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Convex multiresolution analysis
Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96), 1998A standard wavelet multiresolution analysis can be defined via a sequence of projection operators onto a monotone sequence of closed vector subspaces possessing suitable invariance properties. We propose an extension of this framework in which the linear projection operators are replaced by nonlinear retractions onto convex sets.
P.L. Combettes, J.-C. Pesquet
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Wavelets with Frame Multiresolution Analysis
Journal of Fourier Analysis and Applications, 2003Let \(A\) be a \(d\times d\) real expansive matrix, i.e., a matrix whose eigenvalues are all of modulus greater than 1. Then a function \(\psi \in L^2(\mathbb{R}^d)\) is an \(A\)-\textit{dilation wavelet} if the system \(|\text{det} A|^{n/2} \psi (A^n x - l)\), \(n\in \mathbb{Z}\), \(l\in \mathbb{Z}^d\), forms an orthonormal basis for \(L^2(\mathbb{R ...
Dai, X., Diao, Y., Gu, Q., Han, D.
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Multiresolution Analysis and Supercompact Multiwavelets
SIAM Journal on Scientific Computing, 2000Summary: The Haar wavelets can represent exactly any piecewise constant function. The motivation for the present development is Alpert's family of compact orthogonal multiwavelets that can represent exactly any piecewise polynomial function. We choose to derive the algorithm in the style and notation of Harten's multiresolution analysis as extended to ...
Beam, Richard M., Warming, Robert F.
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Color Quantization by Multiresolution Analysis
2009A color quantization method is presented, which is based on the analysis of the histogram at different resolutions computed on a Gaussian pyramid of the input image. Criteria based on persistence and dominance of peaks and pits of the histograms are introduced to detect the modes in the histogram of the input image and to define the reduced colormap ...
Ramella G, Sanniti di Baja G
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Multiresolution Analysis for Image Compression
2006With the advent of the multimedia era and the growth of digital packet networks, the total amount of image data accessed and exchanged by users daily has reached the huge value of several petabytes. Therefore, the compression of continuous-tone still images, either grayscale or color, has grown tremendously in importance.
ALPARONE, LUCIANO +2 more
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Smooth Multiresolution Analysis
2002The axiomatic framework of multiresolution analysis is Fourier analysis in L 2, and the convergence of the wavelet expansion is therefore in the L 2-norm. The smoothness properties of the scaling function and of the mother wavelet are, however, of great interest to obtain fast L 2-convergence of the wavelet expansion, or to obtain pointwise convergence
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About Nonstationary Multiresolution Analysis and Wavelets
Results in Mathematics, 2011Let \(\psi^{(j)} \in L^2(\mathbb R)\) and \(\psi_{j,k} = 2^{j/2}\,\psi^{(j)}(2^j\cdot -k)\) for \(j,k\in \mathbb Z\) be given. In the nonstationary case, \(\psi^{(j)}\) are called mother wavelets, if \(\{\psi_{j,k};\,j,k\in \mathbb Z\}\) is an orthonormal basis of \(L^2(\mathbb R)\).
Bastin, Françoise, Simons, Laurent
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Wavelets and Mallat's Multiresolution Analysis
Fundamenta Informaticae, 1998We present a simple proof of Mallat's theorem about wavelet and multiresolution analysis. We do not use Fourier transform and the proof is accesible even for younger undergraduate students.
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Multiresolution Analysis of Connectivity
2005Multiresolution histograms have been used for indexing and retrieval of images. Multiresolution histograms used traditionally are 2d-histograms which encode pixel intensities. Earlier we proposed a method for decomposing images by connectivity. In this paper, we propose to encode centroidal distances of an image in multiresolution histograms; the image
Atul Sajjanhar +3 more
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Wavelets; Multiresolution Analysis
2016It has been shown in Chap. 12 on time-frequency analysis that how decomposition on a wavelet basis allows highlighting effectively changes with time of the properties of a signal. Wavelet bases with compact support, which could be used by simple filtering operations, have been searched.
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