Ondelettes, filtres miroirs en quadrature et traitement numerique de l'image

Meyer, Yves

doi:10.1007/bfb0083512

Cited by 220 publications

(366 citation statements)

References 13 publications

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“…Working on digital signal processing Stephane Mallat [6] provided a new contribution to wavelet theory by connecting the term filters with mirror symmetry, the pyramid algorithm and orthonormal wavelet basis. Yves Meyer [7] constructed a continuously differentiable wavelet lacking and finally, Ingrid Daubechies [8] managed to add to Haar's work by constructing various families of orthonormal wavelet bases. The WT has many similarities with STFT but is basically different in its basis function called wavelets which are not of fixed length.…”

Section: Literature Reviewmentioning

confidence: 99%

VHDL Modelling of Fixed-point DWT for the Purpose of EMG Signal Denoising

Ahsan

Ibrahimy

Khalifa

2011

2011 Third International Conference on Computational Intelligence, Communication Systems and Networks

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Abstract-Wavelet Transform (WT) has been widely applied in biomedical signal analysis. This paper will present the denoising method of EMG signal using WT and its model processed by VHSIC (Very High Speed Integrated Circuit) Hardware Description Language (VHDL) model of it. The principle of wavelet denoising is first to decompose the signal by performing a WT, followed by applying suitable thresholds to the detail coefficients, zeroing all coefficients below their associated thresholds, and finally to reconstruct the denoised signal based on the modified detail coefficients. Discrete Wavelet Transform (DWT) is a method that uses wavelet analyzer in which case the signal split into small pieces preserving both time and frequency properties. The Second order of Daubechies family (db2) has been used to denoise EMG signals. The simulation, synthesis and verification of the design presents a fast and reliable prototyping of DWT for denoising of EMG signals.

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Section: Literature Reviewmentioning

confidence: 99%

VHDL Modelling of Fixed-point DWT for the Purpose of EMG Signal Denoising

Ahsan

Ibrahimy

Khalifa

2011

2011 Third International Conference on Computational Intelligence, Communication Systems and Networks

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“…General references for the material in this section are Meyer [10] and Daubechies [4]. Let E denote the set of vertices of the cube [0, 1] d and let E denote the set of nonzero vertices.…”

Section: Besov Spaces and Waveletsmentioning

confidence: 99%

“…It is a smoothness space with s giving the order of smoothness (analogous to the number of derivatives), p giving the space in which smoothness is to be measured (namely L p (R d )), and q giving a finer distinction of these spaces which is important in many applications. We refer the reader to any of the standard treatments of Besov spaces ( [6], [10], [11], [1]). …”

Section: Besov Spaces and Waveletsmentioning

confidence: 99%

The averaging lemma

DeVore

Petrova

2000

J. Amer. Math. Soc.

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Averaging lemmas deduce smoothness of velocity averages, such as \[ f ¯ ( x ) := ∫ Ω f ( x , v ) d v , Ω ⊂ R d , \bar f(x):=\int _\Omega f(x,v)\, dv ,\quad \Omega \subset \mathbb {R}^d, \] from properties of f f . A canonical example is that f ¯ \bar f is in the Sobolev space W 1 / 2 ( L 2 ( R d ) ) W^{1/2}(L_2(\mathbb {R}^d)) whenever f f and g ( x , v ) := v ⋅ ∇ x f ( x , v ) g(x,v):=v\cdot \nabla _xf(x,v) are in L 2 ( R d × Ω ) L_2(\mathbb {R}^d\times \Omega ) . The present paper shows how techniques from Harmonic Analysis such as maximal functions, wavelet decompositions, and interpolation can be used to prove L p L_p versions of the averaging lemma. For example, it is shown that f , g ∈ L p ( R d × Ω ) f,g\in L_p(\mathbb {R}^d\times \Omega ) implies that f ¯ \bar f is in the Besov space B p s ( L p ( R d ) ) B_p^s(L_p(\mathbb {R}^d)) , s := min ( 1 / p , 1 / p ′ ) s:=\min (1/p,1/p^\prime ) . Examples are constructed using wavelet decompositions to show that these averaging lemmas are sharp. A deeper analysis of the averaging lemma is made near the endpoint p = 1 p=1 .

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“…Some of these systems, called wavelets, also enjoy many of the properties of orthonormal bases. A (yet unpublished) book on wavelets by Y. Meyer [24] presents this material and its application to the various topics we have discussed. The approach of Frazier and Jawerth is described in [19,20].…”

Section: The Tl Theorem a Calderón-zygmund Operator T Is Bounded On mentioning

confidence: 99%

Book Review: Real variable methods in harmonic analysis

Weiss¹

1989

Bull. Amer. Math. Soc.

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Ondelettes, filtres miroirs en quadrature et traitement numerique de l'image

Cited by 220 publications

References 13 publications

VHDL Modelling of Fixed-point DWT for the Purpose of EMG Signal Denoising

VHDL Modelling of Fixed-point DWT for the Purpose of EMG Signal Denoising

The averaging lemma

Book Review: Real variable methods in harmonic analysis

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