A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newtontype iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.

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Air pollution and postnatal lung function in preterm infantsDescriptor number: 14.3 Total word count: text 3494/3500 Today, approximately 10% of all infants are born prematurely, pre-existing vulnerability means that their lungs are potentially more susceptible to ambient air pollution. This is the first study showing that the effect size of low-to-moderate levels of air pollution exposure during pregnancy on postnatal lung function is significantly higher in preterm than in healthy term infants of similar postconceptional age of 44 weeks. The effect was best detectable in moderate to late preterm infants and these findings are highly relevant, since recent evidence indicates