Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples

DOI10.1016/j.acha.2015.09.006zbMath1401.42030arXiv1405.3111OpenAlexW2962865631MaRDI QIDQ2627890

Milana Gataric, Anders C. Hansen, Ben Adcock

Publication date: 1 June 2017

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.3111

zbMATH Keywords

medical imagingframe boundsmultivariate functionnonuniform samplingdensity conditionstable recoverycompactly supported functionnonuniform Fourier samplesframe of weighted exponentialsweighted Fourier frame

Mathematics Subject Classification ID

Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) General harmonic expansions, frames (42C15) Numerical methods for trigonometric approximation and interpolation (65T40) Sampling theory in information and communication theory (94A20)

Related Items (10)

Riesz bases by replacement ⋮ Infinite dimensional compressed sensing from anisotropic measurements and applications to inverse problems in PDE ⋮ Sampling and reconstruction in distinct subspaces using oblique projections ⋮ Density theorems for nonuniform sampling of bandlimited functions using derivatives or bunched measurements ⋮ Detecting edges from non-uniform Fourier data using Fourier frames ⋮ Computing reconstructions from nonuniform Fourier samples: universality of stability barriers and stable sampling rates ⋮ Investigations of the effects of random sampling schemes on the stability of generalized sampling ⋮ A Practical Guide to the Recovery of Wavelet Coefficients from Fourier Measurements ⋮ A new generalized projection and its application to acceleration of audio declipping ⋮ Undersampled windowed exponentials and their applications

Uses Software

• NFFT
• NFFT3

Cites Work

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• Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon
• A generalized sampling theorem for stable reconstructions in arbitrary bases
• Numerical stability of nonequispaced fast Fourier transforms
• The collected works of Arne Beurling. Volume 1: Complex analysis. Volume 2: Harmonic analysis. Ed. by Lennart Carleson, Paul Malliavin, John Neuberger, John Wermer
• Concrete and abstract Voronoi diagrams
• A density criterion for frames of complex exponentials
• Weighted tight frames of exponentials on a finite interval
• Efficient numerical methods in non-uniform sampling theory
• Numerical analysis of non-uniform sampling problem
• Non-uniform weighted average sampling and reconstruction in shift-invariant and wavelet spaces
• Generalization of the inverse polynomial reconstruction method in the resolution of the Gibbs phenomenon
• On the connection between exponential bases and certain related sequences in \(L^ 2 (-\pi, \pi)\)
• Beurling-Landau-type theorems for non-uniform sampling in shift invariant spline spaces
• On multi-dimensional sampling and interpolation
• On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate
• Necessary density conditions for sampling an interpolation of certain entire functions
• Pseudospectral Fourier reconstruction with the modified inverse polynomial reconstruction method
• Frames, Riesz bases, and discrete Gabor/wavelet expansions
• Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces
• A Practical Guide to the Recovery of Wavelet Coefficients from Fourier Measurements
• Recovering Piecewise Smooth Functions from Nonuniform Fourier Measurements
• Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem
• Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms
• Stability Results for Scattered Data Interpolation by Trigonometric Polynomials
• Reconstruction Algorithms in Irregular Sampling
• Irregular sampling, Toeplitz matrices, and the approximation of entire functions of exponential type
• Sampling-50 years after Shannon
• Random Sampling of Multivariate Trigonometric Polynomials
• Simple quasicrystals are sets of stable sampling
• On Stable Reconstructions from Nonuniform Fourier Measurements
• Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements
• Nonuniform fast fourier transforms using min-max interpolation
• GENERAL FRAMEWORK FOR CONSISTENT SAMPLING IN HILBERT SPACES
• A Class of Nonharmonic Fourier Series
• Modern sampling theory. Mathematics and applications

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