Signal Compression and Reconstruction in Clustered Sensor Networks

We consider a wireless sensor network monitoring a field of interest, and we study the benefits of grouping nodes into clusters. The data gathered within each cluster are compressed by the cluster head and sent to a sink node, where a reconstructed version of the field is obtained. We represent the compressed data through the Fourier coefficients of the field spectrum, and analyze both the case where the sensor positions are known to the sink, and the case where they are available at the cluster head only. We show that clustering significantly reduces the energy expenditure due to data transmission, and, most importantly, we derive the possible degradation of the quality of the reconstructed field due to compression.