We develop efficient iterative methods for solving inverse problems of wave tomography in models incorporating both diffraction effects and attenuation. In the inverse problem the aim is to reconstruct the velocity structure and the function that characterizes the distribution of attenuation properties in the object studied. We prove mathematically and rigorously the differentiability of the residual functional in normed spaces, and derive the corresponding formula for the Fréchet derivative.
P. Verezemskaya, N. Tilinina, S. Gulev, I. A. Renfrew, and M. Lazzara. Southern ocean mesocyclones and polar lows from manually tracked satellite mosaics. Geophysical Research Letters, 44, 2017. [ DOI ]
E. V. Katkova, A. V. Onufriev, B. Aguilar, and V. B. Sulimov. Accuracy comparison of several common implicit solvent models and their implementations in the context of protein-ligand binding. Journal of Molecular Graphics and Modelling, 72:70–80, 2017. [ DOI ]
A. V. Tikhonravov, I. V. Kochikov, and A. G. Yagola. Error self-compensation mechanism in the optical coating production with direct broad band monitoring. Optics Express, 25(22):27225–27233, 2017. [ DOI ]