Related papers: Fast Finite Shearlet Transform
Recently, shearlet systems were introduced as a means to derive efficient encoding methodologies for anisotropic features in 2-dimensional data with a unified treatment of the continuum and digital setting. However, only very few…
In this article we develop an image based rendering technique based on light field reconstruction from a limited set of perspective views acquired by cameras. Our approach utilizes sparse representation of epipolar-plane images in a…
The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various…
This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…
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…
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier…
We discuss efficient algorithms for the accurate forward and reverse evaluation of the discrete Fourier-Bessel transform (dFBT) as numerical tools to assist in the 2D polar convolution of two radially symmetric functions, relevant, e.g., to…
The quantum Fourier transform (QFT), a quantum analog of the classical Fourier transform, has been shown to be a powerful tool in developing quantum algorithms. However, in classical computing there is another class of unitary transforms,…
The algorithm behind the Fast Fourier Transform has a simple yet beautiful geometric interpretation that is often lost in translation in a classroom. This article provides a visual perspective which aims to capture the essence of it.
Secure signal processing is becoming a de facto model for preserving privacy. We propose a model based on the Fully Homomorphic Encryption (FHE) technique to mitigate security breaches. Our framework provides a method to perform a Fast…
The Fast Fourier Transform (FFT) over a finite field $\mathbb{F}_q$ computes evaluations of a given polynomial of degree less than $n$ at a specifically chosen set of $n$ distinct evaluation points in $\mathbb{F}_q$. If $q$ or $q-1$ is a…
Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides…
We show that continuous transform with the complex Morlet wavelet is easily performed if we replace the integration of the fast-oscillation function by the solution of the diffusion differential equations. The most important advantage of…
Fast Fourier transform was included in the Top 10 Algorithms of 20th Century by Computing in Science & Engineering. In this paper, we provide a new simple derivation of both the discrete Fourier transform and fast Fourier transform by means…
This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to…
We propose a transform for signals defined on the sphere that reveals their localized directional content in the spatio-spectral domain when used in conjunction with an asymmetric window function. We call this transform the directional…
We find a new and simple inversion formula of the Radon transform RT with the only use of the shearlet system and of well-known properties of RT. No intertwining relation of differential operators in Euclidean space and Radon domain is…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
As a main research area in applied and computational harmonic analysis, the theory and applications of framelets have been extensively investigated. Most existing literature is devoted to framelet systems that only use one dilation matrix…
In this paper, we introduce the notion of quaternion shearlet transform- which is an extension of the ordinary shearlet transform. Firstly, we study the fundamental properties of quaternion shearlet transforms and then establish some basic…