On the inversion of a generalized Radon transform of seismic type

We consider a generalized Radon transform (GRT) that integrates a function f (x(1), x(2)) on R-2 over a family of curves x(2) = u + s phi(x(1) - c) with respect to the variable x(1), for a real valued continuous function phi on R, u, s is an element of R and a fixed c is an element of R. We investigate the inversion of the GRT via the inversion of the regular Radon transform (RT). Depending on some conditions on f and phi, we obtain some inversion formulas and also describe a method for the numerical reconstruction of f from its GRT. Numerical results are presented to demonstrate the feasibility of the proposed method. (C) 2017 Elsevier Inc. All rights reserved.