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Structures are abundant in both natural and human-made environments andusually studied in the form of images or scattering patterns. To characterizestructures a huge variety of descriptors is available spanning from porosity toradial and correlation functions. In addition to morphological structuralanalysis, such descriptors are necessary for stochastic reconstructions,stationarity and representativity analysis. The most important characteristicof any such descriptor is its information content - or its ability to describethe structure at hand. For example, from crystallography it is well known thatexperimentally measurable $S_2$ correlation function lacks necessaryinformation content to describe majority of structures. The information contentof this function can be assessed using Monte-Carlo methods only for very small2D images due to computational expenses. Some indirect quantitative approachesfor this and other correlation function were also proposed. Yet, to date nomethodology to obtain information content for arbitrary 2D or 3D image isavailable. In this work, we make a step toward developing a general frameworkto perform such computations analytically. We show, that one can assess theentropy of a perturbed random field and that stochastic perturbation of fieldscorrelation function decreases its information content. In addition toanalytical expression, we demonstrate that different regions of correlationfunction are in different extent informative and sensitive for perturbation.Proposed model bridges the gap between descriptor-based heterogeneous mediareconstruction and information theory and opens way for computationallyeffective way to compute information content of any descriptor as applied toarbitrary structure.

Towards effective information content assessment: analytical derivation  of information loss in the reconstruction of random fields with model  uncertainty