Numerical solution of the identification problem for the attenuated Radon transform

The attenuated Radon transform serves as a mathematical tool for single-pho ton emission computerized tomography (SPECT). The identification problem fo r the attenuated Radon transform is to find the attenuation coefficient, wh ich is a parameter of the transform, from the values of the transform alone . Previous attempts to solve this problem used range theorems for the conti nuous attenuated/exponential Radon transform. we consider a matrix represen tation of the transform and formulate the corresponding discrete consistenc y conditions in the form of the orthogonal projection of the data vector on to the orthogonal complement of the column space of the matrix. The singula r value decomposition is applied to compute the orthogonal projector and it s Frechet derivative. The numerical algorithm suggested is based on the New ton method with the Tikhonov regularization. Results of numerical experimen ts and inversion of the measured SPECT data are considered.