Evolutionary Signal Enhancement Based on Hölder Regularity Analysis
We present an approach for signal enhancement based on the analysis of the local Hölder regularity. The method does not make explicit assumptions on the type of noise or on the global smoothness of the original data, but rather supposes that signal enhancement is equivalent to increasing the Hölder regularity at each point. The problem of finding a signal with prescribed regularity that is as near as possible to the original signal does not admit a closed form solution in general. Attempts have been done previously on an analytical basis for simplified cases . We address here the general problem with the help of an evolutionary algorithm. Our method is well adapted to the case where the signal to be recovered is itself very irregular, e.g. nowhere differentiable with rapidly varying local regularity. In particular, we show an application to SAR image denoising where this technique yields good results compared to other algorithms. The implementation of the evolutionary algorithm has been done using the EASEA (EAsy specification of Evolutionary Algorithms) language.
KeywordsEvolutionary Algorithm Original Signal Synthetic Aperture Radar Synthetic Aperture Radar Image Local Regularity
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- 1.J. Lévy Véhel, Statistical denoising of irregular signals, INRIA internal report.Google Scholar
- 2.R.A. Devore, B. Lucier Fast wavelet techniques for near optimal image processing. 1992 IEEE Military Communications Conference, 2–12 (1992).Google Scholar
- 6.J. Lévy Véhel, B. Guiheneuf “Multifractal Image Denoising,” SCIA, 1997.Google Scholar
- 7.B. Guiheneuf, J. Lévy Véhel, 2 micro-local analysis and applications in signal processing, Int. Conf. on Wavelet, Tangier, 1997.Google Scholar
- 9.M. Wall, GAlib home page: http://www.lancet.mit.edu/ga/, MIT.
- 10.K. Daoudi, J. Lévy Véhel, Y. Meyer, Construction of functions with prescribed local regularity, Constructive Approximation, 1989.Google Scholar
- 12.L. Gagnon, F. Drissi Smaili, Speckle noise reduction of airborne SAR images with symetric Daubechies wavelets, Signal and Data Processing of Small Targerts, Proc. SPIE 2759, 1996Google Scholar