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.
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