A Depth-Adaptive Waveform Decomposition Method for Airborne LiDAR Bathymetry

Abstract

Airborne LiDAR bathymetry (ALB) has shown great potential in shallow water and coastal mapping. However, due to the variability of the waveforms, it is hard to detect the signals from the received waveforms with a single algorithm. This study proposed a depth-adaptive waveform decomposition method to fit the waveforms of different depths with different models. In the proposed method, waveforms are divided into two categories based on the water depth, labeled as “shallow water (SW)” and “deep water (DW)”. An empirical waveform model (EW) based on the calibration waveform is constructed for SW waveform decomposition which is more suitable than classical models, and an exponential function with second-order polynomial model (EFSP) is proposed for DW waveform decomposition which performs better than the quadrilateral model. In solving the model’s parameters, a trust region algorithm is introduced to improve the probability of convergence. The proposed method is tested on two field datasets and two simulated datasets to assess the accuracy of the water surface detected in the shallow water and water bottom detected in the deep water. The experimental results show that, compared with the traditional methods, the proposed method performs best, with a high signal detection rate (99.11% in shallow water and 74.64% in deep water), low RMSE (0.09 m for water surface and 0.11 m for water bottom) and wide bathymetric range (0.22 m to 40.49 m).

Depth Measurement Bias in Pulsed Airborne Laser Hydrography Induced by Chromatic Dispersion

“…Table I measurements in air T 1 a , T 2 a . The delay measurements were converted into a group refraction index for water by (19) using the length of the water probe L = 986.3 mm and the group refraction index in air n a g = 1.000 281 which was determined from the environmental conditions. The black dot in Fig.…”

Through-Wall UWB Radar Based on Sparse Deconvolution with Arctangent Regularization for Locating Human Subjects

“…Given the limitation of L2 norm regularization and the noisy characteristic of received signal y , we can easily estimate x to be a sparse signal (spike) from y by minimizing Equation (10) with a convex regularization term of the L1 norm [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ], . where is called L1 norm regularization (convex regularization) represented by the sum of absolute values of vector x , .…”

“…The Equation ( 6) is of four order Z −4 and the coefficients a j and b i are derived from the denominator and numerator in Equation (6) a = [a 0 , a 1 , a 2 , a 3 , a 4 ] = 1, −4r cos(ω 0 ), 4r 2 cos 2 (ω 0 ) + 2r 2 , −4r 3 cos(ω 0 ), r 4 (7) and…”

“…Basic deconvolution is the process of extracting the unknown input signal ( x ) of a linear time-invariant system ( y = Hx in matrix form) when the noise-free output signal ( y ) and wavelet ( H ) are known. However, in real-world applications, the output signal ( y ) is noisy and distorted by inhomogeneous media, such as ground-penetrating radar (GPR) [ 1 , 2 ], seismicity [ 3 , 4 ], radars [ 5 , 6 , 7 , 8 ], astronomy [ 9 ], speech recognition [ 10 , 11 ], and image reconstruction [ 12 , 13 , 14 , 15 ]. Nowadays, sparse deconvolution plays an important role in extracting the original data from the noisy received signal; it has been widely used in denoising, interpolation, super-resolution, and declipping [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ].…”

Remote Sensing Applications in Coastal Areas

“…Xing et al [5] proposed a depth-adaptive waveform decomposition method for airborne LiDAR bathymetry aimed at facilitating coastal water mapping in the Qilianyu Islands (Hainan Province, China). This methodology allowed for the development of two best fitting models for waveforms with different depths.…”