Multiplicative Abrupt Changes (ACs) have been considered in many applicatio
ns. These applications include image processing (speckle) and random commun
ication models (fading). Previous authors have shown that the Continuous Wa
velet Transform (CWT) has good detection properties for ACs in additive noi
se. This work applies the CWT to AC detection in multiplicative noise. CWT
translation invariance allows to define an AC signature. The problem then b
ecomes signature detection in the time-scale domain. A second-order contras
t criterion is defined as a measure of detection performance. This criterio
n depends upon the first- and second-order moments of the multiplicative pr
ocess's CWT. An optimal wavelet (maximizing the contrast) is derived for an
ideal step in white multiplicative noise. This wavelet is asymptotically o
ptimal for smooth changes and can be approximated for small AC amplitudes b
y the Haar wavelet. Linear and quadratic suboptimal signature-based detecto
rs are also studied. Closed-form threshold expressions are given as functio
ns of the false alarm probability for three of the detectors. Detection per
formance is characterized using Receiver Operating Characteristic (ROC) cur
ves computed from Monte-Carlo simulations. (C) 2000 Elsevier Science B.V. A
ll rights reserved.