Reconstruction of missing data in remote sensing images using conditional stochastic optimization with global geometric constraints

This paper addresses the issue of missing data reconstruction for partially sampled, two-dimensional, rectangular grid images of differentiable random fields. We introduce a stochastic gradient–curvature (GC) reconstruction method, which is based on the concept of a random field model defined by means of local interactions (constraints). The GC reconstruction method aims to match the gradient and curvature constraints for the entire grid with those of the sample using conditional Monte Carlo simulations that honor the sample values. The GC reconstruction method does not assume a parametric form for the underlying probability distribution of the data. It is also computationally efficient and requires minimal user input, properties that make it suitable for automated processing of large data sets (e.g. remotely sensed images). The GC reconstruction performance is compared with established classification and interpolation methods for both synthetic and real world data. The impact of various factors such as domain size, degree of thinning, discretization, initialization, correlation properties, and noise on GC reconstruction performance are investigated by means of simulated random field realizations. An assessment of GC reconstruction performance on real data is conducted by removing randomly selected and contiguous groups of points from satellite rainfall data and an image of the lunar surface.