You are accessing a document from the Department of Energy's (DOE) SciTech Connect. This site is a product of DOE's Office of Scientific and Technical Information (OSTI) and is provided as a public service. Visit OSTI to utilize additional information resources in energy science and technology. THE ATTENUATED RADON TRANSFORM: APPLICATION TO SINGLE-PHOTON EMISSION COMPUTED TOMOGRAPHY IN THE PRESENCE OF A VARIABLE ATTENUATING MEDIUM THE ATTENUATED RADON TRANSFORM: APPLICATION TO SINGLE-PHOTON EMISSION COMPUTED TOMOGRAPHY IN THE PRESENCE OF A VARIABLE ATTENUATING MEDIUM A paper copy of this document is also available for sale to the public from the National Technical Information Service, Springfield, VA at The properties of the attenuated Radon transform and its application to single-photon emission computed tomography (ECT) are analyzed in detail. In nuclear medicine and biological research, the objective of ECT is to describe quantitatively the position and strengths of internal sources of injected radiopharmaceuticals and radionuclides where the attenuation between the sources and detector is unknown. The problem is mathematically and practically quite different from well-known methods in transmission computed tomography (TCT) where only the attenuation is unknown. A mathematical structure using function theory and the theory of linear operators on Hilbert spaces is developed to better understand the spectral properties of the attenuated Radon transform. The continuous attenuated Radon transform is reduced to a matrix operator for discrete angular and lateral sampling, and the reconstruction problem reduces to a system of linear equations. For variable attenuation coefficients frequently found in imaging internal organs, the numerical methods developed in this paper involve iterative techniques of performing the generalized inverse. Its application to nuclear medicine is demonstrated by reconstructions of transverse sections of the brain, heart, and liver. Type in a name, or the first few letters of a name, in one or both of appropriate search boxes above and select the search button. An attempt will be made to match authors that most closely relate to the text you typed. No authors are currently selected. Choosing 'Select These Authors' will enter a blank value for author search in the parent form. Source.