Multihypothesis-Based Compressive Sensing Algorithm for Nonscanning Three-Dimensional Laser Imaging

The resolution of nonscanning three-dimensional (3-D) imaging systems is limited by the number and accuracy of the array sensors. Moreover, for space-continuous targets in practical situations, the echo pulses in time-of-flight systems overlap and traditional peak detection is no longer suitable for super-resolution applications. Hence, compressive sensing (CS) has been introduced to achieve super-resolution. However, most of the conventional CS algorithms cannot be used directly for 3-D image reconstruction. In this paper, we propose a novel super-resolution algorithm for nonscanning 3-D laser imaging based on CS reconstruction. To acquire the range information of space-continuous targets, an all-one projection is implemented in advance to estimate the spatial distribution of the targets; a range observation matrix composed of time-interval basis vectors is then constructed to obtain the peak values of each frame from overlapping echo pulses. Because of the spatial continuity of the targets, Tikhonov regularization is utilized to solve the ill-posed inverse problem. Furthermore, to enhance the reconstruction quality of the adjacent frames, multihypothesis prediction is used with displacement and diffusion models to estimate the motion of the contour line. Simulation results based on real data from the ASTER global digital elevation model demonstrate the effectiveness and high accuracy of the proposed algorithm for complex landforms.