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Time-scale analysis of abrupt changes corrupted by multiplicative noise

Chabert, Marie and Tourneret, Jean-Yves and Castanié, Francis Time-scale analysis of abrupt changes corrupted by multiplicative noise. (2000) Signal Processing, 8 (3). 397-411. ISSN 0165-1684

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Official URL: http://dx.doi.org/10.1016/S0165-1684(99)00139-5


Multiplicative Abrupt Changes (ACs) have been considered in many applications. These applications include image processing (speckle) and random communication models (fading). Previous authors have shown that the Continuous Wavelet Transform (CWT) has good detection properties for ACs in additive noise. This work applies the CWT to AC detection in multiplicative noise. CWT translation invariance allows to define an AC signature. The problem then becomes signature detection in the time-scale domain. A second-order contrast criterion is defined as a measure of detection performance. This criterion depends upon the first- and second-order moments of the multiplicative process's CWT. An optimal wavelet (maximizing the contrast) is derived for an ideal step in white multiplicative noise. This wavelet is asymptotically optimal for smooth changes and can be approximated for small AC amplitudes by the Haar wavelet. Linear and quadratic suboptimal signature-based detectors are also studied. Closed-form threshold expressions are given as functions of the false alarm probability for three of the detectors. Detection performance is characterized using Receiver Operating Characteristic (ROC) curves computed from Monte-Carlo simulations.

Item Type:Article
Additional Information:This publication is available at http://www.sciencedirect.com/science/journal/01651684
HAL Id:hal-03607520
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
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Deposited On:16 Sep 2009 15:16

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