Simultaneous reconstruction of undersampled multichannel signals with a decayed and time-delayed common component

This paper presents a new signal model in distributed compressed sensing (DCS) and a reconstruction algorithm to reduce the number of samples required to accurately reconstruct signals obtained via sensors. While the conventional signal models in DCS assume that all signals include exactly the same common component, our model exploits the attenuation and time delay of the common component. With this extension, one can deal with signals originated from a source located in the field. To reconstruct such signals, we developed a new algorithm based on the alternative direction multiplier method. The algorithm efficiently reconstructs computer-generated signals using a reduced number of samples. In addition, we demonstrate the superior reconstruction quality with our method by using real electromyographic signals.