Random Fields Estimation Theory: 48 (Pitman Monographs & Surveys in Pure & Applied Mathematics.) - Hardcover

Ramm, A. G.

Hardcover

ISBN 10: 0582037689 ISBN 13: 9780582037687

Publisher: Longman Higher Education, 1990

Synopsis

This book presents the analytical theory of random fields estimation by the criterion of minimum of variance. The theory generalizes the classical Wiener theory to the case of random functions of several variables, that is, random fields. There are many applied problems which can be formulated as random fields estimation problems. Such problems arise in optics and TV signal processing, geophysics, underwater acoustics, image processing in photography to mention a few. The author developed the theory presented in this monograph in a series of papers which are mentioned in the bibliographical notes. Analytical formulas for the optimal filters are given. These filters are determined generically by distributional kernels. The singularities of the optimal filters are studied in detail and the results are in a final form for the class of random fields introduced in this monograph. A numerical method is developed for solving the basic integral equation of the estimation theory in distributions. A number of applied problems is discussed and a considerable amount of the the auxiliary material from functional analysis and probability theory has to be included.

This material is given partly as a reference material, without proofs, and partly with proofs, especially in the cases when this material cannot be found in the literature. The book should be of particlar interest to engineers and geophysicists.

Edition details

• Publisher: Longman Higher Education
• Publication date: 1990
• Language: English
• ISBN 10: 0582037689
• ISBN 13: 9780582037687
• Binding: Hardcover
• Edition number: 1
• Number of pages: 256