Near-Optimal Sensor Placement for Linear Inverse Problems

TL;DR

This paper introduces FrameSense, a greedy algorithm for sensor placement in linear inverse problems, which guarantees near-optimal mean square error performance with low computational cost.

Contribution

The paper presents FrameSense, the first greedy algorithm with provable near-optimality for sensor placement based on the frame potential, outperforming existing methods.

Findings

FrameSense achieves state-of-the-art accuracy in sensor placement.

It guarantees solutions close to the optimal in mean square error.

The algorithm has the lowest computational cost among greedy methods.

Abstract

A classic problem is the estimation of a set of parameters from measurements collected by only a few sensors. The number of sensors is often limited by physical or economical constraints and their placement is of fundamental importance to obtain accurate estimates. Unfortunately, the selection of the optimal sensor locations is intrinsically combinatorial and the available approximation algorithms are not guaranteed to generate good solutions in all cases of interest. We propose FrameSense, a greedy algorithm for the selection of optimal sensor locations. The core cost function of the algorithm is the frame potential, a scalar property of matrices that measures the orthogonality of its rows. Notably, FrameSense is the first algorithm that is near-optimal in terms of mean square error, meaning that its solution is always guaranteed to be close to the optimal one. Moreover, we show with an extensive set of numerical experiments that FrameSense achieves state-of-the-art performance while having the lowest computational cost, when compared to other greedy methods.