Abstract: We constructed a method of noise reduction for
JPEG-compressed image based on Bayesian inference using the
maximizer of the posterior marginal (MPM) estimate. In this method,
we tried the MPM estimate using two kinds of likelihood, both of
which enhance grayscale images converted into the JPEG-compressed
image through the lossy JPEG image compression. One is the
deterministic model of the likelihood and the other is the probabilistic
one expressed by the Gaussian distribution. Then, using the Monte
Carlo simulation for grayscale images, such as the 256-grayscale
standard image “Lena" with 256 × 256 pixels, we examined the
performance of the MPM estimate based on the performance measure
using the mean square error. We clarified that the MPM estimate via
the Gaussian probabilistic model of the likelihood is effective for
reducing noises, such as the blocking artifacts and the mosquito noise,
if we set parameters appropriately. On the other hand, we found that
the MPM estimate via the deterministic model of the likelihood is not
effective for noise reduction due to the low acceptance ratio of the
Metropolis algorithm.
Abstract: We investigated statistical performance of Bayesian inference using maximum entropy and MAP estimation for several models which approximated wave-fronts in remote sensing using SAR interferometry. Using Monte Carlo simulation for a set of wave-fronts generated by assumed true prior, we found that the method of maximum entropy realized the optimal performance around the Bayes-optimal conditions by using model of the true prior and the likelihood representing optical measurement due to the interferometer. Also, we found that the MAP estimation regarded as a deterministic limit of maximum entropy almost achieved the same performance as the Bayes-optimal solution for the set of wave-fronts. Then, we clarified that the MAP estimation perfectly carried out phase unwrapping without using prior information, and also that the MAP estimation realized accurate phase unwrapping using conjugate gradient (CG) method, if we assumed the model of the true prior appropriately.
Abstract: On the basis of Bayesian inference using the
maximizer of the posterior marginal estimate, we carry out phase
unwrapping using multiple interferograms via generalized mean-field
theory. Numerical calculations for a typical wave-front in remote
sensing using the synthetic aperture radar interferometry, phase
diagram in hyper-parameter space clarifies that the present method
succeeds in phase unwrapping perfectly under the constraint of
surface- consistency condition, if the interferograms are not corrupted
by any noises. Also, we find that prior is useful for extending a phase
in which phase unwrapping under the constraint of the
surface-consistency condition. These results are quantitatively
confirmed by the Monte Carlo simulation.
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.