De-Noising Using Wavelets and Cross Validation

Weyrich, Norman; Warhola, Gregory T.

doi:10.1007/978-94-015-8577-4_36

Cited by 35 publications

(16 citation statements)

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“…Taking expectation with respect to the GGD on both sides of (35), the risk can be written as Sure (37) Comparing (37) with (36), one can conclude that Sure is a data-based approximation to , and the SURE threshold, which minimizes Sure , is an alternative to BayesShrink for minimizing the Bayesian risk.…”

Section: Resultsmentioning

confidence: 99%

“…[1], [8], [9], [18], [24], [27], [29], [32], [35]). With an integral approximation to the pixel-wise MSE distortion measure as discussed earlier, the formulation here is also Bayesian for finding the best soft-thresholding rule under the generalized Gaussian prior.…”

Section: Wavelet Thresholding and Threshold Selectionmentioning

confidence: 99%

“…Thresholding is a nonlinear technique, yet it is very simple because it operates on one wavelet coefficient at a time. Alternative approaches to nonlinear wavelet-based denoising can be found in, for example, [1], [4], [8]- [10], [12], [18], [19], [24], [27]- [29], [32], [33], [35], and references therein.…”

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confidence: 99%

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Adaptive wavelet thresholding for image denoising and compression

Chang

Vetterli

2000

IEEE Trans. on Image Process.

2,467

1,290

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Abstract-The first part of this paper proposes an adaptive, data-driven threshold for image denoising via wavelet soft-thresholding. The threshold is derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution (GGD) widely used in image processing applications. The proposed threshold is simple and closed-form, and it is adaptive to each subband because it depends on data-driven estimates of the parameters. Experimental results show that the proposed method, called BayesShrink, is typically within 5% of the MSE of the best soft-thresholding benchmark with the image assumed known. It also outperforms Donoho and Johnstone's SureShrink most of the time.The second part of the paper attempts to further validate recent claims that lossy compression can be used for denoising. The BayesShrink threshold can aid in the parameter selection of a coder designed with the intention of denoising, and thus achieving simultaneous denoising and compression. Specifically, the zero-zone in the quantization step of compression is analogous to the threshold value in the thresholding function. The remaining coder design parameters are chosen based on a criterion derived from Rissanen's minimum description length (MDL) principle. Experiments show that this compression method does indeed remove noise significantly, especially for large noise power. However, it introduces quantization noise and should be used only if bitrate were an additional concern to denoising.Index Terms-Adaptive method, image compression, image denoising, image restoration, wavelet thresholding.

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Section: Resultsmentioning

confidence: 99%

Section: Wavelet Thresholding and Threshold Selectionmentioning

confidence: 99%

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Adaptive wavelet thresholding for image denoising and compression

Chang

Vetterli

2000

IEEE Trans. on Image Process.

2,467

1,290

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“…Another application of trigonometric wavelets to speech denoising using generalized cross validation can be found in [28]. Besides the discrete wavelet transforms, both applications use the thresholding technique, as described in [14,27]. We also compare our results with those achieved using Daubechies wavelets.…”

Section: Applications In Speech Processingmentioning

confidence: 92%

Algorithms for Trigonometric Wavelet Packets

Weyrich

1997

Applied and Computational Harmonic Analysis

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“…Así, se han introducido nuevos métodos basados en cross-validation [52,[58][59][60][61][62][63], test de hipótesis [64,65], umbralización por bloques [66][67][68][69][70], estimadores Bayesianos [71,72], etc. Para obtener una visión más detallada de estos diferentes métodos de umbralización wavelet, se pueden consultar las revisiones del estado del arte que se ofrecen en [47,49,50,52].…”

Section: Selección Del Umbralunclassified

Trasformadas Wavelet no diezmadas para reducción de ruido y detección de señáles: Aplicaciones en Evaluación No Destructiva por Ultrasonidos

Gómez¹

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x Wavelets no diezmadas. Aplicaciones en END por ultrasonidosThe results show that the new UWT-based methods improve the quality of the traces and the robustness of the processing, in terms of both signal to noise ratio and pulse shape recovery, in relation to the methods that use the traditional DWT. These improvements are obtained regardless of the wavelet family considered. In fact, the UWT processing shows clear preference for the lower order wavelets, irrespective of the wavelet family or the kind of threshold used. In this way, the thesis provides a set of denoising methods that, besides improving the quality of the traces significantly, prove to be very robust in relation to the choice of processing parameters. ResumLa present tesi doctoral està centrada en l'estudi de la transformada wavelet no delmada (undecimated wavelet transform, UWT), així com en la seua aplicació a processos de reducció de soroll i detecció de senyals. Com a principals avantatges davant la wavelet discreta tradicional (discrete wavelet transform, DWT), la wavelet no delmada presenta invariança enfront dels desplaçaments del senyal d'entrada, no produeix pèrdua de resolució temporal en les successives escales de descomposició, i a més a més proporciona una informació addicional que des del punt de vista d'un processat lineal seria redundant, però que en combinació amb processats no lineals pot donar lloc a millores importants en aplicacions tals com l'anàlisi de senyals o la reducció de soroll.En aquest context, els objectius principals de la tesi van a ser dos. D'una banda, es tracta d'aprofundir en l'estudi de la transformada wavelet no delmada, provant d'establir un marc unificat per a les diferents denominacions i implementacions existents en la literatura. D'altra banda, es planteja l'aplicació d'aquesta transformada al desenvolupament d'algoritmes per a la reducció de soroll. En aquest sentit, es considerarà el problema del soroll de gra en inspecció no destructiva per ultrasons. Aquest tipus de soroll és causat per les reflexions en les petites discontinuitats internes dels materials, que s'introduexien en la mateixa banda de freqüències que els defectes a detectar. Per això no es poden eliminar amb els filtrats clàssics per a soroll blanc. La tesi aborda aquest problema plantejant algoritmes específics, que aprofiten la diferent distribució espai-temporal del senyal i el soroll en el domini de la wavelet no delmada.La metodologia emprada per a dur a terme els objectius anteriors, inclou el desenvolupament i implementació de nous mètodes de processament utilitzant el llenguatge MATLAB®. Al llarg de la tesi es plantegen quatre esquemes diferents de reducció de soroll de gra ultrasònic, basats en les diferents possibilitats d'implementació i reconstrucció que ofereix la transformada UWT. Aquests esquemes xii Wavelets no diezmadas. Aplicaciones en END por ultrasonidos s'apliquen a una àmplia mostra de senyals típics d'inspecció per ultrasons, d'origen sintètic i experimental.Els resultats mostren que els nous processats UWT prop...

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De-Noising Using Wavelets and Cross Validation

Cited by 35 publications

References 5 publications

Adaptive wavelet thresholding for image denoising and compression

Adaptive wavelet thresholding for image denoising and compression

Algorithms for Trigonometric Wavelet Packets

Trasformadas Wavelet no diezmadas para reducción de ruido y detección de señáles: Aplicaciones en Evaluación No Destructiva por Ultrasonidos

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