Modeling of Problem Reconstruction Function by its Integral Data on a Family of Circles

We consider the problem of reconstruction a function if its integrals over families of circles are known. An analytical representation is obtained for the Fourier image in the first variable of the desired function. This implies a statement about the strong incorrectness of the solution to the problem. Based on the idea of A.N. Tikhonov on the regularization of ill-posed problems, a sequence of approximate solutions to the exact solution of the problem is constructed.