Representation of a Function by Its Line Integrals, with Some Radiological Applications

作者：Allan M. Cormack · 发表于：Journal of Applied Physics · 年份：1963 · DOI：10.1063/1.1729798 · 被引用次数：1394 · 研究领域：Radiation Therapy and Dosimetry、Advanced Radiotherapy Techniques、Graphite, nuclear technology, radiation studies

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.