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Related papers: Sampling the flow of a bandlimited function

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In this paper we study reconstruction of a function $f$ from its discrete Radon transform data in $\mathbb R^3$ when $f$ has jump discontinuities. Consider a conventional parametrization of the Radon data in terms of the affine and angular…

Numerical Analysis · Mathematics 2019-03-21 Alexander Katsevich

From a sufficiently large point sample lying on a compact Riemannian submanifold of Euclidean space, one can construct a simplicial complex which is homotopy-equivalent to that manifold with high confidence. We describe a corresponding…

Algebraic Topology · Mathematics 2013-10-15 Steve Ferry , Konstantin Mischaikow , Vidit Nanda

The reconstruction of a function from its spectrogram (i.e., the absolute value of its short-time Fourier transform (STFT)) arises as a key problem in several important applications, including coherent diffraction imaging and audio…

Functional Analysis · Mathematics 2023-10-02 Philipp Grohs , Lukas Liehr

We propose an entirely redesigned framework of bandlimited signal reconstruction for the time encoding machine (TEM) introduced by Lazar and T\'oth. As the encoding part of TEM consists in obtaining integral values of a bandlimited input…

Signal Processing · Electrical Eng. & Systems 2020-12-25 Nguyen T. Thao , Dominik Rzepka

Let $X=\{x_i:i\in\mathbb{Z}\}$, $\dots<x_{i-1}<x_i<x_{i+1}<\dots$, be a sampling set which is separated by a constant $\gamma>0$. Under certain conditions on $\phi$, it is proved that if there exists a positive integer $\nu$ such that…

Classical Analysis and ODEs · Mathematics 2017-02-02 A. Antony Selvan

Continuous-time signals are well known for not being perfectly localized in both time and frequency domains. Conversely, a signal defined over the vertices of a graph can be perfectly localized in both vertex and frequency domains. We…

Information Theory · Computer Science 2015-12-03 Mikhail Tsitsvero , Sergio Barbarossa

Diffusion and flow-matching models achieve remarkable generative performance but at the cost of many sampling steps, this slows inference and limits applicability to time-critical tasks. The ReFlow procedure can accelerate sampling by…

Machine Learning · Computer Science 2024-10-11 Beomsu Kim , Yu-Guan Hsieh , Michal Klein , Marco Cuturi , Jong Chul Ye , Bahjat Kawar , James Thornton

We develop a parabolic inf-sup theory for a modified TraceFEM semi-discretization in space of the heat equation posed on a stationary surface embedded in $\mathbb{R}^n$. We consider the normal derivative volume stabilization and add an…

Numerical Analysis · Mathematics 2024-09-24 Lucas Bouck , Ricardo H. Nochetto , Mansur Shakipov , Vladimir Yushutin

Spatiotemporal flows govern diverse phenomena across physics, biology, and engineering, yet modelling their multiscale dynamics remains a central challenge. Despite major advances in physics-informed machine learning, existing approaches…

Material response of real, passive, linear, time-invariant media to external influences is described by complex analytic functions of frequency that can always be written in terms of Stieltjes functions -- a special class of analytic…

Optimization and Control · Mathematics 2022-03-25 Yury Grabovsky

We consider the problem of spatiotemporal sampling in which an initial state $f$ of an evolution process $f_t=A_tf$ is to be recovered from a combined set of coarse samples from varying time levels $\{t_1,\dots,t_N\}$. This new way of…

Other Computer Science · Computer Science 2014-12-04 Akram Aldroubi , Jacqueline Davis , Ilya Krishtal

As a neuromorphic sensor with high temporal resolution, spike camera can generate continuous binary spike streams to capture per-pixel light intensity. We can use reconstruction methods to restore scene details in high-speed scenarios.…

Computer Vision and Pattern Recognition · Computer Science 2024-07-09 Liwen Hu , Ziluo Ding , Mianzhi Liu , Lei Ma , Tiejun Huang

We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain…

Analysis of PDEs · Mathematics 2018-04-04 Gang Bao , Guanghui Hu , Yavar Kian , Tao Yin

This paper considers the problem of restricting the short-time Fourier transform to domains of nonzero measure in the plane and studies sampling bounds of such systems. In particular, we give a quantitative estimate for the lower sampling…

Classical Analysis and ODEs · Mathematics 2019-06-10 Philippe Jaming , Michael Speckbacher

We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost…

Numerical Analysis · Mathematics 2021-12-03 Giovanni Barbarino , Davide Bianchi , Carlo Garoni

We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis. As we…

Numerical Analysis · Mathematics 2010-12-01 Ben Adcock , Anders C. Hansen

Point-spread function (PSF) estimation in spatially undersampled images is challenging because large pixels average fine-scale spatial information. This is problematic when fine-resolution details are necessary, as in optimal photometry…

Instrumentation and Methods for Astrophysics · Physics 2021-02-03 Teresa Symons , Michael Zemcov , James Bock , Yun-Ting Cheng , Brendan Crill , Christopher Hirata , Stephanie Venuto

Optical flow is a powerful tool for the study and analysis of motion in a sequence of images. In this article we study a Horn-Schunck type spatio-temporal regularization functional for image sequences that have a non-Euclidean, time varying…

Numerical Analysis · Mathematics 2014-10-02 Martin Bauer , Markus Grasmair , Clemens Kirisits

Consider the task of sampling and reconstructing a bandlimited spatial field in $\Re^2$ using moving sensors that take measurements along their path. It is inexpensive to increase the sampling rate along the paths of the sensors but more…

Information Theory · Computer Science 2012-11-02 Jayakrishnan Unnikrishnan , Martin Vetterli

We consider the problem to reconstruct a wave speed $c \in C^\infty(M)$ in a domain $M \subset \R^n$ from acoustic boundary measurements modelled by the hyperbolic Dirichlet-to-Neumann map $\Lambda$. We introduce a reconstruction formula…

Analysis of PDEs · Mathematics 2012-10-04 Shitao Liu , Lauri Oksanen