Bayesian estimation of soil parameters from remote sensing data

Considers the problem of finding a mathematically optimal algorithm to estimate soil parameters based on radar and/or other measurements. Specifically, given measurements m₁, m₂ , ..., m_J representing radar cross-sections of a given resolution element at different polarizations and/or different frequency bands, and given an approximate model expressing the dependence of these measurements on the dielectric constant ε and the r.m.s. surface height h of the corresponding resolution element, the authors would like to make an “optimal” estimate of the actual ε and h that gave rise to the particular m₁, m₂, ... observed. By “optimal” they mean that their algorithm should produce estimates that are, on average, as close as possible to the actual values. To obtain such an algorithm, they assume that they have at their disposal a data catalogue consisting of careful measurements of the soil parameters ε and h, on one hand, and the corresponding remote sensing data m₁, m₂, etc., on the other. They also assume that they have used this data to write down, for each j, an approximate formula which computes an average value of m_j to associate to the corresponding values of ε, h. Rather than throw away the data catalogue at this stage, and use the average formulas in a deterministic fashion to solve the inverse problem, they propose to use the data catalogue more fully and quantify the spread of the measurements about the average formula, then incorporate this information into the inversion algorithm. This paper describes how they accomplish this using a Bayesian approach