Related papers: Multidimensional Gabor-Like Filters Derived from G…
In the present paper, details are given on the implementation of a wavelet-based analysis tailored to the processing of acoustical signals. The family of the suitable wavelets (`Reimann wavelets') are obtained in the time domain from a…
Like light, gravitational waves are gravitationally lensed by intervening massive astrophysical objects, such as galaxies, clusters, black holes, and stars, resulting in a variety of potentially observable gravitational-wave lensing…
Using Gabor analysis, we give a complete characterization of all lattice sampling and interpolating sequences in the Fock space of polyanalytic functions, displaying a "Nyquist rate" which increases with $n$, the degree of polyanaliticity…
Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a…
Particle flow Gaussian particle flow (PFGPF) uses an invertible particle flow to generate a proposal density. It approximates the predictive and posterior distributions as Gaussian densities. In this paper, we use bank of PFGPF filters to…
This article is about the architecture of a lossless wavelet filter bank with reprogrammable logic. It is based on second generation of wavelets with a reduced of number of operations. A new basic structure for parallel architecture and…
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
In the recent years, methods to estimate the memory parameter using wavelet analysis have gained popularity in many areas of science. Despite its widespread use, a rigorous semi-parametric asymptotic theory, comparable to the one developed…
We here use notions from the theory linear shift-invariant dynamical systems to provide an easy-to-compute characterization of all rational wavelet filters. For a given N bigger or equql to 2, the number of inputs, the construction is based…
We consider functions $f$ of two real variables, given as trigonometric functions over a finite set $F$ of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle $\frac{2k\pi}{M}$ for some integer $M$.…
By using the formal analogy between the evolution of the state vector in quantum mechanics and the Jones vector in polarization optics, we construct and demonstrate experimentally efficient broadband half-wave polarization retarders and…
The fractional Fourier transform (FrFT), which is a generalization of the Fourier transform, has become the focus of many research papers in recent years because of its applications in electrical engineering and optics. In this paper, we…
Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply…
Image inpainting plays a vital role in restoring missing image regions and supporting high-level vision tasks, but traditional methods struggle with complex textures and large occlusions. Although Transformer-based approaches have…
This paper introduces a design method for densergraph-frequency graph Fourier frames (DGFFs) to enhance graph signal processing and analysis. The graph Fourier transform (GFT) enables us to analyze graph signals in the graph spectral domain…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
We introduce new frames, called \textit{metaplectic Gabor frames}, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions. Namely, we develop the theory of metaplectic atoms in a full-general setting…
It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the non-linear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation…
In this paper we study the general reconstruction of a compactly supported function from its Fourier coefficients using compactly supported shearlet systems. We assume that only finitely many Fourier samples of the function are accessible…
The first part of the paper is devoted to diffraction phenomena that can be expressed by fractional Fourier transforms whose orders are real numbers. According to a scalar theory, diffraction acts on the amplitude of the electric field as…