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We propose a novel Bayesian approach to 2-D phase unwrapping. Modeled as a first-order Gaussian Markov random field, the unwrapped phase is estimated according to a maximum a posteriori (MAP) rule. The estimate is made through a form of 2-D dynamic programming, using a series of row-by-row or column-by-column 1-D dynamic programming optimizations. Increasing the number of states in the dynamic system can improve the unwrapping performance, but also increases the computational complexity. Due to this trade-off, a structured iterated conditional mode (SICM) is used to achieve good performance without examining a large number of states in each iteration. A row-by-row followed by column-by-column raster scan takes previous estimates into account through a weighting. Other raster scans are also possible. The approach can be implemented efficiently in terms of memory usage due to the recyclable memory of dynamic programming. An example of the approach with seven states is given. Experimental results are compared to other algorithms including the least-squares method, the branch-cut method and Flynn's method, using interferometric SAR data. The new SICM algorithm is seen to be superior.