The quantification problem of recovering the original material distribution from secondary ion mass spectrometry data is considered in this paper. It is an inverse problem, is ill-posed and hence it requires special technique for its solution. A thorough analysis of the concept of inverting SIMS data is included in this paper. The quantification problem is essentially an inverse diffusion or (classically) a backward heat conduction problem. In this paper an the operator-splitting method (that is proposed in a previous paper by the authors for the solution of inverse diffusion problems) is developed for the solution of the problem of recovering the orginal structure from the SIMS data. The method also employs the IMPETUS model for the simulation of the SIMS experiment. A detailed development of this inversion method is given. The resulting inversion method is considered alongside the maximum entropy method which has also been developed for the solution of similar problems. The inversion method of this paper is applied to SIMS data that arises from the IMPETUS model. The method is shown to recover a material structure that returns a SIMS profile identical to the input SIMS profile when it is passed through the IMPETUS code.