One of the key challenges in sensor networks is the extraction of trusted and relevant information by fusing data from a multitude of heterogeneous, distinct, but possibly unreliable or irrelevant sensors. Recovering the desirable view of the environment from the maximum number of dependable sensors while specifying the unreliable ones is an issue of paramount importance for active sensing and robust operation of the entire network. This problem of robust sensing is formulated here, and proved to be NP-hard. In the quest of sub-optimum but practically feasible solutions with quantifiable performance guarantees, two algorithms are developed for selecting reliable sensors via convex programming. The first relies on a convex relaxation of the original problem, while the second one is based on approximating the initial objective function by a concave one. Their performance is tested analytically, and through simulations.