**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32731

##### Maximizer of the Posterior Marginal Estimate of Phase Unwrapping Based On Statistical Mechanics of the Q-Ising Model

**Authors:**
Yohei Saika,
Tatsuya Uezu

**Abstract:**

We constructed a method of phase unwrapping for a typical wave-front by utilizing the maximizer of the posterior marginal (MPM) estimate corresponding to equilibrium statistical mechanics of the three-state Ising model on a square lattice on the basis of an analogy between statistical mechanics and Bayesian inference. We investigated the static properties of an MPM estimate from a phase diagram using Monte Carlo simulation for a typical wave-front with synthetic aperture radar (SAR) interferometry. The simulations clarified that the surface-consistency conditions were useful for extending the phase where the MPM estimate was successful in phase unwrapping with a high degree of accuracy and that introducing prior information into the MPM estimate also made it possible to extend the phase under the constraint of the surface-consistency conditions with a high degree of accuracy. We also found that the MPM estimate could be used to reconstruct the original wave-fronts more smoothly, if we appropriately tuned hyper-parameters corresponding to temperature to utilize fluctuations around the MAP solution. Also, from the viewpoint of statistical mechanics of the Q-Ising model, we found that the MPM estimate was regarded as a method for searching the ground state by utilizing thermal fluctuations under the constraint of the surface-consistency condition.

**Keywords:**
Bayesian inference,
maximizer of the posterior
marginal estimate,
phase unwrapping,
Monte Carlo simulation,
statistical mechanics

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1334177

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