A multiresolution approach for modeling of diffusion phenomenon

A multiresolution approach is developed to model the spatio-temporal dispersion of geospatial data such as evolution of population, epidemics, dispersion of chemical/biological agents subsequent to natural or man-made disasters, etc. The basic idea is to make use of diffusion equations with spatially and temporally varying diffusion coefficient to model the evolution of geospatial activities. At the heart of our approach is a recently developed powerful averaging process that allows construction of a global family of local independent approximations with a desired order of continuity and quantifying error bounds. The ability to have independent local approximations enables intuitive and effecient approximation with high accuracy and compression ratio. Numerical simulation results are presented to show the efficacy of the presented ideas.