Iterative SVD method for noise reduction of low-dimensional chaotic time series

Shin, Kihong; Hammond, J.K.; White, P.R.

doi:10.1006/mssp.1998.9999

Cited by 58 publications

(23 citation statements)

References 15 publications

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“…The fluctuating singular values have periodicity, and details of the nature of fluctuating singular values can be found in reference [10]. This characteristic enables us to select the 'order' of the AR model more easily by repeatedly using SVD with different sampling intervals, and examining how pairs of singular values oscillate.…”

Section: Embedding and Ar Order Determinationmentioning

confidence: 98%

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Optimal Autoregressive Modelling of a Measured Noisy Deterministic Signal Using Singular-Value Decomposition

Shin¹,

Feraday

Harris

et al. 2003

Mechanical Systems and Signal Processing

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Section: Embedding and Ar Order Determinationmentioning

confidence: 98%

“…Now, the rank of the matrices (8) and (9) is two, and the two non-zero eigenvalues of (9) are given by [9,10] …”

Section: Embedding and Ar Order Determinationmentioning

confidence: 99%

Optimal Autoregressive Modelling of a Measured Noisy Deterministic Signal Using Singular-Value Decomposition

Shin¹,

Feraday

Harris

et al. 2003

Mechanical Systems and Signal Processing

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“…m þ n À 1 ¼ s and A ij ¼ h iþjÀ1 although the size is doubled. It should be noted Hankel matrix is also utilised elsewhere in speech and audio applications as well as for signal estimation from noisy data [27,30,31]. It is shown later in this paper that the performance of the noise elimination method is affected depending on whether H or h is used in constructing the Hankel matrix.…”

Section: Article In Pressmentioning

confidence: 97%

Noise elimination from measured frequency response functions

Şanlıtürk

Çakar

2005

Mechanical Systems and Signal Processing

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“…The example below will illustrate the elimination of pixel-to-pixel shot noise in a signal as this is the most common use. PCA identifies and (by virtue of exploiting least squares fitting) inherently prioritises the signals that contribute most, in energy or intensity, to a dataset and so favours strong signals that occur reproducibly within the dataset and ranks weaker or inconsistent irreproducible signals lower [14,15]. The calculation differs slightly from Equation (1) in that S is truncated to an o 9 i matrix, and L T is an i 9 v matrix, where i is the number of low noise PC identified.…”

Section: Multivariate De-noising: Eliminating Irreproducible Non-signalmentioning

confidence: 99%

Multivariate Analysis for the Processing of Signals

Beattie¹

2014

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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and available online here Cet article fait partie du dossier thématique ci-dessous publié dans la revue OGST, Vol. 69, n°2, et téléchargeable ici D o s s i e rDOSSIER Edited by/Sous la direction de : L. Duval Advances in Signal Processing and Image Analysis for Physico-Chemical, Analytical Chemistry and Chemical SensingProgrès en traitement des signaux et analyse des images pour les analyses physico-chimiques et la détection chimique Re´sume´-Traitement de signaux par analyse multivarie´e -L'analyse multivarie´e, dont l'analyse en composantes principales (ACP), a transforme´, dans des contextes concrets, l'e´tude de mesures complexes, forme´es de signaux charge´s d'informations. Si la re´duction de dimension permet de simplifier grossie`rement un encheveˆtrement de variations multidimensionnelles, elle est e´galement plus robuste aux perturbations que les me´thodes d'analyse univarie´es. Plus re´cemment, il est apparu que les proprie´te´s des me´thodes multivarie´es les rendaient propices ad 'autres usages que statistiques, comme le traitement des signaux pour l'e´limination des variations/fluctuations non pertinentes pour une analyse ulte´rieure. Il a e´te´montre´que l'exploitation spe´cifique de la re´duction de dimension permet un de´bruitage pre´cis (suppression de "non-signaux/perturbation" non reproductibles), la soustraction fiable et consistante de la ligne de base (suppression de "non-signaux/perturbation" reproductibles), l'e´limination d'interfe´rences (suppression de "signaux" reproductibles et inutiles), ainsi que la standardisation des fluctuations d'amplitude des signaux. Si ce champ d'investigation est encore restreint, les possibilite´s de diffusion de ses applications sont conside´rables. En effet, ces ame´liorations, intrinse`quement lie´es aux signaux eux-meˆmes, sont hautement reproductibles entre les re´pe´titions, posse`dent une grande capacited 'adaptation et d'application a`des situations de bruit, ou de variations complexes dans les signaux. Alors que les disciplines scientifiques sondent des volumes de donne´es toujours plus volumineux, dans des situations de moins en moins e´troitement controˆle´es, la capacite´aà pporter des corrections/ame´liorations pre´cises/hautes re´solutions, de manie`re flexible, devient de plus en plus critique. Aussi les traitements de signaux multivarie´s offrent un e´ventail de solutions potentiellement tre`s large.Abstract -Multivariate Analysis for the Processing of Signals -Real-world experiments are becoming increasingly more complex, needing techniques capable of tracking this complexity. Signal based measurements are often used to capture this complexity, where a signal is a record of a sample's response to a parameter (e.g. time, displacement, voltage, wavelength) that is varied over a range of values. In signals the responses at each value of the varied parameter are related to each other, depending on the composition or state sample being measured. Since signals contain multiple information points, they have rich information content but are genera...

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Iterative SVD method for noise reduction of low-dimensional chaotic time series

Cited by 58 publications

References 15 publications

Optimal Autoregressive Modelling of a Measured Noisy Deterministic Signal Using Singular-Value Decomposition

Optimal Autoregressive Modelling of a Measured Noisy Deterministic Signal Using Singular-Value Decomposition

Noise elimination from measured frequency response functions

Multivariate Analysis for the Processing of Signals

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