  A new algorithm for the stable solution of a three-dimensional scalar inverse
problem of acoustic sounding of an inhomogeneous medium in a cylindrical region
is proposed. The data of the problem is the complex amplitude of the wave
field, measured outside the region of acoustic inhomogeneities in a cylindrical
layer. Using the Fourier transform and Fourier series, the inverse problem is
reduced to solving a set of one-dimensional Fredholm integral equations of the
first kind, to the subsequent calculation of the complex amplitude of the wave
field in the region of inhomogeneity, and then to finding the required sound
velocity field in this region. The algorithm allows solving the inverse problem
on a personal computer of average performance for sufficiently fine
three-dimensional grids in tens of seconds. A numerical study of the accuracy
of the proposed algorithm for solving model inverse problems at various
frequencies is carried out, and the issues of stability of the algorithm with
respect to data perturbations are investigated.
