Redundant wavelet analysis applied to GRB time histories

We apply Redundant Wavelet Transforms (RWTs) to GRB time histories in order to identify significant structures on various time scales. While the classical Discrete Wavelet Transform (DWT) also carries out a data compression and a denoising, it does not lead to a description as a set of peaks. On the contrary, the so-called à trous algorithm (that is a redundant wavelet transform often being considered as a fast continuous wavelet transform for a real wavelet) carries out a time scale analysis which easily allows us to decompose the signal into peaks on different scales. After neglecting insignificant coefficients of the RWT the signal is easily restored while noise is suppressed. Not only is the quality of the smoothing better than the one we get with DWT, but also the thresholded wavelet coefficients contain directly the peak decomposition. It is then possible to use a Multiscale Vision Model that has been originally developed for 2D images that allows one to build oriented trees from the neighboring of significant wavelet coefficients. Each tree is then divided into subtrees taking into account the maxima along the scale axis. This leads to the identification of objects in the scale space, that could be further restored by classical inverse methods.