The input ports (18) of an imaging compressive receiver (20) receive from a tapped delay line (16) progressively delayed versions of a received signal s(t). Because of the delays, a signal component in the received signal appears at least at one of the input ports (18) of the compressive receiver (20) at a time when the compressive receiver (20) will detect it, even if the undelayed version occurs during a time at which the compressive receiver (20) would ordinarily be insensitive to it. Since the compressive receiver (20) is an imaging device, it provides relatively isolated channels between its input terminals (18) and its output terminals (38). The phase relationships between the delays in these channels remain constant despite changes in environmental factors, however, because the various channels are embodied in a common two-dimensional delay line.