Wavelet -based algorithms for scattering and inverse scattering problems
The dissertation consists of two parts: scattering and inverse scattering. In the first part, the Coifman wavelet-based moment method with ratio-progressive approximation (RPA) scheme is developed to evaluate the singular integrals encountered in the magnetic field integral equation. As a result, the computation counts of the moment matrix are reduced from O(N 2) to O(N), owing to the one-point quadrature of the Coiflet. The new algorithm is applied to both the PEC and dielectric rough surfaces. New numerical results show that the backscattering enhancement on [special characters omitted] from the finite conductivity of the surface is unprecedentedly close to that of PEC surfaces with half the physical roughness, while the angular pattern of the cross-polarization part is more dependent on the surface curvature. The simulations using published soil parameters show that the Coiflet-based fast algorithm is sensitive and accurate in predicting small scattering coefficients from dielectric surfaces. Scattering from dielectric surfaces is more complicated than in the PEC case, e.g., backscattering enhancement and complex surface waves, which are observed in these simulations.
In the second part, an efficient deconvolution of the measurement system response is developed for time-domain near-field ISAR imaging. Due to its impulse-like waveform, the backscattering waveform from an electrically large conducting sphere is adopted as the system response to restore the impulse response of the scattered field, and to reconstruct the ISAR imaging. This deconvolution is discretized into a matrix equation, and the least-squares solution to the matrix equation is found by the conjugate gradient method. The resulting images are c with most smearing removed. Furthermore, the Coifman wavelet of the 6th order is employed to replace the system function of the 1st and 3rd derivatives of Gaussian functions. Due to the orthogonality and compact support of the Coiflets, the deconvolution process is accelerated by a factor of 22 without sacrificing the image quality.