Regularizing method for the determination of the backscatter cross section in lidar data

Abstract

The retrieval of the backscatter cross section in lidar data is of great interest in remote sensing. For the numerical calculation of the backscatter cross section, a deconvolution has to be performed; its determination is therefore an ill-posed problem. Most of the common techniques, such as the well-known method of Gaussian decomposition, make implicit assumptions on both the emitted laser pulse and the scatterers. It is well understood that a land surface is quite complicated, and in many cases it cannot be composed of pure Gaussian function combinations. Therefore the assumption of Gaussian decomposition of waveforms may be invalid sometimes. In such cases an inversion method might be a natural choice. We propose a regularizing method with a posteriori choice of the regularizing parameter for solving the problem. The proposed method can alleviate difficulties in numerical computation and can suppress the propagation of noise. Numerical evidence is given of the success of the approach presented for recovering the backscatter cross section in lidar data.

Robust Ground Peak Extraction With Range Error Estimation Using Full-Waveform LiDAR

“…Complete deconvolution [8], [9], aiming at the correction of the full effect of the IR, is generally motivated by the determination of a physical target cross-section. However, it is inappropriate in our case, as we are only interested in the last scatterer.…”

“…However, it is inappropriate in our case, as we are only interested in the last scatterer. This is an ill-posed inverse problem as explained in [8], especially since the waveform sampling rate exceeds twice the Nyquist rate [10] in most scanners. Therefore it requires strong prior knowledge, effective regularization and a good model in order to avoid reconstruction artifacts (even more ringing and noise amplification).…”

“…Simulations confirmed this fact. Updating the estimators to take that into account is possible but the added complexity is not justified by the gain in variance or robustness, hence the use of the proxy (8). To achieve a false alarm rate of 10 −6 we set T = 4σ n .…”

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

“…However, this method is considered challenging in the case of echoes with low signal strength (low SNR) and it is deficient in its calculation of the cross-section in complex waveforms. The method also requires initial determination of the number of targets [16,18,23,26], which is sometimes impractical or of high computational cost. In addition, a symmetric function might not always be sufficiently accurate to describe the target characteristics [17,27].…”

“…The retrieval of target cross-section by signal deconvolution is an ill-posed problem and a unique solution is usually not obtainable without the imposition of appropriate solution constraints [16]. Unlike Gaussian decomposition, deconvolution does not require information regarding the number of signal peaks and there is no essential assumption regarding the pulse shape [7,26].…”