We exploit the sparseness of induced currents on the surfaces of obscured perfectly conducting (PEC) scatterers in developing a single-frequency imaging algorithm in 2-D space. We model the induced currents on the targets by a set of unknown filament currents to which we apply the surface-equivalence theorem. We use l_{1} regularization to promote the solutions with a small number of equivalent sources placed in the vicinity of scatterer surfaces. The restored equivalent sources accurately determine the illuminated portions of the scatterer contours. We compare the performance of the algorithm with that of linear sampling (LSM) and MUSIC. We verify the proposed algorithm on the equivalent 3-D experimental model.