Results 241 to 250 of about 236,630 (266)
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Image denoising using a tight frame
IEEE Transactions on Image Processing, 2006We present a general mathematical theory for lifting frames that allows us to modify existing filters to construct new ones that form Parseval frames. We apply our theory to design nonseparable Parseval frames from separable (tensor) products of a piecewise linear spline tight frame.
Lixin, Shen +5 more
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Doklady Mathematics, 2008
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Vestnik St. Petersburg University: Mathematics, 2009
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Equal-Norm Tight Frames with Erasures
Advances in Computational Mathematics, 2003Given a Hilbert space \(H\), a collection \(\{e_i: i \in I \} \subset H\) is called a frame if there exist constants \(A, B>0\) such that for all \(f\in H\): \[ A \| f\| ^2 \leq \sum_{i \in I} | \langle f, e_i \rangle | ^2 \leq B \| f\| ^2. \] When \(A=B\) we say that the frame is tight. When all elements \(e_i\) have the same norm, we say the frame is
Casazza, Peter G., Kovačević, Jelena
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Construction of Tight Filter Bank Frames
2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings, 2006In this paper, we present an explicit and numerically efficient formulae to construct a tight (paraunitary) FB frame from a given un-tight (non-paraunitary) FB frame. The derivation uses the well developed techniques from modern control theory, which results in the unified formulae for generic IIR and FIR FBs.
Chai, Li +3 more
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Complex equiangular tight frames
SPIE Proceedings, 2005A complex equiangular tight frame (ETF) is a tight frame consisting of N unit vectors in C d whose absolute inner products are identical. One may view complex ETFs as a natural geometric generalization of an orthonormal basis. Numerical evidence suggests that these objects do not arise for most pairs ( d , N).
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Tight Frames and Dual Frame Pairs
2016We have already highlighted the frame decomposition, which shows that a frame \(\{f_{k}\}_{k=1}^{\infty }\) for a Hilbert space \(\mathcal{H}\) leads to the decomposition $$\displaystyle\begin{array}{rcl} f =\sum _{ k=1}^{\infty }\langle f,S^{-1}f_{ k}\rangle f_{k},\ \ \forall f \in \mathcal{H};& &{}\end{array}$$ (6.1) here \(S: \mathcal{H ...
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2018
The angle preserving transformations of \(\mathbb {R}^2\) form the real orthogonal group $${ O}(2) := \{A\in \mathbb {R}^{2\times 2}:A^T A=I\},$$ which can be thought of as the symmetries of the inner product space \({\mathscr {H}}=\mathbb {R}^2\).
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The angle preserving transformations of \(\mathbb {R}^2\) form the real orthogonal group $${ O}(2) := \{A\in \mathbb {R}^{2\times 2}:A^T A=I\},$$ which can be thought of as the symmetries of the inner product space \({\mathscr {H}}=\mathbb {R}^2\).
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Parametric Wavelets: Tight Frames Class
IFAC Proceedings Volumes, 1997Abstract In this paper, several methods to enlarge by parametrization the families of wavelets are proposed. The main goal is to prove that every remarkable classical wavelet can generate a class of wavelets, each one preserving the main characteristics of the original, but offering more mobility for time-frequency representations. Here, an important
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Variational characterisations of tight frames
2018If \((f_j)_{j\in J}\) is a finite tight frame for \(\mathscr {H}\), then (see Proposition 2.1). \(\sum _{j\in J}\sum _{k\in J} |\langle f_j, f_k\rangle |^2 = {1\over d} \Bigl (\sum _{j\in J}\langle f_j, f_j\rangle \Bigr )^2, \qquad d=\dim (\mathscr {H}).\)
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