Data partionning method for convergent volterra inverse scattering series

We report a novel method to improve the convergence of the Volterra Inverse Scattering Series (VISS) presented in (Lesage et al., 2013, 2014). The VISS approach consists in combining two ideas: the renormalization of the Lippmann-Schwinger equation to obtain a Volterra equation framework (Kouri and Vijay, 2003) and the formal series expansion using reflection coefficients (Moses, 1956). The renormalization ensures that the corresponding Born-Neumann series solution is absolutely convergent independent of the strength of the coupling characterizing the interaction. However, the expansion of the interaction in "orders of the data" limits the VISS convergence to low velocity contrast. We introduce a geometrical series expansion to partition the reflection data. We show that for a given velocity contrast for which the VISS diverges, there is a choice of the partitionning series common ratio that permits an optimal series convergence.