Generalized and attenuated radon transforms: restorative approach to the numerical inversion

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Abstract
The problem of the function reconstruction on its line integrals with known weight function is considered. The approach studied consists of treating the attenuated projections by the radon transform inversion formula and considering the result of the inversion as a distorted image. A helpful formula describing the distortion is obtained. The norm of the distortion operator is estimated and several iterative restoration algorithms based on the integral transfers are investigated. The results of the numerical inversion of the attenuated radon transform are presented to demonstrate the features of the algorithms.

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