In this paper, we consider the basis for describing strong scattering in terms of diffusive processes based on the diffusion equation. Intermediate strength scattering is then considered in terms of an (inhomogeneous) fractional diffusion equation which is studied using results from fractional calculus. The diffusion equation for modelling intermediate strength scattering is based on a generalization of the diffusion equation to fractional form. This equation can be justified in terms of the generalization of a random walk model with no statistical bias in the phase to a random walk that has a phase bias and is thus, only ‘partially’ or ‘fractionally’ diffusive. Green’s function solutions to the fractional diffusion equation are studied and results derived that provide a model for an incoherent image obtained from light scattered by a tenuous medium. Applications include image enhancement of star fields and other cosmological bodies imaged through interstellar dust clouds, an example of which is provided in this paper.

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