Enhancing 3D range image measurement density via dynamic Papoulis-Gerchberg algorithm

As one of the most popular range detection methods, lidar is commonly used in various robotic applications. Although most robotic platforms easily adopt 2D lidar for range sensing, 3D lidar is rarely used in mobile robots, owing to its high cost. Some methods reported in the literature obtain 3D range information by rotating a single 2D lidar device. However, for most of these methods, there is a trade-off between 3D scan frequency and measurement density. Existing methods discussed in the literature for increasing the measurement density in high-frequency lidar have high time complexity and require certain conditions on data distribution. In a previous work, we showed the usability of an image super-resolution method, the Papoulis-Gerchberg (P-G) algorithm, on range data represented in the form of a greyscale image. However, the low convergence rate of the original P-G algorithm impedes its use for online applications. In this study, we advanced the P-G algorithm to drastically reduce the convergence time and improve performance by utilizing previous range images. The proposed algorithm now supports application on a mobile robot with online measurement density enhancement for 3D range images collected by rotating a 2D lidar device around its pitch axis with a high 3D scan frequency. We show illustrative examples for different scenarios to present the effectiveness of the proposed method on a 3D range sensor mounted on a mobile robot.