We consider the problem of reconstructing a function from a finite collection of its line integrals. We discretize the function on a logarithmic polar grid. Assuming a special data collection scheme, we derive a large system of linear equations in the unknown discretized function values. This system has a very nice structure, which is used to decompose it into a number of reasonably small systems. After regularization, they can be solved using standard direct methods of numerical linear algebra. Results of experiments are shown.