  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.
