• 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