Iterative inversion schemes for the Born series and the reduced inverse Born series

TL;DR

This paper introduces a fast iterative scheme for inverting the Born series in nonlinear inverse problems, improving computational efficiency and relating it to the reduced inverse Born series.

Contribution

It develops a Newton-type iterative method for the Born series and introduces a faster variant, connecting it to the reduced inverse Born series.

Findings

The fast iterative scheme reduces computational cost.

The relation between the scheme and the reduced inverse Born series is established.

The method improves inversion accuracy without linearization.

Abstract

Nonlinear inverse problems have complicated landscapes. Hence the calculation with naive iterative schemes (e.g., Gauss-Newton or conjugate gradients) is trapped in local minima. The (first) Born approximation can avoid this trapping but linearization is required. Nonlinear inverse problems can be solved without linearization by means of the inverse Born series. However, the computational cost of its standard recursive implementation grows exponentially when nonlinear terms are taken into account. In this work we revisit a Newton-type iterative scheme to invert the Born series and develop a fast variant. The relation between this fast scheme and the reduced inverse Born series is shown.