Investigations of the effects of random sampling schemes on the stability of generalized sampling

Publikation: Bidrag til tidsskriftLetterForskningpeer review

Resumé

Generalized sampling is a mathematical technique for obtaining approximations of signals with respect to different representations in a numerically stable manner. This can for example be relevant in processing MRI images, where hardware often enforces initial frequency measurements, but where a wavelet basis may be better suited for representing the image. Recently the theory of generalized sampling was extended to work with arbitrary patterns in R d. In this article we investigate how the choice of the probability distribution generating random sampling schemes in R 2 affects the numerical stability of generalized sampling.

OriginalsprogEngelsk
TidsskriftApplied and Computational Harmonic Analysis
Vol/bind45
Udgave nummer2
Sider (fra-til)453-461
Antal sider9
ISSN1063-5203
DOI
StatusUdgivet - sep. 2018

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Random Sampling
Sampling
Wavelet Bases
Numerical Stability
Convergence of numerical methods
Probability Distribution
Hardware
Magnetic resonance imaging
Probability distributions
Arbitrary
Approximation
Processing

Citer dette

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title = "Investigations of the effects of random sampling schemes on the stability of generalized sampling",
abstract = "Generalized sampling is a mathematical technique for obtaining approximations of signals with respect to different representations in a numerically stable manner. This can for example be relevant in processing MRI images, where hardware often enforces initial frequency measurements, but where a wavelet basis may be better suited for representing the image. Recently the theory of generalized sampling was extended to work with arbitrary patterns in R d. In this article we investigate how the choice of the probability distribution generating random sampling schemes in R 2 affects the numerical stability of generalized sampling.",
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AU - Rasmussen, Morten Grud

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AB - Generalized sampling is a mathematical technique for obtaining approximations of signals with respect to different representations in a numerically stable manner. This can for example be relevant in processing MRI images, where hardware often enforces initial frequency measurements, but where a wavelet basis may be better suited for representing the image. Recently the theory of generalized sampling was extended to work with arbitrary patterns in R d. In this article we investigate how the choice of the probability distribution generating random sampling schemes in R 2 affects the numerical stability of generalized sampling.

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DO - 10.1016/j.acha.2017.09.004

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