Publications related to Sampling—50 Years After Shannon

Compressed delay-and-sum beamforming for ultrafast ultrasound imaging

Jean-Philippe Thiran, Yves Wiaux, Rafael Eduardo Carrillo Rangel, Adrien Georges Jean Besson, Olivier Bernard

The theory of compressed sensing (CS) leverages upon structure of signals in order to reduce the number of samples needed to reconstruct a signal, compared to the Nyquist rate. Although CS approaches have been proposed for ultrasound (US) imaging with prom ...

Ieee2016

On the well-posedness of the Holm-Staley b-family of equations

Hasan Inci

In this paper we consider the Holm-Staley b-family of equations in the Sobolev spaces H-s (R) for s > 3/2. Using a geometric approach we show that, for any value of the parameter b, the corresponding solution map, u(0) bar right arrow u(T), is nowhere loca ...

Taylor & Francis Ltd2016

Generalized Poisson Summation Formula for Tempered Distributions

Michaël Unser, Quy Ha Nguyen

The Poisson summation formula (PSF), which relates the sampling of an analog signal with the periodization of its Fourier transform, plays a key role in the classical sampling theory. In its current forms, the formula is only applicable to a limited class ...

IEEE2015

Random sampling of bandlimited signals on graphs

Pierre Vandergheynst, Rémi Gribonval, Gilles Puy, Nicolas Tremblay

We study the problem of sampling

k

-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, \ie, independent of the graph structure, and its perform ...

2015

Well-Posedness, Regularity, and Convergence Analysis of the Finite Element Approximation of a Generalized Robin Boundary Value Problem

Alfio Quarteroni, Luca Dede', Claudia Maria Colciago

In this paper, we propose the mathematical and finite element analysis of a second-order partial differential equation endowed with a generalized Robin boundary condition which involves the Laplace--Beltrami operator by introducing a function space $H^1(\O ...

Society for Industrial and Applied Mathematics2015

Sampling based on timing: Time encoding machines on shift-invariant subspaces

Martin Vetterli, David Gontier

Sampling information using timing is an approach that has received renewed attention in sampling theory. The question is how to map amplitude information into the timing domain. One such encoder, called time encoding machine, was introduced by Lazar and To ...

Elsevier2014

Jaggies as aliasing or reconstruction phenomena: a tutorial

Roger Hersch, Isaac Amidror

Jaggies (staircasing effects) along slanted lines or curved edges are omnipresent in digital imaging. They are so widespread in digital display devices that very often they are associated with the modern "computerized" world (and sometimes even intentional ...

Is&T & Spie2014

Calibration and field application of passive sampling for episodic exposure to polar organic pesticides in streams

Rainfall-triggered runoff is a major driver of pesticide input in streams. Only few studies have examined the suitability of passive sampling to quantify such episodic exposures. In this study, we used Empore(TM) styrene-divinylbenzene reverse phase sulfon ...

Elsevier2014

Sparse image reconstruction on the sphere: implications of a new sampling theorem

Jean-Philippe Thiran, Pierre Vandergheynst, Dimitri Nestor Alice Van De Ville, Yves Wiaux, Gilles Puy, Jason Douglas McEwen

A new sampling theorem on the sphere has been developed recently, reducing the number of samples required to represent a band-limited signal by a factor of two for equiangular sampling schemes. For signals sparse in a spatially localised measure, such as i ...

Institute of Electrical and Electronics Engineers2013

Sampling High-Dimensional Bandlimited Fields on Low-Dimensional Manifolds

Martin Vetterli, Jayakrishnan Unnikrishnan

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 expensive to incre ...

Institute of Electrical and Electronics Engineers2013

Sampling—50 Years After Shannon

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Compressed delay-and-sum beamforming for ultrafast ultrasound imaging

On the well-posedness of the Holm-Staley b-family of equations

Generalized Poisson Summation Formula for Tempered Distributions

Random sampling of bandlimited signals on graphs

Well-Posedness, Regularity, and Convergence Analysis of the Finite Element Approximation of a Generalized Robin Boundary Value Problem

Sampling based on timing: Time encoding machines on shift-invariant subspaces

Jaggies as aliasing or reconstruction phenomena: a tutorial

Calibration and field application of passive sampling for episodic exposure to polar organic pesticides in streams

Sparse image reconstruction on the sphere: implications of a new sampling theorem

Sampling High-Dimensional Bandlimited Fields on Low-Dimensional Manifolds

Compressed delay-and-sum beamforming for ultrafast ultrasound imaging

Generalized Poisson Summation Formula for Tempered Distributions

On the well-posedness of the Holm-Staley b-family of equations

Random sampling of bandlimited signals on graphs

Sampling based on timing: Time encoding machines on shift-invariant subspaces

Calibration and field application of passive sampling for episodic exposure to polar organic pesticides in streams

Well-Posedness, Regularity, and Convergence Analysis of the Finite Element Approximation of a Generalized Robin Boundary Value Problem

Sampling High-Dimensional Bandlimited Fields on Low-Dimensional Manifolds

Sparse image reconstruction on the sphere: implications of a new sampling theorem

Jaggies as aliasing or reconstruction phenomena: a tutorial