Analysis of an iterative dynamic programming approach to 2-D phase unwrapping

We consider a novel Bayesian approach to 2-D phase unwrapping. The phase is unwrapped according to a maximum a posteriori (MAP) rule, where the estimate is made through a form of 2-D dynamic programming. The approach uses structured iterated conditional modes to achieve good performance without examining a large number of states in the dynamic system. We analyze the performance of the approach by transforming the problem to one of decoding a convolutional code. An example with seven states in the dynamic program is given. We derive an approximate upper bound for the probability of pixel error based on a Gaussian Markov random field model. Monte Carlo simulation results show that the bound offers a good approximation to the probability of error. A comparison with other phase unwrapping techniques on a real data set suggests that the new approach is superior.