A system of recovering information wide band signal comprising a receiver(s) for receiving data signal responses from a target area; the received data signal responses having information missing at a plurality of frequencies; at least one processor for recovery of data from the data signal responses operatively connected to the receiver(s); a first memory comprising time-shifted responses based upon the wide band signal response, a second memory comprising a plurality of spectrally filtered time-shifted responses; whereby the first and second memories operate to provide data to the at least one processor compensate for the information missing at the plurality of frequencies. Also, a method of the recovery of missing frequency bands comprising receiving data signal responses from a target area using a first dictionary comprising time-shifted responses based upon spectra containing the at least one predetermined spectrum, and a second dictionary comprising a plurality of spectrally filtered time-shifted responses.