Compression and Recovery of Distributed Random Signals

We consider the case when a set of spatially distributed sensors Q1, . . . ,Qp make local observations, y1, . . . ,yp, which are noisy versions of a signal of interest, x. Each sensor Qj transmits compressed information uj about its measurements to the fusion center which should recover the original signal within a prescribed accuracy. Such an information processing relates to a wireless sensor network (WSN) scenario. The key problem is to find models of the sensors and fusion center so that they will be optimal in the sense of minimization of the associated error under a certain criterion, such as the mean square error (MSE). We determine the models from the technique which is a combination of the maximum block improvement (MBI) method [1], [2] and the generic Karhunen-Loève transform (KLT) [3] (based on the work in [4], [5]). Therefore, the proposed method unites the merits of both techniques [1], [2] and [3], [4], [5]. As a result, our approach provides, in particular, the minimal MSE at each step of the version of the MBI method we use. The WSN model is represented in the form called the multicompressor KLT-MBI transform. The multi-compressor KLT-MBI is given in terms of pseudo-inverse matrices and, therefore, it is numerically stable and always exists. In other words, the proposed WSN model provides compression, de-noising and reconstruction of distributed signals for the cases when known methods either are not applicable (because of singularity of associated matrices) or produce larger associated errors. Error analysis is provided.