Numerical simulation of scattering from rough surfaces: A wavelet-based approach

In this paper, a preliminary study is carried out to demonstrate the applic ation of wavelets for improving the computation time and reducing computati onal memory required for evaluating the statistics of the scattered field f rom rough surfaces using the method of moments (MoM) in conjunction with a Monte Carlo simulation. In specific, Haar and the first order B-spline wave let basis functions are applied to the MoM formulation of one-dimensional r ough surfaces in order to compare the computation time and sparsity for wav elets in the same family but of higher order. Since the scattering coeffici ent (the second moment of the backscatter field per unit area) is a gentle function of the surface parameters and the radar attributes, it is demonstr ated that a relatively high thresholding level can be applied to the impeda nce matrix, which leads to a sparser impedance matrix and faster computatio n time. It is also shown that applying a high threshold level the coefficie nts of the high-order wavelets would increase out of proportion, however, t he effect of these current components averages out when computing the scatt ering coefficients. The resulting sparse impedance matrices are solved effi ciently using fast search routines such as the conjugate gradient method. A systematic study is carried out to investigate the effect of different thr eshold levels on the accuracy versus computing speed criterion. The compute d scattering coefficients are compared to previous results computed using a conventional pulse basis function as well as the existing theoretical solu tions for rough surfaces. It is shown that wavelet basis functions provide substantial reductions in both memory requirements and computation time.