Method of the principal informative components for reconstruction problems

A method for the solution of the reconstruction problems of signal processing theory is proposed. The method is based on the series expansion of reconstructing fields in special basis, which is formed from eigenfunctions of Fisher´s information operator. These functions, which satisfy certain conditions, are referred to as principal informative components (PIC). It is shown that the proposed method produces a smaller reconstruction error in comparison with earlier known methods. Reconstruction problems for deterministic and random fields are investigated. General expressions for systematic and statistical errors are obtained. Optimal properties of eigenfunctions of Fisher´s information operator are derived. Conditions for selection of PIC are given. Relations between the proposed method and both the Karhunen-Loeve expansion and singular value decomposition method are established