Everything about Wavelet transform

🧭 Start here: a 6-step reading path

1. Read the overview: Wavelet transformA 5-minute orientation
2. Skim a recent paper: Multi-stage image denoising with the wavelet transformInfluential work since 2022
3. Pick up a classic book: The illustrated wavelet transform handbookThe most-reprinted book on the subject
4. Read the landmark paper: Application of the cross wavelet transform and wavelet coherence to geophysical time seriesCited 5,668 times
5. Go sideways: Discrete wavelet transformA closely related topic
6. Go sideways: Vanishing momentA closely related topic

🏆 Landmark papers (most cited)

• Application of the cross wavelet transform and wavelet coherence to geophysical time series

  A. Grinsted, J. C. Moore, S. Jevrejeva · 2004 · Nonlinear Processes in Geophysics · 5,668 citations

• The wavelet transform, time-frequency localization and signal analysis

  I. Daubechies · 1990 · IEEE Transactions on Information Theory · 5,190 citations

• WAVELET TRANSFORMS AND THEIR APPLICATIONS TO TURBULENCE

  Marie Farge · 1992 · Annual Review of Fluid Mechanics · 2,741 citations

• Image coding using wavelet transform

  M. Antonini, M. Barlaud, P. Mathieu · 1992 · IEEE Transactions on Image Processing · 2,566 citations

• Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool

  Ingrid Daubechies, Jianfeng Lu, Hau-Tieng Wu · 2011 · Applied and Computational Harmonic Analysis · 2,354 citations

• Empirical Wavelet Transform

  Jérôme Gilles · 2013 · IEEE Transactions on Signal Processing · 2,123 citations

• The dual-tree complex wavelet transform

  I.W. Selesnick, R.G. Baraniuk, N.C. Kingsbury · 2005 · IEEE Signal Processing Magazine · 2,028 citations

• The discrete wavelet transform: wedding the a trous and Mallat algorithms

  M.J. Shensa · 1992 · IEEE Transactions on Signal Processing · 1,701 citations

🆕 Influential since 2022

• Multi-stage image denoising with the wavelet transform

  Chunwei Tian, Menghua Zheng, Wangmeng Zuo · 2023 · Pattern Recognition · 445 citations

• Wavelet transform for rotary machine fault diagnosis:10 years revisited

  Ruqiang Yan, Zuogang Shang, Hong Xu · 2023 · Mechanical Systems and Signal Processing · 295 citations

• Short-term offshore wind power forecasting - A hybrid model based on Discrete Wavelet Transform (DWT), Seasonal Autoregressive Integrated Moving Average (SARIMA), and deep-learning-based Long Short-Term Memory (LSTM)

  Wanqing Zhang, Zi Lin, Xiaolei Liu · 2022 · Renewable Energy · 279 citations

• Intelligent fault diagnosis of rolling bearing based on wavelet transform and improved ResNet under noisy labels and environment

  Pengfei Liang, Wenhui Wang, Xiaoming Yuan · 2022 · Engineering Applications of Artificial Intelligence · 262 citations

• Intelligent Diagnosis Using Continuous Wavelet Transform and Gauss Convolutional Deep Belief Network

  Huimin Zhao, Jie Liu, Huayue Chen · 2023 · IEEE Transactions on Reliability · 238 citations

📚 Books worth reading

• The illustrated wavelet transform handbookPaul S. Addison · 2002
• Sparse image and signal processingJean-Luc Starck, Fionn Murtagh · 2010
• Discrete Wavelet TransformationsPatrick J. Van Fleet · 2011
• 📕Introduction to Wavelet TransformsNirdosh Bhatnagar · 2020
• A first course in wavelets with Fourier analysisAlbert Boggess, Francis J. Narcowich · 2011
• Wavelets in physicsJ. C. van den Berg · 1999
• Discrete Wavelet TransformationsPatrick Van Fleet · 2008
• Wavelet theory approach to pattern recognitionYuan Yan Tang · 2009

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics

• Discrete wavelet transform In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled…
• Vanishing moment Vanishing moments are a fundamental concept in wavelet theory, signal processing, and functional analysis. They describe a property of a wavelet or function…
• Fractional wavelet transform Fractional wavelet transform (FRWT) is a generalization of the classical wavelet transform (WT). This transform is proposed in order to rectify the limitations…
• Cauchy wavelet In mathematics, Cauchy wavelets are a family of continuous wavelets, used in the continuous wavelet transform. The Cauchy wavelet of order p {\displaystyle…
• Shannon wavelet In functional analysis, the Shannon wavelet (or sinc wavelets) is a decomposition that is defined by signal analysis by ideal bandpass filters. Shannon…
• Continuous wavelet transform In mathematics, the continuous wavelet transform (CWT) is a formal (i.e., non-numerical) tool that provides an overcomplete representation of a signal…
• Morlet wavelet In mathematics, the Morlet wavelet (or Gabor wavelet) is a wavelet composed of a complex exponential (carrier) multiplied by a Gaussian window (envelope)…
• Hermitian wavelet Hermitian wavelets are a family of discrete and continuous wavelets used in the constant and discrete Hermite wavelet transforms. The n th {\displaystyle…