  A novel Gibbs Markov random field for spatial data on Cartesian grids based
on the modified planar rotator (MPR) model of statistical physics has been
recently introduced for efficient and automatic interpolation of big data sets,
such as satellite and radar images. The MPR model does not rely on Gaussian
assumptions. Spatial correlations are captured via nearest-neighbor
interactions between transformed variables. This allows vectorization of the
model which, along with an efficient hybrid Monte Carlo algorithm, leads to
fast execution times that scale approximately linearly with system size. The
present study takes advantage of the short-range nature of the interactions
between the MPR variables to parallelize the algorithm on graphics processing
units (GPU) in the Compute Unified Device Architecture (CUDA) programming
environment. It is shown that, for the processors employed, the GPU
implementation can lead to impressive computational speedups, up to almost 500
times on large grids, compared to the single-processor calculations.
Consequently, massive data sets comprising millions of data points can be
automatically processed in less than one second on an ordinary GPU.
