Low and high resonance components restoration in multichannel data

A technique for the restoration of low resonance component and high res-onance component of K independently measured signals is presented. The definitionof low and high resonance component is given by the Rational Dilatation WaveletTransform (RADWT), a particular kind of finite frame that provides sparse repre-sentation of functions with different oscillations persistence. It is assumed that thesignals are measured simultaneously on several independent channels and in eachchannel the underlying signal is the sum of two components: the low resonancecomponent and the high resonance component, both sharing some common char-acteristic between the channels. Components restoration is performed by means ofthe lasso-type penalty and back-fitting algorithm. Numerical experiments show theperformance of the proposed method in different synthetic scenarios highlightingthe advantage of estimating the two components separately rather than together.