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In this paper, we consider a mobile cooperative network that is tasked with building a map of the spatial variations of a parameter of interest, such as an obstacle map or an aerial map. We propose a new framework that allows the nodes to build a map of the parameter of interest with a small number of measurements. By using the recent results in the area of compressive sensing, we show how the nodes can exploit the sparse representation of the parameter of interest in the transform domain in order to build a map with minimal sensing. The proposed work allows the nodes to efficiently map the areas that are not sensed directly. We consider three main areas essential to the cooperative operation of a mobile network: building a map of the spatial variations of a field of interest such as aerial mapping, mapping of the obstacles based on only wireless measurements, and mapping of the communication signal strength. For the case of obstacle mapping, we show how our framework enables a novel noninvasive mapping approach (without direct sensing), by using wireless channel measurements. Overall, our results demonstrate the potentials of this framework.