Data-driven restoration of degraded binary MRF images using EM method

Appendix B: Elementary Probability Theory

“…An event [1,5,6] is a subset A of the sample space S, i.e., it is a set of possible outcomes. If the outcome of an experiment is an element of A we say that the event A has occurred.…”

“…Maford [3] has shown that if the coefficient is greater than 3 then the distribution is nonrandom. We [2] have utilized this concept in image understanding and measured the randomness in binary lattice [6] or least significant bit (LSB) lattice [2].…”

NOTE: Blind Restoration of Degraded Binary Markov Random Field Images

“…It is well-known that an 3.1. Iterated Conditional Modes (ICM) Algorithm MRF can be described by a Gibbs distribution [3], having the form Besag [1] has proposed the iterated conditional modes (ICM) method to solve (2) …”

“…reasonable to assume that max 01 ϭ max 10 ϭ 0.5, considering These parameters can be estimated by using the standard the fact that noises with parameters larger than 0.5 estimation methods reported in [5][6][7]. However, these estidegrade the real images to the extent that they cannot mation methods are often time-consuming and cannot be be restored.…”

“…The real image is de-estimate. The same approach has been adopted in [2], scribed by a Markov random field (MRF). The iterative condi-where the estimation is carried out iteratively by estimating tional modes (ICM) algorithm is adopted.…”