Non-uniform weighted average sampling and reconstruction in shift-invariant and wavelet spaces

By Akram Aldroubi. 2002

143 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/ff073004fda12f66f76b8c27d88e5f73cbcc9536

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Oblique dual frames and shift-invariant spaces (2004, methodology): “Among the previous applications of pseudoframes, we that they have been used to define a type of generalized multiresolution analysis in [15]; a furthe aiming at construction of generalized frame sequences via unbounded operators, was reported A related idea appears in the paper [1] by Aldroubi, in ”
Localization of Frames, Banach Frames, and the Invertibility of the Frame Operator (2004, methodology): “A number of recent articles emphasize that a realistic sampling model should use local averages � f, ψj �= � Rd f( t)ψj (t) dt in place of exact pointwise values f( xj ) as the input for reconstruction [ 2 , 4, 31].”
A sample-and-clean framework for fast and accurate query processing on dirty data (2014, methodology): “Techniques similar to our duplicate reweighting scheme have been studied in estimating from non-uniform samples [4], and is also similar to the acceptance ratio used sampling algorithms such as the MetropolisHastings Algorithm and Rejection Sampling [42,45].”
An Introduction to Weighted Wiener Amalgams (2003, unknown): “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.”
Convolution, Average Sampling, and a Calderon Resolution of the Identity for Shift-Invariant Spaces (2005, background): “…underlying space is not the whole space L2, but as is typical in sampling theory and many applications (see, for instance, [1, 5, 6, 10, 14, 16, 27, 28]), a shift-invariant subspace of L2 of the form: (1.2) V 2(Φ) = { ∑ j∈Zd D(j)TΦ(· − j) : D ∈ (`2)(r) } for some vector function Φ = (φ1, . . .…”