Data-Driven Sparse Sensor Placement for Reconstruction
For engineers designing sensor networks for high-dimensional systems, this provides a principled, computationally efficient method to reduce sensor costs and enable faster state estimation.
The paper addresses optimal sparse sensor placement for signal reconstruction by using SVD and QR pivoting to select sensors from a data-driven library. It shows drastic reductions in required sensors and improved reconstruction compared to compressed sensing, demonstrated on facial images and fluid vorticity fields.
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.