Abstract
The possibility of improving the efficiency of the solution of acoustic tomography problems is shown in the present article. It is obtained due to the representation of the field of medium parameters to be restored in the finite-dimensional basis of special form. The proposed approach is based on extreme properties of eigenfunctions of the Fisher's information operator. The coordinate basis of medium characteristics field, formed by these functions, provides minimization of a reconstruction error. The existence of the optimal dimension of the basis, which provides maximum precision of measurements at given conditions of acoustic experiment, is established. The criterion of selection of optimal basis functions, which takes into account both the statistical and systematic components of the resulting error, is formulated. A projective approach to the development of the coordinate basis is also proposed. It combines the advantages of a purely physical origin (clearness, economy) and a statistical-informational approach (minimization of errors). The structure of the information operator for the typical models of acoustic signal fields is investigated. The effectiveness of the proposed approach is illustrated by examples from the ocean acoustic tomography.