DocumentCode
892032
Title
Valid parameter space of 2-D Gaussian Markov random fields
Author
Lakshmanan, Sridhar ; Derin, Haluk
Author_Institution
Dept. of Electr. & Comput. Eng., Michigan Univ., Dearborn, MI, USA
Volume
39
Issue
2
fYear
1993
fDate
3/1/1993 12:00:00 AM
Firstpage
703
Lastpage
709
Abstract
The valid parameter spaces of infinite- and finite-lattice (2-D noncausal) Gaussian Markov random fields (GMRFs) are investigated. For the infinite-lattice fields, the valid parameter space is shown to admit an explicit description; a procedure that yields the valid parameter space is presented. This procedure is applied to the second-order (neighborhood) 2-D GMRFs to obtain an explicit description of their valid parameter spaces. For the finite-lattice fields, it is shown that the valid parameter space does not admit a simple description; the conditions that ensure the positivity of the power spectrum are necessary, sufficient, and irreducible. The set of conditions for the infinite-lattice fields, however, serves as a good set of sufficient conditions for the finite-lattice case. The results readily extend to the class of d -D real and complex GMRFs
Keywords
Markov processes; image processing; information theory; lattice theory and statistics; random processes; 2-D Gaussian Markov random fields; finite-lattice fields; image analysis; infinite-lattice fields; power spectrum; sufficient conditions; valid parameter space; Geometry; Lattices; Markov random fields; Polynomials; Sufficient conditions;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.212307
Filename
212307
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