Compressive sampling of LIDAR: Full-waveforms as signals of finite rate of innovation

The 3D imaging community has begun a transition to full-waveform (FW) LIDAR systems which image a scene by emitting laser pulses in a particular direction and capturing the entire temporal envelope of each echo. By scanning a region, connected 1D profile waveforms of the 3D scenes can be readily obtained. In general, FW systems capture more detailed physical information and characteristic properties of the 3D scenes versus conventional 1st and 2nd generation LIDARs which simply store clouds of range points. Unfortunately, the collected datasets are very large, making tasks like processing, storage, and transmission far more resource-intensive. Current compression approaches addressing these issues rely on collecting large amounts of data and then analyzing it to identify perceptual and statistical redundancies which are subsequently removed. Collecting large amounts of data just to discard most of it is highly inefficiently. Our approach to LIDAR compression models FW return pulses as signals with finite rate of innovation (FRI). We show in this paper that sampling can be performed at the rate of innovation while still achieving good quality reconstruction. Specifically, we show that efficient sampling and compression can be achieved on actual LIDAR FW's within the FRI framework.