Some Smooth Compactly Supported Tight Wavelet Frames with Vanishing Moments
نویسندگان
چکیده
منابع مشابه
Some Smooth Compactly Supported Tight Wavelet Frames with Vanishing Moments
Let A ∈ Rd×d, d ≥ 1 be a dilation matrix with integer entries and | detA| = 2. We construct several families of compactly supported Parseval framelets associated to A having any desired number of vanishing moments. The first family has a single generator and its construction is based on refinable functions associated to Daubechies low pass filters and a theorem of Bownik. For the construction o...
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The notion of vanishing-moment recovery (VMR) functions is introduced in this paper for the construction of compactly supported tight frames with two generators having the maximum order of vanishing moments as determined by the given refinable function, such as the mth order cardinal B-spline Nm. Tight frames are also extended to “sibling frames” to allow additional properties, such as symmetry...
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This paper considers the design of wavelet tight frames based on iterated oversampled filter banks. The greater design freedom available makes possible the construction of wavelets with a high degree of smoothness, in comparison with orthonormal wavelet bases. In particular, this paper takes up the design of systems that are analogous to Daubechies orthonormal wavelets—that is, the design of mi...
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When a Cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L = L(IR) with dilation integer factor M ≥ 2, the standard “matrix extension” approach for constructing compactly supported tight frames has the limitation that at least one of the tight frame generators does not annihilate any polynomial except the constant. The notio...
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Based on the method for constructing tight wavelet frames of [RS2], we show that one can construct, for any dilation matrix, and in any spatial dimension, tight wavelet frames generated by compactly supported functions with arbitrarily high smoothness. AMS (MOS) Subject Classifications: Primary 42C15, Secondary 42C30
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ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2015
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-015-9442-x