Fundamentals of Wavelet Transforms

Mallet, Y.; Vel, Olivier De; Coomans, Danny

doi:10.1016/s0922-3487(00)80028-3

Cited by 10 publications

(14 citation statements)

References 7 publications

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“…A 1-D wavelet transform is similar to a Fourier transform, enabling the underlying frequencies within a signal to be identified. The Fourier transforms treats a signal as a whole or globally which can often cause small perturbations in the signal to be overlooked (Mallet et al, 2000). A 1-D wavelet transform allows a localised analysis of the signal using a window function which translates across the signal analysing discrete sections (Mallet et al, 2000).…”

Section: -D Discrete Wavelet Transformmentioning

confidence: 99%

“…The Fourier transforms treats a signal as a whole or globally which can often cause small perturbations in the signal to be overlooked (Mallet et al, 2000). A 1-D wavelet transform allows a localised analysis of the signal using a window function which translates across the signal analysing discrete sections (Mallet et al, 2000). The continuous wavelet transform performed on a signal f(t) can be given as Antonini et al, 1992).…”

Section: -D Discrete Wavelet Transformmentioning

confidence: 99%

“…The continuous wavelet transform performed on a signal f(t) can be given as Antonini et al, 1992). The wavelet transform is unique because the mother wavelet function has the ability to contract and dilate, allowing high and low frequencies in the signal to be well represented (Mallet et al, 2000). There are a number of families of wavelet functions including: Daubechies, coiflets and symlets each having its optimum use upon different signal types (Mallet et al, 2000).…”

Section: -D Discrete Wavelet Transformmentioning

confidence: 99%

“…The wavelet transform is unique because the mother wavelet function has the ability to contract and dilate, allowing high and low frequencies in the signal to be well represented (Mallet et al, 2000). There are a number of families of wavelet functions including: Daubechies, coiflets and symlets each having its optimum use upon different signal types (Mallet et al, 2000). The symlet family however, has properties which lend themselves ideally to image analysis (Mallet et al, 2000).…”

Section: -D Discrete Wavelet Transformmentioning

confidence: 99%

“…There are a number of families of wavelet functions including: Daubechies, coiflets and symlets each having its optimum use upon different signal types (Mallet et al, 2000). The symlet family however, has properties which lend themselves ideally to image analysis (Mallet et al, 2000). An image I(x,y), can be decomposed using a 2-D discrete wavelet transform (DWT) similar to how a 1-D signal f(t) can be analysed using a 1-D wavelet transform.…”

Section: -D Discrete Wavelet Transformmentioning

confidence: 99%

See 4 more Smart Citations

Seasonal Climate Prediction for the Australian Sugar Industry Using Data Mining Techniques

McKinna¹,

Everingham²

2011

Knowledge-Oriented Applications in Data Mining

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Section: -D Discrete Wavelet Transformmentioning

confidence: 99%

Section: -D Discrete Wavelet Transformmentioning

confidence: 99%

Section: -D Discrete Wavelet Transformmentioning

confidence: 99%

Section: -D Discrete Wavelet Transformmentioning

confidence: 99%

Section: -D Discrete Wavelet Transformmentioning

confidence: 99%

See 3 more Smart Citations

Seasonal Climate Prediction for the Australian Sugar Industry Using Data Mining Techniques

McKinna¹,

Everingham²

2011

Knowledge-Oriented Applications in Data Mining

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N‐way modeling for wavelet filter determination in multivariate image analysis

Prats-Montalbán

Cocchi

Ferrer

2015

Journal of Chemometrics

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When trying to analyze spatial relationships in image analysis, wavelets appear as one of the state-of-the-art tools. However, image analysis is a problem dependent issue and different applications might require different wavelets in order to gather the main sources of variation in the acquired images with respect to the specific task to be performed. This paper provides a methodology based on N-way modeling for properly selecting the best wavelet choice to use, or at least to provide a range of possible wavelets choices (in terms of families, filters and decomposition levels), for each image and problem at hand. The methodology has been applied on two different data sets with exploratory and monitoring objectives.

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Coupling 2D‐wavelet decomposition and multivariate image analysis (2D WT‐MIA)

Vigni

Prats-Montalbán

Ferrer

et al. 2017

Journal of Chemometrics

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The use of 2D discrete wavelet transform in the feature enhancement phase of multivariate image analysis is discussed and implemented in a comparative way with respect to previous publications. In the proposed approach, all the resulting subimages obtained by discrete wavelet transform decomposition are unfolded pixel-wise and midlevel data fused to a feature matrix that is used for the feature analysis phase. Congruent subimages can be obtained either by reconstruction of each decomposition block to the original pixel dimensions or by using the stationary wavelet transform decomposition scheme. The main advantage is that all possible relationships among blocks, decomposition levels, and channels are assessed in a single multivariate analysis step (feature analysis). This is particularly useful in a monitoring context where the aim is to build multivariate control charts based on images. Moreover, the approach can be versatile for contexts where several images are analyzed at a time as well as in the multispectral image analysis.Both a set of simple artificial images and a set of real images, representative of the on-line quality monitoring context, will be used to highlight the details of the methodology and show how the wavelet transform allows extracting features that are informative of how strong the texture of the image is and in which direction it varies.

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Fundamentals of Wavelet Transforms

Cited by 10 publications

References 7 publications

Seasonal Climate Prediction for the Australian Sugar Industry Using Data Mining Techniques

Seasonal Climate Prediction for the Australian Sugar Industry Using Data Mining Techniques

N‐way modeling for wavelet filter determination in multivariate image analysis

Coupling 2D‐wavelet decomposition and multivariate image analysis (2D WT‐MIA)

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