Wireless Sensor Networks (WSN), i.e. networks of autonomous, wireless sensing nodes spatially deployed over a geographical area, are often faced with acquisition of spatially sparse fields. In this paper, the authors present a novel bandwidth/energy efficient CS scheme for acquisition of spatially sparse fields in a WSN. The paper contribution is twofold. Firstly, they introduce a sparse, structured CS matrix and they analytically show that it allows accurate reconstruction of bi-dimensional spatially sparse signals, such as those occurring in several surveillance application. Secondly, they analytically evaluate the energy and bandwidth consumption of their CS scheme when it is applied to data acquisition in a WSN.