Related papers: Wavelet frames: Spectral techniques and extension …
We present a wavelet-based dual-stream network that addresses color cast and blurry details in underwater images. We handle these artifacts separately by decomposing an input image into multiple frequency bands using discrete wavelet…
We present a new method for the generation of atmospheric turbulence phase screens based on the frequency shift property of the Fourier transform. This method produces low spatial frequency distortions without additional computation time…
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…
We consider the problem of characterizing the wavefront set of a tempered distribution $u\in\mathcal{S}'(\mathbb{R}^{d})$ in terms of its continuous wavelet transform, where the latter is defined with respect to a suitably chosen dilation…
Within the expansive domain of optical sciences, achieving the precise characterization of light beams stands as a fundamental pursuit, pivotal for various applications, including telecommunications and imaging technologies. This study…
In this article we introduce a broad family of adaptive, linear time-frequency representations termed superposition frames, and show that they admit desirable fast overlap-add reconstruction properties akin to standard short-time Fourier…
Doppler radars are routinely used for the remote sensing of oceanic surface currents and atmospheric wind profiles. Even though they operate at different frequencies and address different media, they follow very similar processing for the…
The spectral decomposition for an explicit second-order differential operator $T$ is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with…
Novel optical elements containing semitransparent wavelike films embedded into the bulk of transparent material, which form a reflection image without transmitted light distortion, are studied. The dynamic theory of light diffraction by a…
A closed formula for the spectral determinant for the wave equation on a bounded interval, subject to Dirichlet boundary conditions and an $\alpha$-multiple of the Dirac $\delta$-type damping, is derived. Depending on the choice of the…
In order to completely eliminate, or greatly reduce the number of phase wraps in 2D wrapped phase map, Gdeisat et al. proposed an algorithm, which uses shifting the spectrum towards the origin. But the spectrum can be shifted only by an…
The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…
The major goal of the paper is to prove that discrete frames of (directional) wavelets derived from an approximate identity exist. Additionally, a kind of energy conservation property is shown to hold in the case when a wavelet family is…
The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar…
A discrete frame for $L^2({\mathbb R}^d)$ is a countable sequence $\{e_j\}_{j\in J}$ in $L^2({\mathbb R}^d)$ together with real constants $0<A\leq B< \infty$ such that $$ A\|f\|_2^2 \leq \sum_{j\in J}|\langle f,e_j \rangle |^2 \leq…
In this paper, a family of radial deformations of the realization of the Lie superalgebra osp(1|2) in the theory of Dunkl operators is obtained. This leads to a Dirac operator depending on 3 parameters. Several function theoretical aspects…
A semi-analytical computational algorithm to model the wavefield generated by paraxial diffraction of a class of Laguerre-Gauss beams by sharp-edge elliptic apertures is here developed. Thanks to such a powerful computational tool, some…
In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…
In the past decade, several multi-resolution representation theories for graph signals have been proposed. Bipartite filter-banks stand out as the most natural extension of time domain filter-banks, in part because perfect reconstruction,…
In this paper, we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by illuminating it with probing waves and recording the…