Linear reconstructions and the analysis of the stable sampling rate

zbMath1411.94036arXiv1907.12286MaRDI QIDQ4631279

Anders C. Hansen, L. Thesing

Publication date: 24 April 2019

Full work available at URL: https://arxiv.org/abs/1907.12286

zbMATH Keywords

waveletssamplinglinear reconstructiongeneralized samplingbinary measurements

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Numerical methods for inverse problems for integral equations (65R32) Sampling theory in information and communication theory (94A20)

Related Items (5)

Non-uniform recovery guarantees for binary measurements and infinite-dimensional compressed sensing ⋮ On Reconstructing Functions from Binary Measurements ⋮ Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling ⋮ Weak-Type Estimates for the Metaplectic Representation Restricted to the Shearing and Dilation Subgroup of $$SL(2,\mathbb {R})$$ ⋮ Recovering Wavelet Coefficients from Binary Samples Using Fast Transforms

Cites Work

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• A Mathematical Theory of Communication
• On greedy algorithm approximating Kolmogorov widths in Banach spaces
• A consistent and stable approach to generalized sampling
• Generalized sampling and infinite-dimensional compressed sensing
• A generalized sampling theorem for stable reconstructions in arbitrary bases
• Convergence analysis of the finite section method and Banach algebras of matrices
• On dyadic analysis based on the pointwise dyadic derivative
• Wavelets on the interval and fast wavelet transforms
• Data assimilation and sampling in Banach spaces
• Greedy algorithms for reduced bases in Banach spaces
• On the approximation of spectra of linear operators on Hilbert spaces
• On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate
• Pseudospectral Fourier reconstruction with the modified inverse polynomial reconstruction method
• A Practical Guide to the Recovery of Wavelet Coefficients from Fourier Measurements
• A prioriconvergence of the Greedy algorithm for the parametrized reduced basis method
• Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem
• Electron Tomography and Multiscale Biology
• A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics
• Convergence Rates for Greedy Algorithms in Reduced Basis Methods
• The Shannon sampling theorem—Its various extensions and applications: A tutorial review
• Sampling-50 years after Shannon
• Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements
• Data Assimilation in Reduced Modeling

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