Efficient Sensor Placement for Signal Reconstruction Based on Recursive Methods

Abstract

Selection of sparse sensors to recover the global signal field is a crucial task in many areas. Most of the existing algorithms tackle this problem by optimizing the surrogates of reconstruction criterion which relies on structural assumptions or low-dimensional models. In this paper, we propose a novel sensor placement method using signal reconstruction error as the cost function, sequentially minimize it with greedy procedures. Furthermore, we employ a recursive formula that leads to time and memory efficient evaluation of the criterion. We also develop a fast reconstruction-oriented local optimization technique, by deriving update formulae for computationally intensive items, which can be applied to improve the initial solutions of suboptimal algorithms in terms of reconstruction accuracy. We show the superiority of the proposed objective function under the same greedy selection procedure. Experiments on both numerical and real-world datasets demonstrate the advantages of our algorithm over the state-of-the-art methods.