Signal detection with a shift invariant noise model based on wavelet bases

This paper proposes the use of translation invariant dual-tree discrete wavelet transform (DT DWT) noise model to the problem of multipath signals detection in underwater sound. The design procedures for an adaptive model of the background noise, using recursive density estimation of the joint distribution of the multivariate vectors of its shift-invariant DT DWT, which allows the transform to provide shift invariance are described. When the input signal is shifted as in a multipath environment, this shift-invariant DT DWT can generate multiresolution subspaces, that keep more of their coefficient energy in each of these subspaces than in DWTs. For this improvement, the performance of this method can be increased by reducing the false alarm probability of detecting a multipath signal in a range of different signal-to-noise ratios.