Restoration of noisy images modeled by Markov random fields with Gibbs distribution

Iterative Decoding and Estimation of Two-Dimensional Channels with Memory

“…Instead we can use the local dependencies between bits to do a local optimization along the lines of the PDFE in [9], [10] or the partial binary segmentation algorithm of [12]. It is apparent that when V(x) is expressed as in (15), we can always choose the value of x i so that each term in the sum becomes positive, and thus the sum is non-decreasing.…”

“…In this paper, we will study systems where the information is disrupted by two dimensional bursts or clusters of bidirectional errors. Using techniques known from statistical physics [13] and digital image processing [12] combined with an iterative decoder, we develop a new method for correcting two dimensional cluster errors.…”

An Application of Digital Image Restoration Techniques to Error Control Coding

“…Instead we can use the local dependencies between bits to do a local optimization along the lines of the PDFE in Neifeld & King (1998);Neifield et al (1996) or the partial binary segmentation algorithm of Shridhar et al (1989). It is apparent that when V (x) is expressed as in (14), we can always choose the value of x i so that each term in the sum becomes positive, and thus the sum is non-decreasing.…”

“…One technique for describing such properties is the use of Markov random field theory which uses conditional probabilities to describe spatial dependencies in an n-dimensional system. This approach is based on the results of Shridhar, Ahmadi and El-Gabali who developed the applied techniques in Shridhar et al (1989), El-Gabali et al (1987), El-Gabali et al (1988) and El-Gabali et al (1990) but similar techniques are also presented in Geman & Geman (1993), Zhang (1993), Jeng & Woods (1991) and Chalmond (1988). The basis for all of these image restoration techniques is that simulated annealing is used to produce an estimate of the maximum a posteriori probability of the original image and the techniques has been extensively used for different purposes within the field of image processing, including image restoration, image segmentation, object identification and texture analysis.…”

“…In both of our cases, finding a global maximum of the conditional probabilities with respect to x would become computationally infeasible as the size of x increases. Instead, we use the local dependencies between bits to do a local optimization along the lines of the PDFE in Neifeld & King (1998); Neifield et al (1996) or the partial binary segmentation algorithm of Shridhar et al (1989).…”