Abstract
An exact form of the inversion formula for the attenuated Radon transform with constant attenuation in a convex domain for use in Single-Photon Computerized Tomography is presented. This problem is reduced to solving a generalized Abel integral equation and the conditions for the existence of a unique continuous solution are given. Implementation of this method involves a preprocessing step (modified attenuated Radon transform), a convolution by an attenuation-dependent function and a weighted backprojection. Therefore, only slight modifications of existing reconstruction algorithms are needed. If the attenuation is zero, this formula reduces to Radon's original inversion formula. When attenuation is not constant, the conditions for a unique continuous solution can be established with a similar approach. Many results found empirically by previous authors are consistent with this theory.
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