Research On Image Restoration Algorithms Based On Variational Bayesian Theory

Due to the error operating or the environment, vary degrees of image degradation ofenoccurred when acquisition and preservation image. This article have a main research onmotion blur restoration algorithm caused by error operation. In this paper, the coretechnology is to find a clear image and blur kernel which makes maximum po steriorprobability to be largest. Image restoration involves two steps. In the fist step, blur kernelis estimated using Variation Bayesian theory. The second step is to estimate a clear imageusing non-blind restoration algorithm.When estimating the blur kernel based on the Variation Bayesian theory, thisarticle bring in expected maximum algorithm to help solving problem by separationthis problem into two small problem which is called E step and M step. E step aim toestimate the gradient map of a potential clear image. After assuming a blur kernel,solving the gradient map of a potential clear image and insure its distribution follows aMixture of Gaussians distribution. When solving objective function, we useKullback-Leibler divergence to measure similarity between the gradient distribution ofclear image and the MOG distribution. This process involves numbers of unknownvariables, including mean and variance of MOG distribution, the weights of eachGaussian distribution in the MOG distribution. Using Alternating Minimizationmethod to optimize the problem, fixing other variables when solving some variable. Mstep aim to update blur kernel using the constraint condition that the gradient map ofblur image is equal to the convolution of blur kernel and gradient map of clear imagecalculated in E step. Then normalized blur kernel to ensure its elements arenon-negative and sum equal one. Finally, use non-blind convolution algorithm toestimates a clear image. Making the convolution of clear image and blur kernelapproach given blurred image, besides the sum of clear image gradient are small.During the process, bring in a upper bound function concept, which makes the value ofupper bound function is larger than the given constraint for every possible clear image.Minimize the upper bound function is equal to estimate the given constraint. TheInitialization value of the function is set to be sum of clear image gradient squares.Andupdate the boundary function using the estimated clear image. Experiments show that this restoration algorithm proposed in this article is suitable fordifferent type of image and blur kernel, effectively restore texture and edge information.