Wavelet optimization for classification

Lucas,; Doncarli,; Hitti,; Dechamps,

doi:10.1109/icassp.2002.1005976

Cited by 5 publications

(6 citation statements)

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“…In consequence, the problem of the selection of the most appropriate features for a given application and for a given signal is of interest. There are some papers dealing with the selection of the most appropriate features of the WT for a given application: compression [8][9][10], denoising [11] or classification [12][13][14] and for a given class of signals, speech [8], myoelectric signals [11], images [9,10]. Some criteria for the selection of the most appropriate MW as: The length of its support, its smoothness or its time or frequency localizations, were already been proposed [15].…”

Section: Introductionmentioning

confidence: 99%

Space-Frequency Localization as Bivariate Mother Wavelets Selecting Criterion for Hyperanalytic Bayesian Image Denoising

Isar

2012

Fluct. Noise Lett.

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Communicated by Stefania ResidoriThroughout recent years, many wavelet transforms (WTs) were used in digital image processing: the discrete WT (DWT), the stationary WT (SWT) or the hyperanalytic WT (HWT). All these transforms have in common a feature, the mother wavelets (MW). A great number of MWs was already proposed in literature. The purpose of this paper is the selection of MW for hyperanalytic Bayesian image denoising on the basis of its space-frequency localization. The MW with the same space-frequency localization as the elements of the input image gives the better results. Some procedures for the evaluation of the space-frequency localization of MWs and input images are proposed and applied to optimize the results obtained by the simulations of denoising, indicating the most appropriate MW. Keywords: Mother wavelets; space-frequency; denoising. 1250009-1 Fluct. Noise Lett. 2012.11. Downloaded from www.worldscientific.com by MCMASTER UNIVERSITY on 02/06/15. For personal use only. A. IsariH{ψ} and ψ a = ψ + iH{ψ} are also MWs. H denotes the Hilbert transform operator. This wavelets pair (ψ, iH{ψ}) defines a complex discrete wavelet transform (CDWT). A complex wavelet coefficient is obtained by interpreting the wavelet coefficient from one DWT tree as being its real part, whereas the corresponding coefficient from the other tree is considered its imaginary part. In [4], the DTCWT, which is a quadrature pair of DWT trees similar to the CDWT, is developed. The DTCWT coefficients may be interpreted as arising from the DWT associated with a quasi-analytic wavelet. Both DTCWT and CDWT are invertible and quasi shiftinvariant. The implementation of analytic wavelet transform (AWT) is presented in [6]. First, a Hilbert transform is applied to the data. The real wavelet transform is then applied to the analytical signal associated to the input data, obtaining complex coefficients. The DTCWT and the AWT are equivalent because: d DTCWT [m, n] = x(t), ψ m,n (t) + iH{ψ m,n (t)} = x(t), ψ m,n (t) − i x(t), H{ψ m,n (t)} = x(t), ψ m,n (t) + i H{x(t)}, ψ m,n (t) = x(t) + iH{x(t)}, ψ m,n (t) = d AWT [m, n]

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Section: Introductionmentioning

confidence: 99%

Space-Frequency Localization as Bivariate Mother Wavelets Selecting Criterion for Hyperanalytic Bayesian Image Denoising

Isar

2012

Fluct. Noise Lett.

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“…The classification is based on the wavelet packets coefficients and is related to the filter h. In [2] the authors propose to select h (and the related mother wavelet) which yields the best classification results.…”

Section: ) Wavelet Packets Decomposition On Best Basismentioning

confidence: 99%

“…In [I] The choice of the mother wavelet is fixed a priori. We follow the approach proposed in [2], optimizing the mother wavelet to adapt it to the signal to be discriminated. Once the expansion coefficients of the signal in this basis are computed, we want to reduce the dimension of the feature vector.…”

Section: Introductionmentioning

confidence: 99%

Classification of sonar measures using optimized wavelets

Barat¹,

Rendas²

Oceans '02 MTS/IEEE

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“…This paper proposes an analytical optimization yielding a closed form expression of the optimal wavelet. This expression does not require a priori parametric model for the wavelet as in [7]. The optimal wavelet is then studied for AC detection in multiplicative noise models.…”

Section: Introduction and Problem Statementmentioning

confidence: 98%

“…This optimal wavelet maximizes a performance criterion expressed as a time-scale contrast. It is interesting to note that the problem of wavelet optimization has already been considered in [7] for classi¿cation purposes. The criterion to be optimized was expressed as a function of the classi¿cation error for this application.…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

Optimal wavelet for abrupt change detection in multiplicative noise

Chabert

Ruíz

Tourneret

2004 IEEE International Conference on Acoustics, Speech, and Signal Processing

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This paper addresses abrupt change detection in multiplicative noise using the continous wavelet transform. An optimal wavelet, maximizing a well-chosen time-scale contrast criterion is derived. The analytical optimization gives the optimal wavelet closed expression. The inÀuence of the mother wavelet on signature-based detector performance is then demonstrated. Detection performance is characterized using Receiver Operating Characteristic curves computed from Monte-Carlo simulations. The optimal wavelet obviously improves performance with respect to other wavelets classicaly used for singularity detection.

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Wavelet optimization for classification

Cited by 5 publications

References 0 publications

Space-Frequency Localization as Bivariate Mother Wavelets Selecting Criterion for Hyperanalytic Bayesian Image Denoising

Space-Frequency Localization as Bivariate Mother Wavelets Selecting Criterion for Hyperanalytic Bayesian Image Denoising

Classification of sonar measures using optimized wavelets

Optimal wavelet for abrupt change detection in multiplicative noise

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