Abstract
This paper generalizes time-discrete autoregressive source coding results of rate-distortion theory to two dimensions. A 2-D discrete autoregressive source is defined and shown to produce a 2-D widesense Markovian field. The rate distortion function of the source is then obtained under assumption of Gaussian field statistics and a squared error fidelity criterion. A procedure for generating an ensemble of 2-D codewords whose statistics satisfy the variational equations for R(D) is given. These 2-D codewords are, by space-time mappings, 1-D tree codes, and it is noted that a tree coding theorem of Jelinek, Berger, Davis and Hellman applies. The problem of instrumenting nearly optimum 2-D sequential encoding is discussed briefly. The paper stresses potential application to image coder design.
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