Related papers: Pair of Dual Wavelet Frames on Local Fields
Recently, the reference functions for the synthesis and analysis of the autostereoscopic multiview and integral images in three-dimensional displays we introduced. In the current paper, we propose the wavelets to analyze such images. The…
In this paper, we present a novel solution for optimal beamforming in a two-way relay (TWR) systems with perfect channel state information. The solution makes use of properties of quadratic surfaces to simplify the solution space of the…
Bayesian image restoration has had a long history of successful application but one of the limitations that has prevented more widespread use is that the methods are generally computationally intensive. The authors recently addressed this…
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the…
Vector beams are often regarded as non-separable superpositions of spatial and polarization degrees of freedom that satisfy the wave equation. This interpretation ties their polarization structure to their spatial shape. Here, we introduce…
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…
This work proposes a new precoded filter bank (FB) system via a two-dimensional (2D) fast Fourier transform (2D-FFT). Its structure is similar to Orthogonal Time Frequency Space (OTFS) systems, where the OFDM transmitter is changed to a…
The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging…
We present a new approach for constructing optical phase-space-time-frequency tomography (OPSTFT) of an optical wave field. This tomography can be measured by using a novel four-window optical imaging system based on two local oscillator…
We present a Parseval tight wavelet frame for the representation and analysis of velocity vector fields of incompressible fluids. Our wavelets have closed form expressions in the frequency and spatial domains, are divergence free in the…
We present a generalization of the bilateral filter that can be applied to feature-preserving smoothing of signals on images, meshes, and other domains within a single unified framework. Our discretization is competitive with…
This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames, respectively. The goal of the…
Optical approaches for wavefront shaping traditionally rely on phase modulation through holographic techniques. Shaping the phase determines a wave's diffraction and hence its intensity distribution in space. We instead show that shaping…
The multiresolution analysis (MRA) associated with the Special affine Fourier transform (SAFT) provides a structured approach for generating orthonormal bases in \( L^2(\mathbb R) \), making it a powerful tool for advanced signal analysis.…
A set of orthogonal polynomials on the unit disk $B(0,1)$ known as Zernike polynomials are commonly used in the analysis and evaluation of optical systems. Here Zernike polynomials are used to construct wavelets for polynomial subspaces of…
We introduce an algorithm to piecewise dualise linear quivers into their mirror dual. The algorithm uses two basic duality moves and the properties of the $S$-wall which can all be derived by iterative applications of Seiberg-like…
The topological charge of an electromagnetic vortex beam depends on its wavefront helicity. For mixed vortex beams composed of several different coaxial vortices, the topological charge spectrum can be obtained by Fourier transform.…
Fourier transform is applied to annular beams of simplified flat two-level geometry: bright outer ring with a darker core. The pattern of focal beam profile (i.e. far field) is calculated and characterized with respect of its intensity…
Highly localized kernels constructed by orthogonal polynomials have been fundamental in recent development of approximation and computational analysis on the unit sphere, unit ball and several other regular domains. In this work we first…
We investigate the optical properties of layered structures with graphene at the interface for arbitrary linear polarization at finite temperature including full retardation by working in the Weyl gauge. As a special case, we obtain the…