A comparison of signal deconvolution algorithms based on small-footprint LiDAR waveform simulation

A raw incoming (received) Light Detection And Ranging (LiDAR) waveform typically exhibits a stretched and relatively featureless character, e.g., the LiDAR signal is smeared and the effective spatial resolution decreases. This is attributed to a fixed time span allocated for detection, the sensor's variable outgoing pulse signal, receiver impulse response, and system noise. Theoretically, such a loss of resolution can be recovered by deconvolving the system response from the measured signal. In this paper, we present a comparative controlled study of three deconvolution techniques, namely, Richardson-Lucy, Wiener filter, and nonnegative least squares, in order to verify which method is quantitatively superior to others. These deconvolution methods were compared in terms of two use cases: 1) ability to recover the true cross-sectional profile of an illuminated object based on the waveform simulation of a virtual 3-D tree model and 2) ability to differentiate herbaceous biomass based on the waveform simulation of virtual grass patches. All the simulated waveform data for this study were derived via the "Digital Imaging and Remote Sensing Image Generation" radiative transfer modeling environment. Results show the superior performance for the Richardson-Lucy algorithm in terms of small root mean square error for recovering the true cross section, low false discovery rate for detecting the unobservable local peaks in the stretched raw waveforms, and high classification accuracy for differentiating herbaceous biomass levels.