Denoising using wavelet packets and the kurtosis: application to transient detection

The problem addressed in this paper is the detection of an unknown transient signal corrupted by additive Gaussian noise. We have shown in a previous study that Malvar wavelets can be successfully used when the noise is white Gaussian. The criterion to choose the best basis is based on the Gaussianity of the wavelet coefficients: when two adjacent segments have Gaussian coefficients they are merged, otherwise they are kept separated. If the noise is colored, this criterion fails to give good results. For this case we use wavelet packets instead. The best basis is chosen in the same way: merging “Gaussian frequency bands”. To get a time dependent detection statistic, we perform a denoising: Gaussian wavelet coefficients are set to zero. After reconstruction of the denoised signal, a standard detection procedure is performed. The performances of this detection scheme are studied experimentally. Furthermore, an application of the method is described for a real case