Singularity detection and processing with wavelets

@article{Mallat1992SingularityDA,
  title={Singularity detection and processing with wavelets},
  author={St{\'e}phane Mallat and Wen Liang Hwang},
  journal={IEEE Trans. Information Theory},
  year={1992},
  volume={38},
  pages={617-643}
}
Most of a signal information is often carried by irregular structures and transient phenomena. The mathematical characterization of singularities with Lipschitz exponents is explained. Theorems are reviewed that estimate local Lipschitz exponents of functions from the evolution across scales of their wavelet transform. It is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their Lipschitz… CONTINUE READING
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