We consider large sensor networks where the cost of collecting data from the network nodes to the data gathering sink is critical.~We propose several algorithms that use limited local communication and distributed signal processing to make communication more efficient in terms of transmission cost.~We consider a model that uses distributed wavelets-based signal processing.~We first propose an algorithm that performs processing at nodes as data is forwarded to the sink.~Then, we analyze algorithms that perform network division into groups of adaptive size and for which signal processing is applied separately to each group.~We show by numerical simulations that such multiresolution approaches result in significant improvements for data gathering in terms of total communication costs.