Semi-Huber Half Quadratic Function and Comparative Study of Some MRFs for Bayesian Image Restoration

The present work introduces an alternative method to deal with digital image restoration into a Bayesian framework, particularly, the use of a new half-quadratic function is proposed which performance is satisfactory compared with respect to some other functions in existing literature. The bayesian methodology is based on the prior knowledge of some information that allows an efficient modelling of the image acquisition process. The edge preservation of objects into the image while smoothing noise is necessary in an adequate model. Thus, we use a convexity criteria given by a semi-Huber function to obtain adequate weighting of the cost functions (half-quadratic) to be minimized. The principal objective when using Bayesian methods based on the Markov Random Fields (MRF) in the context of image processing is to eliminate those effects caused by the excessive smoothness on the reconstruction process of image which are rich in contours or edges. A comparison between the new introduced scheme and other three existing schemes, for the cases of noise filtering and image deblurring, is presented. This collection of implemented methods is inspired of course on the use of MRFs such as the semi-Huber, the generalized Gaussian, the Welch, and Tukey potential functions with granularity control. The obtained results showed a satisfactory performance and the effectiveness of the proposed estimator with respect to other three estimators

Unsupervised bayesian convex deconvolution based on a field with an explicit partition function

This paper proposes a non-Gaussian Markov field with a special feature: an explicit partition function. To the best of our knowledge, this is an original contribution. Moreover, the explicit expression of the partition function enables the development of an unsupervised edge-preserving convex deconvolution method. The method is fully Bayesian, and produces an estimate in the sense of the posterior mean, numerically calculated by means of a Monte-Carlo Markov Chain technique. The approach is particularly effective and the computational practicability of the method is shown on a simple simulated example

Semi-Huber quadratic function and comparative study of some MRFs for Bayesian image restoration

The present work introduces an alternative method to deal with digital image restoration into a Bayesian framework, particularly, the use of a new half-quadratic function is proposed which performance is satisfactory compared with respect to some other functions in existing literature. The bayesian methodology is based on the prior knowledge of some information that allows an efficient modelling of the image acquisition process. The edge preservation of objects into the image while smoothing noise is necessary in an adequate model. Thus, we use a convexity criteria given by a semi-Huber function to obtain adequate weighting of the cost functions (half-quadratic) to be minimized. The principal objective when using Bayesian methods based on the Markov Random Fields (MRF) in the context of image processing is to eliminate those effects caused by the excessive smoothness on the reconstruction process of image which are rich in contours or edges. A comparison between the new introduced scheme and other three existing schemes, for the cases of noise filtering and image deblurring, is presented. This collection of implemented methods is inspired of course on the use of MRFs such as the semi-Huber, the generalized Gaussian, the Welch, and Tukey potential functions with granularity control. The obtained results showed a satisfactory performance and the effectiveness of the proposed estimator with respect to other three estimators

A Comparative Study of Some Markov Random Fields and Different Criteria Optimization in Image Restoration

The present chapter illustrates the use of some recent alternative methods to deal with digital image filtering and restoration. This collection of methods is inspired on the use of Markov Random Fields (MRF), which introduces prior knowledge of information that will allow, more efficiently, modeling the image acquisition process. The methods based on the MRF are analyzed and proposed into a Bayesian framework and their principal objective is to eliminate noise and some effects caused by excessive smoothness on the reconstruction process of images which are rich in contours or edges. In order to preserve object edges into the image, the use of certain convexity criteria into the MRF is proposed obtaining adequate weighting of cost functions in cases where discontinuities are remarked and, even better, for cases where such discontinuities are very smooth

New approach of entropy estimation for robust image segmentation

In this work we introduce a new approach for robust image segmentation. The idea is to combine two strategies within a Bayesian framework. The first one is to use a Márkov Random Field (MRF), which allows to introduce prior information with the purpose of preserve the edges in the image. The second strategy comes from the fact that the probability density function (pdf) of the likelihood function is non Gaussian or unknown, so it should be approximated by an estimated version, and for this, it is used the classical non-parametric or kernel density estimation. This two strategies together lead us to the definition of a new maximum a posteriori (MAP) estimator based on the minimization of the entropy of the estimated pdf of the likelihood function and the MRF at the same time, named MAP entropy estimator (MAPEE). Some experiments were made for different kind of images degraded with impulsive noise and the segmentation results are very satisfactory and promising

Development Of A High Performance Mosaicing And Super-Resolution Algorithm

In this dissertation, a high-performance mosaicing and super-resolution algorithm is described. The scale invariant feature transform (SIFT)-based mosaicing algorithm builds an initial mosaic which is iteratively updated by the robust super resolution algorithm to achieve the final high-resolution mosaic. Two different types of datasets are used for testing: high altitude balloon data and unmanned aerial vehicle data. To evaluate our algorithm, five performance metrics are employed: mean square error, peak signal to noise ratio, singular value decomposition, slope of reciprocal singular value curve, and cumulative probability of blur detection. Extensive testing shows that the proposed algorithm is effective in improving the captured aerial data and the performance metrics are accurate in quantifying the evaluation of the algorithm

Ensemble Kalman methods for high-dimensional hierarchical dynamic space-time models

We propose a new class of filtering and smoothing methods for inference in high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models. The main idea is to combine the ensemble Kalman filter and smoother, developed in the geophysics literature, with state-space algorithms from the statistics literature. Our algorithms address a variety of estimation scenarios, including on-line and off-line state and parameter estimation. We take a Bayesian perspective, for which the goal is to generate samples from the joint posterior distribution of states and parameters. The key benefit of our approach is the use of ensemble Kalman methods for dimension reduction, which allows inference for high-dimensional state vectors. We compare our methods to existing ones, including ensemble Kalman filters, particle filters, and particle MCMC. Using a real data example of cloud motion and data simulated under a number of nonlinear and non-Gaussian scenarios, we show that our approaches outperform these existing methods