Second Degree Model for Multi-Compression and Recovery of Distributed Signals

TL;DR

This paper introduces a second degree polynomial model for multi-compression and reconstruction of distributed signals, improving accuracy and stability over linear models through a novel optimization technique combining SDT, MBI, and matrix approximation.

Contribution

It develops a new non-linear second degree polynomial model for sensors and fusion center, enhancing signal estimation accuracy in distributed compression scenarios.

Findings

Models are always existent and numerically stable.

Improved accuracy over linear models.

Applicable to cases where known methods fail or produce larger errors.

Abstract

We study the problem of multi-compression and reconstructing a stochastic signal observed by several independent sensors (or compressors) that transmit compressed information to a fusion center. { The key aspect of this problem is to find models of the sensors and fusion center that are optimized in the sense of an error minimization under a certain criterion, such as the mean square error (MSE).} { A novel technique to solve this problem is developed. The novelty is as follows. First, the multi-compressors are non-linear and modeled using second degree polynomials. This may increase the accuracy of the signal estimation through the optimization in a higher dimensional parameter space compared to the linear case. Second, the required models are determined by a method based on a combination of the second degree transform (SDT) with the maximum block improvement (MBI) method and the generalized rank-constrained matrix approximation. It allows us to use the advantages of known methods to further increase the estimation accuracy of the source signal. Third, the proposed method is justified in terms of pseudo-inverse matrices. As a result, the models of compressors and fusion center always exist and are numerically stable.} In other words, the proposed models may provide compression, de-noising and reconstruction of distributed signals in cases when known methods either are not applicable or may produce larger associated errors.