A method for remote object sensing on-board a vehicle includes employing compressive sensing to analyze a waveform originating from an on-vehicle low-resolution radar imaging system and reflected from a remote object. The compressive sensing includes generating a matrix including a temporal projection, a Fourier transform, and an integral term configured to analyze the reflected waveform. Leading and trailing edges of the remote object are identified by employing a norm minimization procedure to reconstruct a range profile based upon the reflected waveform analyzed by the compressive sensing.