An efficiency estimate for a hierarchical reconstruction method in the problem of reconstructing the locations of discrete scattering centers from a set of projections

Abstract

Under consideration is the problem of determining a maximal set for a family of points from a restricted collection of their two-dimensional projections. This problem arises naturally in the applications of physical hydroaerodynamics to optical diagnostics of real liquid and gas flows by measuring the instantaneous velocity fields in a flow volume. We propose some methods for reconstructing the original set and determining the sufficiency of measurement for solving uniquely the inverse problem for parallel and perspective projections. We statistically evaluate the efficiency of the reconstruction method.