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In the framework of nondestructive evaluation and testing (NDE/NDT), this paper presents an innovative tomographic microwave imaging approach based on the use of the Sherman-Morrison-Woodbury (SMW) updating formula for electric field computation. Starting from the integral forms of the inverse scattering equations, the problem of determining the presence of an unknown defect in a known host domain is recast into an optimization problem by defining a suitable cost function and reducing the problem unknowns only to the flaw "descriptors." By considering an effective inversion technique, the estimation of secondary unknowns (namely, the electric field distributions) is performed in a cost-effective way. Selected numerical results are presented to validate the approach, showing current potentialities and limitations. For completeness, an application to civil engineering is also reported.