Wavelets and multiresolution analysis: Nature of ε(∞) Cantorian space–time

Iovane, Gerardo; Giordano, P.

doi:10.1016/j.chaos.2005.11.097

Cited by 123 publications

(29 citation statements)

References 26 publications

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“…To eliminate this distortion, the signals c 0,1 (n), c 0,2 (n) are extended by two kinds of symmetrical extensions. The first one is a whole sample symmetric (WSS) extension and the second one is a half sample symmetric (HSS) extension [7,22]. Figure 4 shows the input signal f (n) (peaks ended by dark spot) and its possible extensions f ′ (n).…”

Section: Input Signal Preprocessingmentioning

confidence: 99%

Convolution implementation with a novel approach of DGHM multiwavelet image transform

Kováč

Mihalik

Gladisova

2017

Journal of Electrical Engineering

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The purpose of this paper is to develop convolution implementation of DGHM (Donovan, Geronimo, Harding, Massopust) multiwavelet image transform using a new approach of ordering wavelet coefficients at the second and higher levels. Firstly, the method of implementation of one-dimensional discrete multiwavelet transform (1D DMWT) for DGHM multiwavelet using discrete convolution and scalar filters is presented. Then, convolution implementation of DGHM multiwavelet image transform by application of 1D DMWT for two dimensions (2D) in a separable way is proposed. Next, the second level of 2D DMWT is performed in three possible ways. The novelty of the proposed implementation is in reordering of L subband wavelet coefficients at the first level into one subimage. The results are evaluated as the energy ratios between the transformed images in L subband at the second level and the input original image. According to the experimental results, the developed implementation of 2D DMWT is approximately 5 % more effective in energy compression than the ones most commonly mentioned in the literature. This paper shows a possibility of convolution implementation of 2D DMWT with higher energy compression.K e y w o r d s: multiwavelet transform,

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Section: Input Signal Preprocessingmentioning

confidence: 99%

Convolution implementation with a novel approach of DGHM multiwavelet image transform

Kováč

Mihalik

Gladisova

2017

Journal of Electrical Engineering

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“…Multiwavelets can simultaneously possess many desired properties such as short support, orthogonality, symmetry, and vanishing moments, which a sin-gle wavelet cannot possess simultaneously. Already they have led to exciting applications in signal analysis [1], fractals [2] and image processing [3],and so on. Vector-valued wavelets are a sort of special multiwavelets Chen [4] introduced the notion of orthogonal vector-valued wavelets.…”

Section: Introductionmentioning

confidence: 99%

The Nice Features of Two-Direction Poly-scale Trivariate Small-Wave Packages with Finite Support

Huang

2011

Advances in Intelligent and Soft Computing

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Abstract. The rise of wavelet analysis in applied mathematics is due to its applications and the flexibility. In this article, the notion of biorthogonal twodirectional compactly supported trivariate wavelet wraps with poly-scale is developed. Their properties are investigated by algebra theory, means of timefrequency analysis method and, operator theory. An approach for designing a sort of affine triariate dual frames in three-dimensional space is presented. The direct decomposition relationship is provided. In the final, new Riesz bases of space

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“…The main advantage of wavelets is their timefrequency localization property. Wavelet packets, due to their nice characteristics, have been widely applied to signal processing [1], image compression [2], and fractal [3] and so on. The introduction for biorthogonal wavelet packets attributes to Cohen and Daubechies Yang and Cheng [4] constructed a-scale orthogonal multiwavelet packets which were more flexible in applications.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, it is significant and necessary to generalize the concept of univariate wavelet packets to the case of multivariate matrix-valued wavelets. The goal of this paper is to give the definition and the construction of matrix -valued wavelet packets and construct several new Riesz bases of space 2 …”

Section: Introductionmentioning

confidence: 99%

The Characterization of a class of Multivariate Wavelet Packets with an Integer-valued Dilation Matrix

Wang

2010

2010 Asia-Pacific Power and Energy Engineering Conference

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In this paper, the notion of matrix-valued multiresolu--tionanalysis is introduced. A novel way for designing biorthogonal matrix-valued multivariate wavelet packets is presented and their properties are investigated by means of time-frequency analysis method, matrix theory and operator theory. Three biorthogonality formulas concerning these wavelet packets are obtained. Finally, new Riesz bases of three dimensional matrixvalued function space are constructed by designing a series of subspaces of biorthogonal matrix wavelet packets.

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Wavelets and multiresolution analysis: Nature of ε(∞) Cantorian space–time

Cited by 123 publications

References 26 publications

Convolution implementation with a novel approach of DGHM multiwavelet image transform

Convolution implementation with a novel approach of DGHM multiwavelet image transform

The Nice Features of Two-Direction Poly-scale Trivariate Small-Wave Packages with Finite Support

The Characterization of a class of Multivariate Wavelet Packets with an Integer-valued Dilation Matrix

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