Due to non-homogeneous spread of sunlight, sensing nodes typically have non-uniform energy profiles in rechargeable Wireless Sensor Networks (WSNs). An energy-aware work load distribution is therefore necessary for good data accuracy while ensuring an energy-neutral operation. Recently proposed signal approximation strategies, in form of Compressive Sensing, assume uniform sampling and thus cannot be deployed to facilitate energy neutral operation in rechargeable WSNs. We propose a sparse approximation driven sensing technique (EAST) that adapts sensor node sampling workload according to solar energy availability. To the best of our knowledge, we are the first to propose sparse approximation for modeling energy-aware work load distribution in order to improve signal approximation from rechargeable WSNs. Experimental result, by using data from an outdoor WSN deployment, suggests that EAST significantly improves the approximation accuracy while supporting approximately 50% higher sens...