Greedy sensor placement with cost constraints and noise

The problem of optimally placing sensors under a cost constraint arises naturally in the design of industrial and commercial products, as well as in scientific experiments, including the reconstruction of fluid flows from incomplete measurements. We consider a relaxation of the full optimization formulation of this problem and extend a well-established greedy algorithm for the optimal sensor placement problem without cost constraints. We then modify our framework to account for the more realistic case of noisy measurements, and consider the problem of placing two different types of sensors: expensive high-fidelity sensors, and cheaper, noisier sensors. We develop guidelines for choosing the number and location of each type given a set budget. We demonstrate the effectiveness our methods on data sets related to fluid mechanics, geophysical fluid flows, and facial recognition.