Related papers: Pair of Dual Wavelet Frames on Local Fields
This paper introduces some foundations of wavelets over Galois fields. Standard orthogonal finite-field wavelets (FF-Wavelets) including FF-Haar and FF-Daubechies are derived. Non-orthogonal FF-wavelets such as B-spline over GF(p) are also…
(Bi)orthogonal (multi)wavelets on the real line have been extensively studied and employed in applications with success. A lot of problems in applications are defined on bounded intervals or domains. Therefore, it is important in both…
We introduce and develop the concept of oblique duality for fusion frames. This concept provides a mathematical framework to deal with problems in distributed signal processing where the signals, considered as elements in a Hilbert space…
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…
We provide constructive necessary and sufficient conditions for a family of periodic wavelets to be a Parseval wavelet frame. The criterion generalizes unitary and oblique extension principles. The case of one wavelet generator and…
Orthogonal wavelet transforms are a cornerstone of modern signal and image denoising because they combine multiscale representation, energy preservation, and perfect reconstruction. In this paper, we show that these advantages can be…
We present All-Pairs Multi-Field Transforms (AMT), a new network architecture for video frame interpolation. It is based on two essential designs. First, we build bidirectional correlation volumes for all pairs of pixels, and use the…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
The windowed quadratic phase Fourier transform (WQPFT) combines the localization capabilities of windowed transforms with the phase modulation structure of the quadratic phase Fourier transform (QPFT). This paper investigates fundamental…
We consider the design of an orthogonal symmetric/antisymmetric multiwavelet from its matrix product filter by matrix spectral factorization (MSF). As a test problem, we construct a simple matrix product filter with desirable properties,…
Orthogonal time frequency space (OTFS) is a promising technology for high-mobility wireless communications. However, the equalization realization in practical OTFS systems is a great challenge when the non-ideal rectangular waveforms are…
Orthogonal polynomials with respect to a weight function defined on a wedge in the plane are studied. A basis of orthogonal polynomials is explicitly constructed for two large class of weight functions and the convergence of Fourier…
Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the…
We consider the design of polyphase waveforms for ground moving target detection with airborne multiple-input-multiple-output (MIMO) radar. Due to the constant-modulus and finite-alphabet constraint on the waveforms, the associated design…
We present a new method for constructing an orthogonal step scaling function on local fields of positive characteristic, which generates multiresolution analysis.
Finite tight frames for polynomial subspaces are constructed using monic Hahn polynomials and Krawtchouk polynomials of several variables. Based on these polynomial frames, two methods for constructing tight frames for the Euclidean spaces…
This paper studies wavelet coorbit spaces on disconnected local fields $K$, associated to the quasi-regular representation of $G = K \rtimes K^*$ acting on $L^2(K)$. We show that coorbit space theory applies in this context, and identify…
We summarise the construction of exact axisymmetric scale-discretised wavelets on the sphere and on the ball. The wavelet transform on the ball relies on a novel 3D harmonic transform called the Fourier-Laguerre transform which combines the…
Gabardo and Nashed have studied nonuniform wavelets based on the theory of spectral pairs for which the associated translation set $\Lambda =\left\{ 0,r/N\right\}+2\,\mathbb Z$ is no longer a discrete subgroup of $\mathbb R$ but a spectrum…
The quantum mechanical harmonic oscillator Hamiltonian generates a one-parameter unitary group W(\theta) in L^2(R) which rotates the time-frequency plane. In particular, W(\pi/2) is the Fourier transform. When W(\theta) is applied to any…