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In this work, we develop a localized numerical scheme with low regularity requirements for solving time-fractional integro-differential equations. First, a fully discrete numerical scheme is constructed. Specifically, for temporal…

Numerical Analysis · Mathematics 2025-12-02 Lijing Zhao , Rui Zhao , Wenyi Tian , Yufeng Nie

Performing a large number of spatial measurements enables high-resolution photoacoustic imaging without specific prior information. However, the acquisition of spatial measurements is time-consuming, costly, and technically challenging. By…

Numerical Analysis · Mathematics 2021-01-12 Gerhard Zangerl , Markus Haltmeier

We develop a novel sampling theorem on the sphere and corresponding fast algorithms by associating the sphere with the torus through a periodic extension. The fundamental property of any sampling theorem is the number of samples required to…

Information Theory · Computer Science 2012-01-18 J. D. McEwen , Y. Wiaux

In object recognition, Fisher vector (FV) representation is one of the state-of-art image representations ways at the expense of dense, high dimensional features and increased computation time. A simplification of FV is attractive, so we…

Computer Vision and Pattern Recognition · Computer Science 2014-10-16 Xiankai Lu , Zheng Fang , Tao Xu , Haiting Zhang , Hongya Tuo

Using a local analog of the Wiener-Levi theorem, we investigate the class of measures on Euclidean space with discrete support and spectrum. Also, we find a new sufficient conditions for a discrete set in Euclidean space to be a coherent…

Classical Analysis and ODEs · Mathematics 2019-10-30 Serhii Favorov

The generation of curves and surfaces from given data is a well-known problem in Computer-Aided Design that can be approached using subdivision schemes. They are powerful tools that allow obtaining new data from the initial one by means of…

Numerical Analysis · Mathematics 2024-12-03 Sergio López-Ureña , Dionisio F. Yáñez

We review scale-discretized wavelets on the sphere, which are directional and allow one to probe oriented structure in data defined on the sphere. Furthermore, scale-discretized wavelets allow in practice the exact synthesis of a signal…

Information Theory · Computer Science 2013-12-10 J. D. McEwen , P. Vandergheynst , Y. Wiaux

Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…

Numerical Analysis · Mathematics 2015-02-09 Ashley Prater

Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges…

Information Theory · Computer Science 2019-05-30 Diego Valsesia , Giulia Fracastoro , Enrico Magli

In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…

Astrophysics · Physics 2011-10-28 J. D. McEwen

Surface plasmons are usually described as surface waves with either a complex wavevector or a complex frequency. When discussing their merits in terms of field confinment or enhancement of the local density of states, controversies…

We propose a simple and efficient time-series clustering framework particularly suited for low Signal-to-Noise Ratio (SNR), by simultaneous smoothing and dimensionality reduction aimed at preserving clustering information. We extend the…

Machine Learning · Computer Science 2015-10-20 Tom Hope , Avishai Wagner , Or Zuk

The Fr\'echet distance is a popular distance measure for curves which naturally lends itself to fundamental computational tasks, such as clustering, nearest-neighbor searching, and spherical range searching in the corresponding metric…

Computational Geometry · Computer Science 2018-08-07 Anne Driemel , Amer Krivošija

It is a challenge to manage infinite- or high-dimensional data in situations where storage, transmission, or computation resources are constrained. In the simplest scenario when the data consists of a noisy infinite-dimensional signal, we…

Statistics Theory · Mathematics 2024-01-30 Eduard Belitser

Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…

Classical Analysis and ODEs · Mathematics 2017-03-07 Stefan Lafon , Jacques Lévy Véhel , Jacques Peyrière

The Fourier spectrum at a fractional period is often examined when extracting features from biological sequences and time series. It reflects the inner information structure of the sequences. A fractional period is not uncommon in time…

Spectral Theory · Mathematics 2017-11-03 Jiasong Wang , Changchuan Yin

We construct a directional spin wavelet framework on the sphere by generalising the scalar scale-discretised wavelet transform to signals of arbitrary spin. The resulting framework is the only wavelet framework defined natively on the…

Information Theory · Computer Science 2017-06-06 Jason D. McEwen , Boris Leistedt , Martin Büttner , Hiranya V. Peiris , Yves Wiaux

We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…

Methodology · Statistics 2023-08-04 Jia Zhang , Runxiong Wu , Xin Chen

The extraction of oscillatory components and their properties from different time-frequency representations, such as windowed Fourier transform and wavelet transform, is an important topic in signal processing. The first step in this…

Computational Engineering, Finance, and Science · Computer Science 2015-09-29 Dmytro Iatsenko , Peter V. E. McClintock , Aneta Stefanovska

This paper considers efficient sampling of simultaneously sparse and correlated (S$\&$C) signals. Such signals arise in various applications in array processing. We propose an implementable sampling architecture for the acquisition of…

Information Theory · Computer Science 2023-01-19 Ali Ahmed , Fahad Shamshad , Humera Hameed