Bayesian Restoration of Digital Images Employing Markov Chain Monte Carlo a Review

We treat an image restoration problem with a Poisson noise chan- nel using a Bayesian framework. The Poisson randomness might be appeared in observation of low contrast object in the field of imaging. The noise observation is often hard to treat in a theo- retical analysis. In our formulation, we interpret the observation through the Poisson noise channel as a likelihood, and evaluate the bound of it with a Gaussian function using a latent variable method. We then introduce a...

Quantum fluctuation is introduced into the Markov random fields (MRF's) model for image restoration in the context of Bayesian approach. We investigate the dependence of the quantum fluctuation on the quality of BW image restoration by making use of statistical mechanics. We find that the maximum posterior marginal (MPM) estimate based on the quantum fluctuation gives a fine restoration in comparison with the maximum a posterior (MAP) estimate or the thermal fluctuation based...

Photon-limited images are often seen in fields such as medical imaging. Although the number of collected photons on an image sensor statistically follows Poisson distribution, this type of noise is intractable, unlike Gaussian noise. In this study, we propose a Bayesian restoration method of Poisson corrupted image using Integrated Nested Laplace Approximation (INLA), which is a computational method to evaluate marginalized posterior distributions of latent Gaussian models (L...

We attempt image restoration in the framework of the Baysian inference. Recently, it has been shown that under a certain criterion the MAP (Maximum A Posterior) estimate, which corresponds to the minimization of energy, can be outperformed by the MPM (Maximizer of the Posterior Marginals) estimate, which is equivalent to a finite-temperature decoding method. Since a lot of computational time is needed for the MPM estimate to calculate the thermal averages, the mean field meth...

Dynamical properties of image restoration and hyper-parameter estimation are investigated by means of statistical mechanics. We introduce an exactly solvable model for image restoration and derive differential equations with respect to macroscopic quantities. From these equations, we evaluate relaxation processes of the system to the equilibrium state. Our statistical mechanical approach also enable us to investigate the hyper-parameter estimation by means of maximization of ...

Bayesian methods are commonly applied to solve image analysis problems such as noise-reduction, feature enhancement and object detection. A primary limitation of these approaches is the computational complexity due to the interdependence of neighboring pixels which limits the ability to perform full posterior sampling through Markov chain Monte Carlo (MCMC). To alleviate this problem, we develop a new posterior sampling method that is based on modeling the prior and likelihoo...

Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational inference techniques. This has driven the development of statistical SP methods based on stochastic simulation and optimization. Stochastic simulation and optimization algorithms are computationally intensive tools for performing statistical inf...

This paper presents a new Expectation Propagation (EP) framework for image restoration using patch-based prior distributions. While Monte Carlo techniques are classically used to sample from intractable posterior distributions, they can suffer from scalability issues in high-dimensional inference problems such as image restoration. To address this issue, EP is used here to approximate the posterior distributions using products of multivariate Gaussian densities. Moreover, imp...

We investigated the use of the Bayesian inference to restore noise-degraded images under conditions of spatially correlated noise. The generative statistical models used for the original image and the noise were assumed to obey multi-dimensional Gaussian distributions whose covariance matrices are translational invariant. We derived an exact description to be used as the expectation for the restored image by the Fourier transformation and restored an image distorted by spatia...

The network flow optimization approach is offered for restoration of grayscale and color images corrupted by noise. The Ising models are used as a statistical background of the proposed method. The new multiresolution network flow minimum cut algorithm, which is especially efficient in identification of the maximum a posteriori estimates of corrupted images, is presented. The algorithm is able to compute the MAP estimates of large size images and can be used in a concurrent m...