  A new technique for nonparametric regression of multichannel signals is
presented. The technique is based on the use of the Rational-Dilation Wavelet
Transform (RADWT), equipped with a tunable Q-factor able to provide sparse
representations of functions with different oscillations persistence. In
particular, two different frames are obtained by two RADWT with different
Q-factors that give sparse representations of functions with low and high
resonance. It is assumed that the signals are measured simultaneously on
several independent channels and that they share the low resonance component
and the spectral characteristics of the high resonance component. Then, a
regression analysis is performed by means of the grouped lasso penalty.
Furthermore, a result of asymptotic optimality of the estimator is presented
using reasonable assumptions and exploiting recent results on group-lasso like
procedures. Numerical experiments show the performance of the proposed method
in different synthetic scenarios as well as in a real case example for the
analysis and joint detection of sleep spindles and K-complex events for
multiple electroencephalogram (EEG) signals.
