The canonical problem of detecting and localizing missing scatterers (faults) inside a known grid of small cross section perfect electric conducting cylinders is dealt with. The case of a TM scalar two-dimensional geometry is considered. The scattering by a fault is modeled as the radiation of a proper magnetic current, by exploiting the Green's function of the complete grid. An approximated linear model of the scattering is proposed and discussed in terms of the achievable probability of detection, also in the case of two faults, and checked against model error and noisy synthetic data.