Invariant approximations and their application in MR-tomography

A method of reduction of the artefact influence on МR images using the theory of invariants is considered. This task is reduced to synthesis of groups of measuring transformations leaving dimension without distortions, i.e. solving the problem of invariant approximation of a given function by functions of less variables. The construction of allowable groups, calculation of invariants and functions using the invariants are described, examples are given.