Unidirectional graph-based wavelet transforms for efficient data gathering in sensor networks

We design lifting-based wavelet transforms for any arbitrary communication graph in a wireless sensor network (WSN). Since transmitting raw data bits along the routing trees in WSN usually requires more bits than transmitting encoded data, we seek to minimize raw data transmissions in the network. We especially focus on unidirectional transforms which are computed as data is forwarded towards the sink on a routing tree. We formalize the problem of minimizing the number of raw data transmitting nodes as a weighted set cover problem and provide greedy approximations. We compare our method with existing distributed wavelet transforms on communication graphs. The results validate that our proposed transforms reduce the total energy consumption in the network with respect to existing designs.