In this article, contrary to current research trend which consists of fusing (big) data from many different sensors, we focus on one-dimensional samples collected by a unique mobile sensor (e.g., temperature, pressure, magnetic field, etc.), without explicit positioning information (such as GPS). We demonstrate that this stream of 1D data contains valuable 2D geometric information that can be unveiled by adequate processing—using a high-accuracy Finite Rate of Innovation (FRI) algorithm: “FRI Sensing”. Our key finding is that, despite the absence of any position information, the basic sequence of 1D sensor samples makes it possible to reconstruct the sampling trajectory (up to an affine transformation), and then the image that represents the physical field that has been sampled. We state the FRI Sensing sampling theorem and the hypotheses needed for this trajectory and image reconstruction to be successful. The proof of our theorem is constructive and leads to a very efficient and robust algorithm, which we validate in various conditions. Moreover, although we essentially model the images as finite sums of 2D sinusoids, we also observe that our algorithm works accurately for real textured images.

中文翻译：

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FRI 传感：从时间样本中检索移动传感器的轨迹

在本文中，与当前由融合来自许多不同传感器的（大）数据组成的研究趋势相反，我们专注于由独特的移动传感器（例如，温度、压力、磁场等）收集的一维样本，而没有显式定位信息（如 GPS）。我们证明了这一一维数据流包含有价值的二维几何信息，这些信息可以通过使用高精度有限创新率 (FRI) 算法：“FRI 传感”进行充分处理来揭示。我们的主要发现是，尽管没有任何位置信息，但一维传感器样本的基本序列可以重建采样轨迹（直至仿射变换），然后是表示已采样的物理场的图像. 我们陈述了 FRI 传感采样定理以及该轨迹和图像重建成功所需的假设。我们定理的证明是有建设性的，并导致了一个非常有效和健壮的算法，我们在各种条件下对其进行了验证。此外，虽然我们基本上将图像建模为 2D 正弦曲线的有限和，但我们也观察到我们的算法对真实纹理图像准确地工作。