Topic
Morlet wavelet
About: Morlet wavelet is a research topic. Over the lifetime, 1215 publications have been published within this topic receiving 32197 citations. The topic is also known as: Morlets wavelet & Gabor wavelet.
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TL;DR: In this article, a step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nino-Southern Oscillation (ENSO).
Abstract: A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nino–Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmoller, cross-wavelet spectra, and coherence are described. The statistical significance tests are used to give a quantitative measure of change...
12,803 citations
TL;DR: In this paper, the performance of wavelet decomposition-based de-noising and wavelet filter based denoising methods are compared based on signals from mechanical defects, and the comparison result reveals that wavelet filters are more suitable and reliable to detect a weak signature of mechanical impulse-like defect signals, whereas the wavelet transform has a better performance on smooth signal detection.
1,104 citations
15 Jul 2002
TL;DR: The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance as discussed by the authors is a comprehensive overview of wavelet transform applications in science, engineering, medicine and finance.
Abstract: (The correction deals with the fact that the complex Morlet wavelet has a non-zero See for example: The Illustrated Wavelet Transform Handbook: Introductory. The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance. CRC Press, Boca Raton. Tags: synchrosqueezing time-frequency analysis wavelet transform P.S. Addison, The Illustrated Wavelet Transform Handbook: Introductory Theory.
942 citations
TL;DR: A Bayesian classifier with class-conditional probability density functions described as Gaussian mixtures is used, yielding a fast classification, while being able to model complex decision surfaces, for automated segmentation of the vasculature in retinal images.
Abstract: We present a method for automated segmentation of the vasculature in retinal images. The method produces segmentations by classifying each image pixel as vessel or non-vessel, based on the pixel's feature vector. Feature vectors are composed of the pixel's intensity and continuous two-dimensional Morlet wavelet transform responses taken at multiple scales. The Morlet wavelet is capable of tuning to specific frequencies, thus allowing noise filtering and vessel enhancement in a single step. We use a Bayesian classifier with class-conditional probability density functions (likelihoods) described as Gaussian mixtures, yielding a fast classification, while being able to model complex decision surfaces and compare its performance with the linear minimum squared error classifier. The probability distributions are estimated based on a training set of labeled pixels obtained from manual segmentations. The method's performance is evaluated on publicly available DRIVE and STARE databases of manually labeled non-mydriatic images. On the DRIVE database, it achieves an area under the receiver operating characteristic (ROC) curve of 0.9598, being slightly superior than that presented by the method of Staal et al.
859 citations
TL;DR: In this paper, a denoising method based on wavelet analysis is applied to feature extraction for mechanical vibration signals, which is an advanced version of the famous soft thresholding denoizing method proposed by Donoho and Johnstone.
823 citations