Optimization of inverse problems involving surface reconstruction: least squares application

This article addresses the least-squares method, which is vital in inverse scattering problems involving the reconstruction of inaccessible rough surface profiles from the measured scattered field data. The unknown surface profile is retrieved by a regularized recursive Newton algorithm which is regularized by the Tikhonov method. The importance of the least-squares application reveals at this point, where the unknown surface profile is expressed as a linear combination of some appropriate basis functions. Thus, the problem of obtaining the unknown rough surface is reduced to finding the unknown coefficients of these functions. As an optimization problem, the choice of appropriate basis functions, as well as the number of their expansions for rough surface imaging problems are essential for the iterative solutions. The validation limits and the performances of different basis functions are presented via several numerical examples.