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Purpose The paper addresses exact inversion of the integral transform, called the Compton (or cone) transform, that maps a three-dimensional (3-D) function to its integrals over conical surfaces in R 3 . Compton transform arises in passive detection of gamma-ray sources with a Compton camera, which has promising applications in medical and industrial imaging as well as in homeland security imaging and astronomy. Approach A generalized identity relating the Compton and the Radon transforms was formulated. The proposed relation can be used