Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces

By Akram Aldroubi, Karlheinz Gröchenig. SIAM Review, 2001

781 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/0ae3ef5157788c04d5c7a026575451ce9f6e5b8e

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Wiener's lemma for infinite matrices with polynomial off-diagonal decay (2005, background): “frequency analysis [2,10–13,19], shift-invariant spaces and polynomial spline spaces [1,8,15,19], and non sampling [6,19].”
Structured Compressed Sensing: From Theory to Applications (2011, background): “A signal class that plays an important role in sampling theory are signals in SI spaces [151]–[154].”
Convolution, Average Sampling, and a Calderon Resolution of the Identity for Shift-Invariant Spaces (2005, background): “Thus, by removing some pathological situations as described in the Theorem above, our intuition is validated.”
Convex Optimization in Signal Processing and Communications (2009, background): “A SI subspace A of L2, is a space of signals that can be expressed as linear combinations of shifts of a generator a(t) [7]:”
Synchrosqueezing-Based Recovery of Instantaneous Frequency from Nonuniform Samples (2010, background): “The analysis of signals from samples spaced nonuniformly in time is also an important problem in several applications, arising in radar detection, audio processing, seismology and many other ﬁelds [1, 12].”
Non-uniform weighted average sampling and reconstruction in shift-invariant and wavelet spaces (2002, background): “see, for example, [2–6,9,10,17,18,21–25] and the references therein.”
Wiener’s Lemma for Infinite Matrices II (2007, background): “The lw-stability is one of the basic assumptions for infinite matrices arising in many fields of mathematics (see [2, 4, 24, 28, 29, 39, 42, 43] for a sample of papers), but little is known about practical criteria for the lw-stability of an infinite matrix, see [46] for the diagonalblocks-dominated”
History and Evolution of the Density Theorem for Gabor Frames (2007, background): “range of areas, including, for example, sampling theory [1], operator theory [100], nonlinear sparse approximation [84], pseudodifferential operators [94], wavelet theory [49], wireless communications [171], data transmission with erasures [83], signal processing [24], and quantum computing [58].”
Shannon sampling and function reconstruction from point values (2004, methodology): “See [2], [31] for some background and some generalizations.”
Sampling Expansions in Reproducing Kernel Hilbert and Banach Spaces (2009, background): “That is why the existence of a reconstruction operator is often assumed in the denition of Banach frames [ 1 , 3, 8, 9, 11].”
Linear Independence of Finite Gabor Systems (2006, result): “For a recent research-survey of shift-invariant spaces in sampling theory, we suggest [ 2 ].”
The Zak transform and the structure of spaces invariant by the action of an LCA group (2014, background): “Closed spaces that are invariant under a certain kind of unitary operators are of particular importance in several areas of Harmonic Analysis such as wavelets, spline systems, Gabor systems and approximation theory [1, 19, 24, 30, 33].”
An Introduction to Weighted Wiener Amalgams (2003, background): “Amalgam spaces provide a useful context for developing sampling theory, and we refer to [ 1 ], [2], [3], [4], [32] for recent results in this direction.”