Random distributed multiresolution representations with significance querying

We propose random distributed multiresolution representations of sensor network data, so that the most significant encoding coefficients are easily accessible by querying a few sensors, anywhere in the network. Less significant encoding coefficients are available by querying a larger number of sensors, local to the region of interest. Significance can be defined in a multiresolution way, without any prior knowledge of the source data, as global summaries versus local details. Alternatively, significance can be defined in a data-adaptive way, as large differences between neighboring data values. We propose a distributed encoding algorithm that is robust to arbitrary wireless communication connectivity graphs, where links can fail or change with time. This randomized algorithm allows distributed computation that does not require strict global coordination or awareness of network connectivity at individual sensors. Because computations involve sensors in local neighborhoods of the communication graph, they are communication-efficient. Our framework uses local interaction among sensors to enable flexible information retrieval at the global level.