Compression and Recovery of Distributed Random Signals

TL;DR

This paper introduces a stable, numerically reliable algorithm combining the Karhunen-Loève transform and maximum block improvement method for optimal compression and recovery of distributed noisy signals in wireless sensor networks.

Contribution

It develops a novel multi-compressor KLT-MBI algorithm that effectively compresses, denoises, and reconstructs signals where existing methods face limitations due to matrix singularities.

Findings

The algorithm is numerically stable and always exists.

It outperforms existing methods in cases of matrix singularity.

Error analysis confirms its effectiveness.

Abstract

We consider the case when a set of spatially distributed sensors make local observations which are noisy versions of a signal of interest. Each sensor transmits compressed information 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 and the generic Karhunen-Lo\`{e}ve transform (KLT). The resulting multi-compressor KLT-MBI algorithm is given in terms of pseudo-inverse matrices and, therefore, it is numerically stable and always exists. The proposed 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.