A Sparsity-Based Regularization Approach for Deconvolution of Full-Waveform Airborne Lidar Data

Abstract

Full-waveform lidar systems capture the complete backscattered signal from the interaction of the laser beam with targets located within the laser footprint. The resulting data have advantages over discrete return lidar, including higher accuracy of the range measurements and the possibility of retrieving additional returns from weak and overlapping pulses. In addition, radiometric characteristics of targets, e.g., target cross-section, can also be retrieved from the waveforms. However, waveform restoration and removal of the effect of the emitted system pulse from the returned waveform are critical for precise range measurement, 3D reconstruction and target cross-section extraction. In this paper, a sparsity-constrained regularization approach for deconvolution of the returned lidar waveform and restoration of the target cross-section is presented. Primal-dual interior point methods are exploited to solve the resulting nonlinear convex optimization problem. The optimal regularization parameter is determined based on the L-curve method, which provides high consistency in varied conditions. Quantitative evaluation and visual assessment of results show the superior performance of the proposed regularization approach in both removal of the effect of the system waveform and reconstruction of the target cross-section as compared to other prominent deconvolution approaches. This demonstrates the potential of the proposed approach for improving the accuracy of both range measurements and geophysical attribute retrieval. The feasibility and consistency of the presented approach in the processing of a variety of lidar data acquired under different system configurations is also highlighted.

Improved Urban Scene Classification Using Full-Waveform Lidar

“…These features range from geometric to radiometric, and extend to additional features extracted from the waveform itself. Retrieval of the target response (cross-section) is based upon a robust deconvolution method developed in previous work (Azadbakht et al, 2016). Two ensemble classifiers are then applied to examine the role of both waveform features and the size of the training dataset in the identification of various target classes.…”

“…Suppose P is a vector representing the waveform recorded by the receiver, σ a vector including the differential backscatter cross-section, S the blur matrix with elements from the system waveform, and λ the regularization parameter value. The cost function is then considered to be minimized in order to retrieve the proper target response with minimal oscillations (Azadbakht et al, 2016):…”

“…Radiometric features including the pulse amplitude A, the target cross-section σ, the total backscatter cross-section of the whole waveform σ T , and the backscatter coefficient γ are also extracted from the retrieved waveforms in Equation 1 after calibrating them for range, and also with regard to an asphalt target which is considered as a standard Lambertian surface with a specified reflectivity at the required wavelength (Alexander et al, 2010;Azadbakht et al, 2016;Mallet et al, 2011).…”

Multi-Channel Deconvolution for Forward-Looking Phase Array Radar Imaging

“…Besides the Poisson distribution, sparse prior information based on compressed sensing has also been applied to forward-looking imaging since the number of strong scattering targets is sparse relative to the imaging area grids [25,26,33]. However, sparse-based method can only serve as an auxiliary mean of imaging since it shows high sensitivity and unreliable performance in real data processing.…”

“…Unfortunately, deconvolution is inherently an ill-posed problem under noise environment that typically involves a great number of unknowns due to the receiver noise and low-pass characteristic of antenna pattern, which brings about amplifying system noise and blurring effects [10][11][12][13][14][15][16][17]. Recently, deconvolution algorithms in Bayesian framework or sparse signal reconstruction have been used in the application of radar imaging to improve cross-range resolution [18][19][20][21][22][23][24][25][26][27], but the tradeoff between robustness and resolution performance cannot be easily adjusted. In [28][29][30], a constrained iterative deconvolution (CID) algorithm was proposed to obtain well-behaved results due to positive constraint, but the angular resolution improvement is still limited by noise when the signal-to-noise ratio (SNR) is relatively low.…”