A sparse data fast Fourier transform (SDFFT) - Algorithm and implementation

An algorithm that efficiently Fourier transforms sparse spatial data to sparse spectral data with controllable error is presented. Unlike the ordinary nonuniform last Fourier transform (NUFFT), which becomes O(N 2) for sparse k-space and sparse k-space data, the sparse data fast Fourier transform (SDFFT) presented herein decreases the cost to O(N log N) while preserving the O(N log N) memory complexity. The algorithm can be readily employed in general signal processing applications where only part of the k-space is to be computed - regardless of whether it is a regular region like an angular section of the Ewald's sphere or it consists completely of arbitrary points. Among its applications in electromagnetics are back-projection tomography, diffraction tomography, synthetic aperture radar imaging, and the computation of far field patterns due to general aperture antennas and antenna arrays.link_to_subscribed_fulltex

3-D imaging of large scale buried structure by 1-D inversion of very early time electromagnetic (VETEM) data

A simple and efficient method for large scale three-dimensional (3-D) subsurface imaging of inhomogeneous background is presented. One-dimensional (1-D) multifrequency distorted Born iterative method (DBIM) is employed in the inversion. Simulation results utilizing synthetic scattering data are given. Calibration of the very early time electromagnetic (VETEM) experimental waveforms is detailed along with major problems encountered in practice and their solutions. This discussion is followed by the results of a large scale application of the method to the experimental data provided by the VETEM system of the U.S. Geological Survey. The method is shown to have a computational complexity that is promising for on-site inversion.link_to_subscribed_fulltex