We consider soft-gluon evolution at the amplitude level. Our evolution includes Coulomb exchanges and applies to generic hard-scattering processes involving any number of coloured partons. We emphasise the special role played by a…