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Image restoration has been a popular and active field of research for decades. Images are destroyed when exposed to ‘noise’ which can occur due to physical contact or electrical/electronic interference. Here, Bayesian statistical techniques and Markov random field (MRF) theory were used to restore a black and white binary image corrupted by additive Gaussian noise with zero mean and constant variance. The binary image was used as a Markov random eld. An image is comprised of pixels and these pixels have a regular two-dimensional lattice structure. A matrix including ±1 values was generated randomly. It was represented and interpreted as an Ising model in Statistical Mechanics. The probability distribution of the Ising model was used as the prior distribution (a Gibbs or Boltzmann distribution). Likelihood function was obtained by using the random matrix and the observed corrupted image. Markov Chain Monte Carlo (MCMC) method was used to simulate posterior distribution which again turns out to be a Gibbs or Boltzmann distribution. More specifically, Metropolis-Hastings algorithm which is one of the popular MCMC algorithms was used in this simulation. In this study, Peak Signal to Noise Ratio (PSNR) and Mean Squared Error (MSE) methods were used to measure the quality of restored images. MATLAB (R2013a (8.1.0.604)) was used to construct the program in this research work. Finally, high quality images were restored which were almost similar to the original image. A decrease in restored image quality was observed with the increase in noise. When the image size was increased, a higher number of iterations was required to obtain an acceptable level of quality in the restored image.

A Study on Application of Markov Random Fields in Image Restoration and its Efficiency