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Phase unwrapping (PU) is a process to obtain the absolute value of a phase field from the wrapped one. Ideally, without phase noise, singularity, and aliasing problems, the phase information can be unwrapped easily. However, the phase data are always contaminated by noise and discontinuities, making the PU process more complicated. Hence, a suitable PU algorithm is required to address the problems appropriately. Markov Chain Monte Carlo (MCMC) Energy Minimization is usually used to partially remove phase noise. In this letter, the MCMC energy minimization that yields the unwrapped phase is shown. Furthermore, the capability of the proposed method to unwrap simulated and actual InSAR phase images is also demonstrated (Fujiyama Mount).