[Reconstruction of images in emission tomography]

The algorithm of back projection with filtration for exponential Radon transform leads to strong distortion for big diameter objects. The main reason for this distortion is mainly the exponential increase of errors in the quadrature formula for a weighed back projection operator. So it is sometimes more convenient to use the back Radon transform R-1 and then to correct the result, taking into account attenuation. For this purpose, the approximation formulas are given, which connect f and R-1 R mu f. An appropriate iteration reconstruction algorithm is also considered. Application exponential Radon identities for projection data analysis are also discussed.