A Wavelet-based Optimal Filtering Method for Adaptive Detection: Application to Metallic Magnetic Calorimeters

摘要

Optimal filtering allows the maximization of signal-over-noise ratio for the improvement of both energy threshold and resolution. Nevertheless, its effective efficiency depends on the estimation of signal and noise spectra. In practice, these are often estimated by averaging over a set of carefully chosen data. In case of time-varying noise, adaptive non-linear algorithms can be used if the shape of the signal is known. However, their convergence is not guaranteed, especially with 1/f-type noise. In this paper, a new method is presented for adaptive noise whitening and template signal estimation. First, the noise is continuously characterized in the wavelet domain, where the signal is decomposed over a set of scales, corresponding to band-pass filters. Both time resolution and decorrelation properties of the wavelet transform allow an accurate and robust estimation of the noise structure, even if pulses or correlated noise are present. The whitening step then amounts to a normalization of each scale by the estimated noise variance. A matched filter is then applied on the whitened signal. The required signal template is constructed from a single event, denoised by a filtering technique called wavelet thresholding. As an example, application to metallic magnetic calorimeter data is presented. The method reaches the precision of conventional optimal filtering, further allowing noise monitoring, adaptive threshold and improving the energy resolution of up to 8% in some cases.