Sub-pixel Mapping of Coarse Satellite Remote Sensing Images with Stochastic Simulations from Training Images

Super-resolution or sub-pixel mapping is the process of providing fine scale land cover maps from coarse-scale satellite sensor information. Such a procedure calls for a prior model depicting the spatial structures of the land cover types. When available, an analog of the underlying scene (a training image) may be used for such a model. The single normal equation simulation algorithm (SNESIM) allows extracting the relevant pattern information from the training image and uses that information to downscale the coarse fraction data into a simulated fine scale land cover scene. Two non-exclusive approaches are considered to use training images for super-resolution mapping. The first one downscales the coarse fractions into fine-scale pre-posterior probabilities which is then merged with a probability lifted from the training image. The second approach pre-classifies the fine scale patterns of the training image into a few partition classes based on their coarse fractions. All patterns within a partition class are recorded by a search tree; there is one tree per partition class. At each fine scale pixel along the simulation path, the coarse fraction data is retrieved first and used to select the appropriate search tree. That search tree contains the patterns relevant to that coarse fraction data. To ensure exact reproduction of the coarse fractions, a servo-system keeps track of the number of simulated classes inside each coarse fraction. Being an under-determined stochastic inverse problem, one can generate several super resolution maps and explore the space of uncertainty for the fine scale land cover. The proposed SNESIM sub-pixel resolution mapping algorithms allow to: (i) exactly reproduce the coarse fraction, (ii) inject the structural model carried by the training image, and (iii) condition to any available fine scale ground observations. Two case studies are provided to illustrate the proposed methodology using Landsat TM data from southeast China.