Conical diffraction of electromagnetic waves from one-dimensional lossy dielectric rough surfaces by using the wavelet transform

Scattering by a random rough surface is an important problem in remote sensing. The classical analytic techniques of Kirchhoff approximation and small perturbation theory are limited in domains of validity. Recently, the authors have developed a fast computational technique based on the banded matrix iterative approach/canonical grid method; however, the matrix-vector multiplication still dominates the computational efficiency if the bandwidth is very large due to the significant strong near-interactions involved. To enhance the solving performance, a screening window in conjunction with the wavelet transform matrix is proposed so as to reduce the required storage and computational CPU time. It is noted that the wavelet-transformed matrix for each sub-matrix is implemented only once. Based on the idea of multiresolution analysis, the matrix-vector multiplication in an iterative solver is then efficiently evaluated for its higher sparsity. Typical examples of the conical diffraction from one-dimensional lossy dielectric rough surfaces are therefore investigated to validate the proposed method and applied to passive microwave remote sensing problems.