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Numerical simulation of the functional approach in acoustic tomography problems

Acoustic tomography is a powerful tool for studying natural media that are transparent to acoustic waves. In particular, acoustic tomography methods are applied in medical diagnostics, tomography of an oceanic medium, and nondestructive testing of solid state structures. However, most of the known methods for solving acoustic tomography problems are approximate. For example, a linear approximation is used, and iterative procedures are implemented to improve reconstruction results.

In this talk we consider the numerical implementation and discuss the possibilities of the two-dimensional functional-analytic algorithm for the purposes of acoustic tomography. This algorithm is sufficiently rigorous ; it takes into account the multiple scattering processes and does not require either linearization of the model or iterations. Moreover, the discussed algorithm allows the joint reconstruction of different components of the scatterer, i.e. the vector and scalar inhomogeneities. As examples of vector inhomogeneities, one can consider the blood flow velocity in medical applications or the speed of currents in oceanographic problems ; the scalar components are presented by inhomogeneities of the sound speed and absorption coefficient. Results of numerical simulations show that the noise resistance of the considered functional algorithm is rather high for practice.

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