Imaging reconstruction for light scattering from a tenuous random medium

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 a fractional diffusion equation which is studied using results from fractional calculus. This approach is 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. A Green´s function solution to the fractional diffusion equation is studied and a result derived that provides a model for an incoherent image generated by light scattering from a tenuous random medium. Applications include image enhancement of star fields and other cosmological bodies imaged through interstellar dust clouds. An example of this application is given.