# Data-Driven Sparse Sensor Placement for Reconstruction

## TL;DR

This paper presents a data-driven method for optimal sparse sensor placement that leverages low-dimensional representations to improve signal reconstruction efficiency and accuracy in high-dimensional systems.

## Contribution

It introduces a novel approach combining singular value decomposition and QR pivoting for optimized sensor placement based on training data.

## Key findings

- Significant reduction in the number of sensors needed for accurate reconstruction.
- Enhanced reconstruction quality compared to universal compressed sensing methods.
- Applicable to diverse fields like image analysis and fluid dynamics.

## Abstract

Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent compressibility enables sparse sensing. This article explores optimized sensor placement for signal reconstruction based on a tailored library of features extracted from training data. Sparse point sensors are discovered using the singular value decomposition and QR pivoting, which are two ubiquitous matrix computations that underpin modern linear dimensionality reduction. Sparse sensing in a tailored basis is contrasted with compressed sensing, a universal signal recovery method in which an unknown signal is reconstructed via a sparse representation in a universal basis. Although compressed sensing can recover a wider class of signals, we demonstrate the benefits of exploiting known patterns in data with optimized sensing. In particular, drastic reductions in the required number of sensors and improved reconstruction are observed in examples ranging from facial images to fluid vorticity fields. Principled sensor placement may be critically enabling when sensors are costly and provides faster state estimation for low-latency, high-bandwidth control. MATLAB code is provided for all examples.