Optimal wavelet for abrupt change detection in multiplicative noise

Abstract

This paper addresses abrupt change detection in multiplicative noise using the continous wavelet transform. An optimal wavelet, maximizing a well-chosen time-scale contrast criterion is derived. The analytical optimization gives the optimal wavelet closed expression. The inÀuence of the mother wavelet on signature-based detector performance is then demonstrated. Detection performance is characterized using Receiver Operating Characteristic curves computed from Monte-Carlo simulations. The optimal wavelet obviously improves performance with respect to other wavelets classicaly used for singularity detection.

Adaptive wavelet estimation of a density from mixtures under multiplicative censoring

“…An overview of sensor networks can be found in Akyildiz et al (2002). The reader may be referred to Chabert et al (2004) and references therein for applications in multiplicative noise set-up in signal processing.…”

Monitoring Incremental Histogram Distribution for Change Detection in Data Streams

“…Due to the exploratory nature of data and to time restrictions, a user may prefer a fast but approximate answer to an exact but slow answer. Methods to deal with these issues consist of applying synopsis techniques, such as histograms [12,16,19,26], sketches [8] and wavelets [7,15]. Histograms are one of the techniques used in data stream management systems to speed up range queries and selectivity estimation (the proportion of tuples that satisfy a query), two illustrative examples where fast but approximate answers are more useful than slow and exact ones.…”