Satellite Image Restoration using the VMCA Model

Abstract

One of the most common patterns of the geographic landscape is the fractal or nearfractal form. Unfortunately, most traditional methods of spatial interpolation assume some type of continuous and regionalizeable variation of the underlying geographic form, an assumption at odds with the observed fractal properties of many landscapes. An extremely simple iterative algorithm, the voter model cellular automata (CA), produces discontinuous fractal patterns useful for interpolation while at the same preserving a realistic amount of spatial autocorrelation, extracted from neighboring existing data, also found in these landscapes. This adaptive algorithm is based on the principle of iteratively interpolating a missing data point using the value of a randomly selected neighbor cell. The model can also be extended to interpolate field-like variables by adding random deviations from the randomly chosen neighbor cell value. In this paper we explore the effect of satellite image restoration using a simple VMCA over obscured by clouds areas. This model is computationally advantageous, given its localty and restricted underlying computational model. Thus, an adequate computer implementation may perform significantly faster than other restoration methods, with roughly similar overall results. Also the local/scalable/parallelizable nature of CAs allows hardware FPGA implementation that might be embedded within the imager devices in satellites and remote sensors. On the other end, a GPU implementation might take advantage of highly specialized parallel processors capablde of restoring huge images in real time.