Abstract: Apparatus and methods for estimating the internal structure of a physical domain (16), such as a volume of earth or of a human body, based on tomographic signals (18) having passed there through. Measurements of signals are inverted using an approximate extended Kalman filter to condition estimates of first and second spatial moments of stochastic random variables representing discrete estimates of one or more parameters describing the domain's internal structure. Measurement conditioning is alternated with upscaling in order to reduce the number of random variables used and also for the purpose of determining the geometry of the spatial regions of the domain represented by each of the random variables. Upscaling includes the use of cluster analysis for identification of random variables to merge, followed by random variable merging using random field union. Upscaling improves computational properties of the invention and can be used to identify discrete structural features in the domain.