Optimal wavelet for abrupt change detection in multiplicative noise
This paper addresses abrupt change detection in multiplicative noise using the continuous 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 influence 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 classically used for singularity detection.