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

This paper presents a new variational inference framework for image restoration and a convolutional neural network (CNN) structure that can solve the restoration problems described by the proposed framework. Earlier CNN-based image restoration methods primarily focused on network architecture design or training strategy with non-blind scenarios where the degradation models are known or assumed. For a step closer to real-world applications, CNNs are also blindly trained with t...

Diffusion models (DMs) have recently shown outstanding capability in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on approximations in the generative process to be generic to different inverse problems, leading to inaccurate sample distributions that deviate from the target posterior defined within the Bayesian framework. To harness the generative power of DMs whil...

Natural images are often affected by random noise and image denoising has long been a central topic in Computer Vision. Many algorithms have been introduced to remove the noise from the natural images, such as Gaussian, Wiener filtering and wavelet thresholding. However, many of these algorithms remove the fine edges and make them blur. Recently, many promising denoising algorithms have been introduced such as Non-local Means, Fields of Experts, and BM3D. In this paper, we ex...

Acquired images for medical and other purposes can be affected by noise from both the equipment used in the capturing or the environment. This can have adverse effect on the information therein. Thus, the need to restore the image to its original state by removing the noise. To effectively remove such noise, pre knowledge of the type of noise model present is necessary. This work explores different noise removal filters by first introducing noise to an image and then applying...

In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding inversion problem is presented. Then, after showing the inadequacy of the classical analytical and least square methods for these ill posed inverse problems, a Bayesian estimation framework is presented which can handle, in a coherent way, all the...

In this paper, an algorithm is proposed for Image Restoration. Such algorithm is different from the traditional approaches in this area, by utilizing priors that are learned from similar images. Original images and their degraded versions by the known degradation operators are utilized for designing the Quantization. The code vectors are designed using the blurred images. For each such vector, the high frequency information obtained from the original images is also available....

Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the maximum likelihood (ML) or maximum a posteriori (MAP) estimators, or by performing a multi-dimensional integration, as in the minimum mean squared error (MMSE) estimators. Unfortunately, analytical expressions for these estimators cannot be...

We address the image restoration problem under Poisson noise corruption. The Kullback-Leibler divergence, which is typically adopted in the variational framework as data fidelity term in this case, is coupled with the second-order Total Generalized Variation (TGV$^2$). The TGV$^2$ regularizer is known to be capable of preserving both smooth and piece-wise constant features in the image, however its behavior is subject to a suitable setting of the parameters arising in its exp...

Noise removal from images is a part of image restoration in which we try to reconstruct or recover an image that has been degraded by using apriori knowledge of the degradation phenomenon. Noises present in images can be of various types with their characteristic Probability Distribution Functions (PDF). Noise removal techniques depend on the kind of noise present in the image rather than on the image itself. This paper explores the effects of applying noise reduction filters...

Markov Chain Monte Carlo based Bayesian data analysis has now become the method of choice for analyzing and interpreting data in almost all disciplines of science. In astronomy, over the last decade, we have also seen a steady increase in the number of papers that employ Monte Carlo based Bayesian analysis. New, efficient Monte Carlo based methods are continuously being developed and explored. In this review, we first explain the basics of Bayesian theory and discuss how to s...