Statistical Mechanics of Phase Unwrapping Problem by the g-Ising Model

We construct the statistical mechanical formulation for the problem of phase unwrapping, appearing in adaptive optics. We estimate the performance of our method using the replica theory and the time-dependent Ginzburg Landau theory for the infinite-range model. The replica theory clarifies that our method works well if we select appropriate model of the prior. Then, the time-dependent Ginzburg Landau theory estimates the dynamical property of the simulated annealing. These results are qualitatively confirmed by the Monte Carlo simulations for the realistic model.