Geostatistical inverse modeling for super-resolution mapping of continuous spatial processes

Abstract

The increasing availability of satellite images derived from multiple sensors creates opportunities for broader spatial and temporal coverage but also methodological challenges. We present a geostatistical inverse modeling (GIM) approach for merging coarse-resolution images with variable resolutions and for super-resolution (i.e., predictions at the sub-pixel level) mapping of continuous spatial processes. GIM can explicitly account for the differences in spatial supports of multiple datasets. The restricted maximum likelihood method was used for parameter estimations associated with the change-of-support problem. We used GIM to produce both spatial predictions of a target image and prediction uncertainties, while preserving the values of original measurements. GIM is totally data driven, and covariance parameters for a target resolution can be directly derived from measurements. We also developed a moving-window GIM approach to accommodate spatial nonstationarity and reduce computational burden associated with large image data. First, we demonstrated GIM and moving-window GIM on synthetic images. Aggregated synthetic images with variable resolutions were merged to produce a single resolution image. The results show that the two approaches can produce accurate spatial predictions and generate prediction uncertainties. Second, we applied moving-window GIM for merging aerosol optical depth (AOD) data with variable resolutions, which were derived from two satellite sensors. The modeling results show that moving-window GIM can be applied for merging complementary AOD data from two sensors and for super-resolution mapping of global AOD distributions. Therefore, we can conclude that GIM is a practical solution for merging complementary coarse-resolution images and for super-resolution mapping of continuous spatial processes.