Time-scale analysis of abrupt changes corrupted by multiplicative noise

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.