Exponential Decomposition with Implicit Deconvolution of Lidar Backscatter from the Water Column

Abstract

Bathymetric laser scanning is a powerful tool to obtain information about the morphology of coastal, river, and inland waters. Laser scanning in general is a method to sense the shape of remote objects by sweeping a laser beam across the objects while measuring the distance to every surface point. In bathymetric applications the electromagnetic light wave also needs to penetrate the water column resulting in a spread reflection from below the surface of the water body complicating the interpretation of the received wave. As the signal seen by the sensor's receiver is the result of a convolution of the system waveform with the differential backscatter cross-section, one approach is to use a deconvolution method to recover the object shape. An alternative approach is to fit a parametrised model to the measured receiver signal. While deconvolution methods are not capable to directly deliver object parameters such as distance to water surface or bottom, modelling methods suffer from neglecting the system waveform. We present a new waveform decomposition method that avoids current shortcomings. The

Remote Sensing of Suspended Sediment Concentrations Based on the Waveform Decomposition of Airborne LiDAR Bathymetry

“…Although the accuracy of quadrilateral function is slightly better than that of the triangle function [32], the number of parameters used in the former (six parameters) is more than that used in the latter (four parameters) and thus increase the complexity of waveform decomposition. Schwarz et al [34] proposed an If the volume backscatter returns can be separated accurately from the superposed surface returns and its waveform range (b-c in Figure 2) can be enlarged relative to that in the raw waveform (t 1 -t 2 in Figure 2), then the parameters of volume backscatter returns can be estimated from the green-pulse waveform for retrieving SSCs (Figures 1b and 2). Waveform decomposition is widely used in ALB depth estimation [28][29][30].…”

“…Although the accuracy of quadrilateral function is slightly better than that of the triangle function [32], the number of parameters used in the former (six parameters) is more than that used in the latter (four parameters) and thus increase the complexity of waveform decomposition. Schwarz et al [34] proposed an exponential decomposition method that uses a model composed of segments of exponential functions to fit waveforms and considers the influence of system waveforms. This method can undo the blurring of a differential backscatter cross section caused by a laser sensor and result in a stable estimation of the water surface [34].…”

“…Schwarz et al [34] proposed an exponential decomposition method that uses a model composed of segments of exponential functions to fit waveforms and considers the influence of system waveforms. This method can undo the blurring of a differential backscatter cross section caused by a laser sensor and result in a stable estimation of the water surface [34]. The quadrilateral function and the exponential decomposition need to be verified further by a lot of ALB data and water turbidity information.…”

A Case Study on Through-Water Dense Image Matching

“…In both cases knowledge of exact water level heights are a precondition for refraction and run-time correction of the raw measurements. The advantage of bathymetric LiDAR over multi-media photogrammetry is hereby two-fold: (i) LiDAR is a polar data acquisition strategy, meaning that a single measurement is sufficient to obtain a 3D point and (ii) the employed green laser light interacts with the water surface, the water column, and the water bottom and, thus, simultaneously delivers height estimates of the surface and the bottom (Guenther et al, 2000;Schwarz et al, 2017). While image based water level estimation remains a challenging task due to the specular and dynamic surface (Rupnik et al, 2015), especially the infrared channel of multi-spectral images can be used to detect the waterland-boundary from which the water level can be derived at least for calm water surfaces.…”

Improvement of Full Waveform Airborne Laser Bathymetry Data Processing based on Waves of Neighborhood Points

“…Deconvolution: this method consists of removing components of the emitted wave from the received signal. Examples of this method include Wiener filter deconvolution [20], Richardson-Lucy deconvolution [21], expectation maximization (EM) deconvolution [22], exponential decomposition with implicit deconvolution [23], and wavelet deconvolution [24].…”