Invariant of group of random samples mappings in the sample space with lattice properties

Authors

DOI:

https://doi.org/10.3103/S0735272715090046

Keywords:

sample space, sample, invariant, lattice, L-group

Abstract

The characteristic of statistical interrelationship of random samples has been obtained, that is invariant with respect to the group of their mappings and that has been developed based upon the sample space with lattice properties. The possibility of its utilization for the analysis of quality of the images processing is being investigated.

References

GONZALES, R.C.; WOODS, R.E. Digital Image Processing, 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2002, 1072 p.

LIM, J.S. Two-Dimensional Signal and Image Processing. Englewood Cliffs, NJ: Prentice Hall, 1989, 468 p.

PRATT, W.K. Digital Image Processing, 3d ed. N.Y.: John Wiley & Sons Inc., 2001, 738 p.

KENDALL, M.G.; STUART, A. Advanced Theory of Statistics. Macmillan Pub. Co., 1983.

CRAMER, H. Mathematical Methods of Statistics. Princeton University Press, 1999.

POPOV, A.A. Invariants of one-to-one functional transformation of random processes. Izv. Vyssh. Uchebn. Zaved., Radioelektron., 2007, v.50, n.11, p.35-43 [Radioelectron. Commun. Syst., 2007, v.50, n.11, p.609-615, DOI: http://dx.doi.org/10.3103/S0735272707110040].

BIRKHOFF, G. Lattice Theory, 3rd ed. Providence: Amer. Math. Soc., 1940.

ARTAMONOV, V.A.; SALIY, V.N.; SKORNYAKOV, L.A.; ET AL. General Algebra, Vol. 2. Moscow: Nauka, 1991 [in Russian, ed. by L. A. Skornyakov].

ARTAMONOV, V.A.; SALIY, V.N.; SKORNYAKOV, L.A.; ET AL. General Algebra, Vol. 1. Moscow: Nauka, 1991 [in Russian, ed. by L. A. Skornyakov].

TIKHONOV, V.I. Statistical Radio Engineering. Moscow: Radio i Svyaz’, 1982 [in Russian].

BOROVKOV, A.A. Mathematical Statistics. Novosibirsk: Nauka, 1997 [in Russian].

Published

2015-09-21

Issue

Section

Research Articles