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This paper presents an innovative microwave technique, which is suitable for the detection of defects in nondestructive-test and nondestructive-evaluation (NDT/NDE) applications where a lot of a priori information is available. The proposed approach is based on the equations of the inverse scattering problem, which are solved by means of a minimization procedure based on a genetic algorithm. To reduce the number of problem unknowns, the available a priori information is efficiently exploited by introducing an updating procedure for the electric field computation based on the Sherman-Morrison-Woodbury formula. The results of a representative set of numerical experiments as well as comparisons with state-of-the-art methods are reported. They confirm the effectiveness, feasibility, and robustness of the proposed approach, which shows some interesting features by a computational point of view as well.