1. A method, comprising: transmitting, by a transmitter or a transceiver of a device, a plurality of electromagnetic pulse waveforms towards a target using an undersampling method; receiving, by a receiver or the transceiver of the device, a plurality of reflected electromagnetic pulse waveforms that are reflected by the target; processing, by at least one hardware processor of the device, the plurality of reflected electromagnetic pulse waveforms to create a first collection of waveform measurements by converting each reflected electromagnetic pulse waveform into a waveform measurement, wherein the first collection of waveform measurements is a compressed representation of a second collection of waveform measurements; constructing, by the at least one hardware processor of the device, the second collection of waveform measurements based on the first collection of waveform measurements using an optimization method that comprises estimating any waveform measurements of the second collection of waveform measurements not present in the first collection of waveform measurements; and creating, by the at least one hardware processor of the device, a radar image of the target using the second collection of waveform measurements.