The physical and mathematical aspects of inverse problems in radiation detection and applications

The inverse problem is the problem of converting detectable measurements into useful quantifiable indications. It is the problem of spectrum unfolding, image reconstruction, identifying a threat material, or devising a radiotherapy plan. The solution of an inverse problem requires a forward model that relates the quantities of interest to measurements. This paper explores the physical issues associated with formulating a radiation-transport forward model best suited for inversion, and the mathematical challenges associated with the solution of the corresponding inverse problem.