Maximizing Entropy of Pickard Random Fields for 2x2 Binary Constraints

Jacob Søgaard, Søren Forchhammer

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Abstract

This paper considers the problem of maximizing the entropy of two-dimensional (2D) Pickard Random Fields (PRF) subject to constraints. We consider binary Pickard Random
Fields, which provides a 2D causal finite context model and use it to define stationary probabilities for 2x2 squares, thus allowing us to calculate the entropy of the field. All possible binary 2x2 constraints are considered and all constraints are categorized into groups according to their properties. For constraints which can be modeled by a PRF approach and with positive entropy, we characterize and provide statistics of the maximum PRF entropy. As examples, we consider the well known hard square constraint along with a few other constraints.
Original languageEnglish
Title of host publicationProceedings of 2014 IEEE International Symposium on Information Theory
PublisherIEEE
Publication date2014
Pages2022-2026
DOIs
Publication statusPublished - 2014
Event2014 IEEE International Symposium on Information Theory - Honolulu, Hawaii, United States
Duration: 29 Jun 20144 Jul 2014

Conference

Conference2014 IEEE International Symposium on Information Theory
Country/TerritoryUnited States
CityHonolulu, Hawaii
Period29/06/201404/07/2014

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