A real algebra perspective on multivariate tight wavelet frames
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Cites background from "A real algebra perspective on multi..."
...An interesting discussion of the complexity of the extension problem for wavelet systems in higher dimensions, together with several deep results, recently appeared in [2]....
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9 citations
Cites background from "A real algebra perspective on multi..."
..., the papers [3, 6, 14, 17, 19], just to mention a few out of many)....
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"A real algebra perspective on multi..." refers background in this paper
...It has been observed in [14] that redundancy of wavelet frames has advantages for applications in signal denoising - if the data is redundant, then loosing some data during transmission does not necessarily affect the reconstruction of the original signal....
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1,020 citations
"A real algebra perspective on multi..." refers background in this paper
...This establishes a connection between constructions of tight wavelet frames and moment problems, see [24, 30, 31] for details....
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872 citations
"A real algebra perspective on multi..." refers background or methods in this paper
...We illustrate this method on the example of the so-called butterfly scheme from [19]....
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...The butterfly scheme describes an interpolatory subdivision scheme that generates a smooth regular surface interpolating a given set of points [19]....
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...13 illustrates the advantage of the representation in (32) for the butterfly scheme [19], an interpolatory subdivision method with the corresponding mask p ∈ C[T ] of a larger support, some of whose coefficients are negative....
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764 citations
"A real algebra perspective on multi..." refers background or methods in this paper
...The starting point of our study is the so-called Unitary Extension Principle (UEP) from [33], a special case of the above mentioned characterizations in [8, 9, 16]....
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...We list some existing constructions of compactly supported MRA wavelet tight frames of L2(R ) [7, 10, 16, 23, 29, 33, 38] that employ the Unitary Extension Principle....
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...1 Formulations of UEP in wavelet frame literature Most formulations of the UEP are given in terms of identities for trigonometric polynomials, see [16, 33]....
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...1 is a wavelet tight frame of L2(R ), see [16, 33]....
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