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.

中文翻译：

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基于递归方法的信号重构高效传感器放置

在许多领域中，选择稀疏传感器以恢复全局信号场是一项至关重要的任务。现有的大多数算法通过优化依赖于结构假设或低维模型的重建准则的替代方案来解决该问题。在本文中，我们提出了一种新的传感器放置方法，该方法将信号重建误差作为代价函数，并通过贪婪的过程将其最小化。此外，我们采用了一种递归公式，该公式可导致对该标准进行时间和内存有效的评估。通过推导计算密集型项目的更新公式，我们还开发了一种面向重建的快速局部优化技术，该方法可用于改善重建精度方面次优算法的初始解。我们展示了在相同的贪婪选择程序下提出的目标函数的优越性。在数值和真实数据集上进行的实验证明了我们的算法优于最新方法的优势。