We investigate the use of impediographic tomography to achieve high sensitivity and high resolution damage identification in plate-like structures. The impediographic approach exploits the coupled piezo-resistive and electrostatic response of the host structure to generate high sensitivity and high resolution maps of its internal electrical conductivity. Focused acoustic waves are used to generate localized electrical conductivity perturbations that allow a drastic improvement in the conditioning of the inverse problem. The localized acoustic perturbations are obtained by exploiting the concept of Frequency Selective Structures (FSS) in which intentional mistuning of periodically distributed structural features, such as thin notches, enables self-focusing and vibration localization by using a single ultrasonic transducer. The impediographic reconstruction is achieved by using two different methods: the 0-Laplacian and the Levenberg-Marquardt. Both methodologies are compared in terms of accuracy of the reconstructed electrical conductivity and of their ability to deal with important practical issues such as limited view and limited perturbation data. Numerical results show that, although both approaches perform well in terms of damage identification, localization, and sizing, the LM technique allows higher flexibility in handling imperfect data.