ИСТИНА

We consider the numerical implementation and discuss the possibilities of the two-dimensional functional-analytic algorithm for the reconstruction of vector inhomogeneities in the problems of acoustic tomography. As examples of vector inhomogeneities, one can consider the blood flow velocity in medical applications or the speed of currents in oceanographic problems. It is shown that reconstruction of a full vector field consisting of solenoidal and irrotational components is possible by using several (at least two) frequencies. In this case, together with the reconstruction of the solenoidal component, it becomes possible to reconstruct the function of divergence of the full vector field of the current speed and then to reconstruct the irrotational component based on the estimated divergence. As a result, the full vector field is obtained by summation of the solenoidal and irrotational components. Moreover, the discussed algorithm allows the joint reconstruction of different components of the scatterer, i.e. the vector and scalar inhomogeneities; the scalar components are presented by inhomogeneities of the sound speed and absorption coefficient. Meanwhile, the considered scatterer can significantly distort the incident field, being beyond the Born approximation.