Document Type

Conference Paper

Rights

Available under a Creative Commons Attribution Non-Commercial Share Alike 4.0 International Licence

Disciplines

Applied mathematics

Publication Details

Irish Signals and Systems Conference, ISSC 2009, UCD, June 10-11th 2009 , University College Dublin,

Abstract

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.

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