- PROBLEMS IN INVERSE SCATTERING-ILLPOSEDNESS, RESOLUTION, LOCAL MINIMA, AND UNIQUENESSE
- Ra, Jung-Woong ;
- Communications of the Korean Mathematical Society, volume 16, issue 3, 2001, Pages 445~458
Abstract
The shape and the distribution of material construction of the scatterer may be obtained from its scattered fields by the iterative inversion in the spectral domain. The illposedness, the resolution, and the uniqueness of the inversion are the key problems in the inversion and inter-related. The illposedness is shown to be caused by the evanescent modes which carries and amplifies exponentially the measurement errors in the back-propagation of the measured scattered fields. By filtering out all the evanescent modes in the cost functional defined as the squared difference between the measured and the calculated spatial spectrum of the scattered fields from the iteratively chosen medium parameters of the scatterer, one may regularize the illposedness of the inversion in the expense of the resolution. There exist many local minima of the cost functional for the inversion of the large and the high-contrast scatterer and the hybrid algorithm combining the genetic algorithm and the Levenberg-Marquardt algorithm is shown to find efficiently its global minimum. The resolution of reconstruction obtained by keeping all the propating modes and filtering out the evanescent modes for the regularization becomes 0.5 wavelength. The super resolution may be obtained by keeping the evanescent modes when the measurement error and instance, respectively, are small and near.