Applications of wavelet packet bases to computational electromagnetics and radar imaging

Applications of wavelet packet basis to computational electromagnetics and Synthetic Aperture Radar (SAR) image processing are investigated in this dissertation. First, wavelet packet bases are used to sparsify moment matrices for facilitating the iterative solution of electromagnetic integral equations. Adaptive Wavelet Packet Transform (AWPT) is proposed to search the best wavelet packet basis for achieving maximum sparsity in the transformed moment matrix. An information cost function is chosen to measure the sparsity of the transformed moment matrix. It is found that the AWPT-transformed moment matrices have about O(N1.4) non-zero elements for typical two-dimensional (2-D) scatterers. Second, the Pre-defined Wavelet Packet (PWP) basis is designed to match the oscillatory nature of free space Green's function. With the PWP basis, the cost to search for the best basis in the AWPT approach can be avoided. Numerical results show that the number of nonzero elements in the PWP-based moment matrices grows approximately at a rate of O(N1.3) for small problem sizes and O(NlogN) for large problem sizes. Third, to accelerate the convergence rate of iterative solution of electromagnetic integral equations, an effective preconditioner is constructed for 2-D moment equations from the PWP-based moment matrix. The computational cost and memory requirement are limited to O(NlogN) for the construction of the preconditioner and the preconditioning operation. Test results demonstrate that the preconditioner is very effective for ill-conditioned scatterers such as cavity structures. Results to extend the algorithm to three-dimensional (3-D) moment equations are also presented. Finally an algorithm for SAR image clutter reduction is developed based on adaptive wavelet packet transform. It is based on the assumption that the target image can be concentrated through basis transformation, while the clutter remains statistically uncorrelated in the transform process. Thus a higher target signal-to-clutter ratio is achieved in the transform domain. The AWPT algorithm is used to perform the quadtree decomposition and determine the best wavelet packet basis that maximizes signal-toclutter ratio in the transform domain. The de-cluttered SAR images are obtained by thresholding the transformed images and inverse-transforming them back to the original image domain. The effectiveness of the new clutter-removal algorithm is demonstrated using the MSTAR data set.