Journal Article10.1007/S00041-001-4027-2
Irregular Sampling in Wavelet Subspaces.
Y.M. Liu,Gilbert G. Walter +1 more
83
TL;DR: In this paper, the irregular sampling problem in wavelet subspaces has been discussed and a regular sampling theorem has been established for the Paley-Wiener space with both regular and irregular sampling.
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Abstract: As a particular wavelet subspace, the Paley-Wiener space \(B_{\pi}\) has both regular and irregular sampling theorems A regular sampling theorem in general wavelet subspaces has been established for several years In this paper, we discuss the irregular sampling problem in wavelet subspaces
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Citations
Sampling-50 years after Shannon
Michael Unser
- 01 Apr 2000
TL;DR: The standard sampling paradigm is extended for a presentation of functions in the more general class of "shift-in-variant" function spaces, including splines and wavelets, and variations of sampling that can be understood from the same unifying perspective are reviewed.
Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces
TL;DR: A unified framework for uniform and nonuniform sampling and reconstruction in shift-invariant subspaces is provided by bringing together wavelet theory, frame theory, reproducing kernel Hilbert spaces, approximation theory, amalgam spaces, and sampling.
Beurling-Landau-Type Theorems for Non-Uniform Sampling in Shift Invariant Spline Spaces
TL;DR: In this paper, it was shown that sampling density ≥ 1 is sufficient for the stable reconstruction of a function f from its samples, a result similar to Beurling's result for the Paley-Wiener space.
176
Sampling and reconstruction of signals in a reproducing kernel subspace of Lp(Rd)
M. Zuhair Nashed,Qiyu Sun +1 more
TL;DR: It is shown that a signal in a reproducing kernel subspace of Lp(Rd) associated with an idempotent integral operator whose kernel has certain off-diagonal decay and regularity can be reconstructed in a stable way from its samples taken on a relatively- separated set with sufficiently small gap.
123
Nonuniform average sampling and reconstruction in multiply generated shift-invariant spaces
TL;DR: In this paper, the problem of reconstructing a function f from a set of nonuniformly distributed, weighted-average sampled values { R d f(x)ψxj (x) dx : j ∈ J } is stud- ied in the context of shift-invariant subspaces of L p (R d ) generated by p-frames.
90
References
Ten Lectures on Wavelets
TL;DR: In this article, the regularity of compactly supported wavelets and symmetry of wavelet bases are discussed. But the authors focus on the orthonormal bases of wavelets, rather than the continuous wavelet transform.
14.2K
Ten Lectures on Wavelets.
TL;DR: Introduction Preliminaries and notation The what, why, and how of wavelets The continuous wavelet transform Discrete wavelet transforms: Frames Time-frequency density and orthonormal bases Orthonormal wavelet bases of compactly supported wavelets and multiresolutional analysis.
13.5K
A sampling theorem for wavelet subspaces
TL;DR: The classical Shannon sampling theorem is extended to the subspaces used in the multiresolution analysis in wavelet theory, and is first shown to have a Riesz basis formed from the reproducing kernels.
340
Cardinal spline filters: stability and convergence to the ideal sinc interpolator
TL;DR: It is proved that the frequency responses of the cardinal spline filters converge to the ideal lowpass filter in all Lfnorms with 1 ~
188
Polynomial spline signal approximations: filter design and asymptotic equivalence with Shannon's sampling theorem
TL;DR: This work has shown that the B-spline interpolation of order 2n+1 of the sampled filtered sequence are identical to the coefficients of the least-squares approximation of g(t) of order n, which confirms the parallel with the classical sampling/reconstruction procedure for bandlimited signals.
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