In this paper, we present an innovative algorithm for sparse imaging of perfect electric conducting (PEC) targets. The algorithm is based on higher order sources or multipoles, rather than zero-order ones as in the standard sparse imaging. We demonstrate that, due to the directivity of higher order sources, the imaging capabilities of the algorithm are enhanced. Particular improvements are achieved when dealing with complex-shaped targets. As a matter of fact, through several illustrative examples, we show that the zero-order sources are more suitable for the reconstruction of the convex parts of target boundaries, whereas the higher order sources are more appropriate for the concave parts of the boundaries. Taking advantage of some analytical considerations in a canonical case, we devise a strategy to select the optimal orders to consider in the imaging procedure without needing any a priori information on the target.