We develop a new model for spatial random field reconstruction of a binary-valued spatial phenomenon. In our model, sensors are deployed in a wireless sensor network across a large geographical region. Each sensor measures a non-Gaussian inhomogeneous temporal process which depends on the spatial phenomenon. Two types of sensors are employed: one collects point observations at specific time points, while the other collects integral observations over time intervals. Subsequently, the sensors transmit these time-series observations to a Fusion Center (FC), and the FC infers the spatial phenomenon from these observations. We show that the resulting posterior predictive distribution is intractable and develop a tractable two-step procedure to perform inference. Firstly, we develop algorithms to perform approximate Likelihood Ratio Tests on the time-series observations, compressing them to a single bit for both point sensors and integral sensors. Secondly, once the compressed observations are transmitted to the FC, we utilize a Spatial Best Linear Unbiased Estimator (S-BLUE) to reconstruct the binary spatial random field at any desired spatial location. The performance of the proposed approach is studied using simulation. We further illustrate the effectiveness of our method using a weather dataset from the National Environment Agency (NEA) of Singapore with fields including temperature and relative humidity.

翻译：我们开发了一种用于二元空间现象的空间随机场重建新模型。在该模型中，传感器部署于覆盖广阔地理区域的无线传感器网络中。每个传感器测量一个依赖于空间现象的非高斯非平稳时间过程。我们采用了两种类型的传感器：一种在特定时间点采集点观测数据，另一种在时间区间内采集积分观测数据。随后，这些传感器将时间序列观测数据传输至融合中心（FC），而融合中心则基于这些数据推断空间现象。研究表明，得到的后验预测分布难以处理，因此我们开发了一种易于处理的两步推断方法。首先，我们设计了算法对时间序列观测进行近似似然比检验，将其压缩为单个比特信息（适用于点传感器和积分传感器）。其次，压缩后的观测数据被传输至融合中心后，我们利用空间最佳线性无偏估计量（S-BLUE）重建任意空间位置上的二元空间随机场。通过仿真研究了所提出方法的性能。我们进一步利用新加坡国家环境局（NEA）提供的包含温度和相对湿度等字段的天气数据集验证了该方法的有效性。