On the inversion of a generalized Radon transform of seismic type

We consider a generalized Radon transform (GRT) that integrates a function f(x1,x2) on R2 over a family of curves x2=u+sφ(x1−c) with respect to the variable x1, for a real valued continuous function φ on R, u,s∈R and a fixed c∈R. We investigate the inversion of the GRT via the inversion of the regular Radon transform (RT). Depending on some conditions on f and φ, 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.