Compressive Sensing is a technique that can help reduce the sampling rate of sensing tasks. In mobile crowdsensing applications or wireless sensor networks, the resource burden of collecting samples is often a major concern. Therefore, compressive sensing is a promising approach in such scenarios. An implicit assumption underlying compressive sensing - both in theory and its applications - is that every sample has the same cost: its goal is to simply reduce the number of samples while achieving a good recovery accuracy. In many networked sensing systems, however, the cost of obtaining a specific sample may depend highly on the location, time, condition of the device, and many other factors of the sample. In this paper, we study compressive sensing in situations where different samples have different costs, and we seek to find a good trade-off between minimizing the total sample cost and the resulting recovery accuracy. We design CostAware Compressive Sensing (CACS), which incorporates the cost-diversity of samples into the compressive sensing framework, and we apply CACS in networked sensing systems. Technically, we use regularized column sum (RCS) as a predictive metric for recovery accuracy, and use this metric to design an optimization algorithm for finding a least cost randomized sampling scheme with provable recovery bounds. We also show how CACS can be applied in a distributed context. Using traffic monitoring and air pollution as concrete application examples, we evaluate CACS based on large-scale real-life traces. Our results show that CACS achieves significant cost savings, outperforming natural baselines (greedy and random sampling) by up to 4x
