Two-dimensional linear prediction: Autocorrelation arrays, minimum-phase prediction error filters, and reflection coefficient arrays

In this paper, a number of results in one-dimensional (1-D) linear prediction theory are extended to the two-dimensional (2-D) case. It is shown that the class of 2-D minimum mean-square linear prediction error filters with continuous support have the minimum-phase property and the correlation-matching property, and that they can be solved by means of a 2-D Levinson algorithm. A significant practical result to emerge from this theory is a reflection coefficient representation for 2-D minimum-phase filters. This representation provides a domain in which to construct 2-D filters, such that the minimum-phase condition is automatically satisfied.