Abstract
The mathematical characterization of singularities with Lipschitz exponents is reviewed. Theorems that estimate local Lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed. 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 exponents. The wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately. The local frequency of such oscillations is measured from the wavelet transform modulus maxima. It has been shown numerically that one- and two-dimensional signals can be reconstructed, with a good approximation, from the local maxima of their wavelet transform modulus. As an application, an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales. In two dimensions, the wavelet transform maxima indicate the location of edges in images.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Keywords
Wavelet transformWaveletMaximaMaxima and minimaMathematicsMathematical analysisHarmonic wavelet transformLipschitz continuityStationary wavelet transformWavelet packet decompositionGravitational singularityContinuous wavelet transformDiscrete wavelet transformAlgorithmArtificial intelligenceComputer science
Affiliated Institutions
Related Publications
Effect of fading correlation on adaptive arrays in digital mobile radio
In this paper, we investigate the effect of correlations among the fading signals at the antenna elements of an adaptive array in a digital wireless communication system. With a...
Performance evaluation of genetic algorithms for flowshop scheduling problems
The aim of this paper is to evaluate the performance of genetic algorithms for the flowshop scheduling problem with an objective of minimizing the makespan. First we examine var...
Reception of multiple co-channel digital signals using antenna arrays with applications to PCS
Antenna arrays can be used to increase system capacity in PCS networks by supporting multiple co-channel users per cell in receive and in transmit. We propose a novel approach f...
Matched filter performance bounds for diversity combining receivers in digital mobile radio
By employing the technique known as the matched filter bound, the authors derive analytical expressions for the distribution and average of the bit-error-rate in an ideal space ...
CDMA-IC: a novel code division multiple access scheme based on interference cancellation
Third generation cellular systems will need to increase capacity significantly from previous generations. A system based on code division multiple access may be of interest prov...
Publication Info
- Year
- 1992
- Type
- article
- Volume
- 38
- Issue
- 2
- Pages
- 617-643
- Citations
- 3843
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
3843
OpenAlex
Cite This
Stéphane Mallat,
Wen-Liang Hwang
(1992).
Singularity detection and processing with wavelets.
IEEE Transactions on Information Theory
, 38
(2)
, 617-643.
https://doi.org/10.1109/18.119727
Identifiers
- DOI
- 10.1109/18.119727