Spline Sketches: An Efficient Approach for Photon Counting Lidar

Photon counting lidar has become an invaluable tool for 3D depth imaging due to the fine depth precision it can achieve over long ranges, with emerging applications in robotics, autonomous vehicles and remote sensing. However, high frame rate, high resolution lidar devices produce an enormous amount of time-of-flight (ToF) data which can cause a severe data processing bottleneck hindering the deployment of real-time systems. In this paper, we show that this bottleneck can be avoided through the use of a hardware-friendly compressed statistic, or a so-called spline sketch, of the ToF data, massively reducing the data rate without sacrificing the quality of the recovered depth image. Specifically, as with the previously proposed Fourier sketches, piecewise linear or quadratic spline sketches are able to reconstruct real-world depth images with negligible loss of resolution whilst achieving 95% compression compared to the full ToF data, as well as offering multi-peak detection performance. However, unlike Fourier sketches, splines sketches require minimal on-chip arithmetic computation per photon detection. We also show that by building in appropriate range-walk correction, spline sketches can be made robust to photon pile-up effects associated with bright reflectors. We contrast this with previously proposed solutions such as coarse binning histograms that trade depth resolution for data compression, suffer from a highly nonuniform accuracy across depth and can fail catastrophically when imaging bright reflectors. By providing a practical means of overcoming the data processing bottleneck, spline sketches offer a promising route to low cost high rate, high resolution lidar imaging.