Extrapolating the Fractal Characteristics of an Image Using Scale-Invariant Multiple-Point Statistics

The resolution of measurement devices can be insufficient for certain purposes. We propose to stochastically simulate spatial features at scales smaller than the measurement resolution. This is accomplished using multiple-point geostatistical simulation (direct sampling in the present case) to interpolate values at the target scale. These structures are inferred using hypothesis of scale invariance and stationarity on the spatial patterns found at the coarse scale. The proposed multiple-point super-resolution mapping method is able to deal with "both continuous and categorical variables", and can be extended to multivariate problems. The advantages and limitations of the approach are illustrated with examples from satellite imaging.