From Sparse Signals to Sparse Residuals for Robust Sensing

TL;DR

This paper introduces novel robust sensing schemes that leverage sparse residuals to identify reliable sensors in networks, employing convex relaxations and algorithms suitable for noisy data, with proven effectiveness through simulations.

Contribution

It develops four new sensing schemes based on sparse residuals, including convex and concave relaxations, tailored for noisy and reliable sensor detection, advancing robust sensor network data fusion.

Findings

SOCP can recover optimal solutions with high probability for Gaussian matrices

The proposed methods effectively identify reliable sensors in noisy environments

Simulations confirm the robustness and accuracy of the schemes

Abstract

One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while specifying the unreliable ones is critical for robust sensing. This sensing task is formulated here as that of finding the maximum number of feasible subsystems of linear equations, and proved to be NP-hard. Useful links are established with compressive sampling, which aims at recovering vectors that are sparse. In contrast, the signals here are not sparse, but give rise to sparse residuals. Capitalizing on this form of sparsity, four sensing schemes with complementary strengths are developed. The first scheme is a convex relaxation of the original problem expressed as a second-order cone program (SOCP). It is shown that when the involved sensing matrices are Gaussian and the reliable measurements are sufficiently many, the SOCP can recover the optimal solution with overwhelming probability. The second scheme is obtained by replacing the initial objective function with a concave one. The third and fourth schemes are tailored for noisy sensor data. The noisy case is cast as a combinatorial problem that is subsequently surrogated by a (weighted) SOCP. Interestingly, the derived cost functions fall into the framework of robust multivariate linear regression, while an efficient block-coordinate descent algorithm is developed for their minimization. The robust sensing capabilities of all schemes are verified by simulated tests.