A method is given of finding a real function in a finite region of a plane given its line integrals along all straight lines intersecting the region. The solution found is applicable to three problems of interest for precise radiology and radiotherapy: (1) the determination of a variable x-ray absorption coefficient in two dimensions; (2) the determination of the distribution of positron annihilations when there is an inhomogeneous distribution of the positron emitter in matter; and (3) the determination of a variable density of matter with constant chemical composition, using the energy loss of charged particles in the matter.
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A. M. Cormack (1963) studied this question.
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