Restoration of noisy regions modeled by noncausal Markov random fields of unknown parameters

The problem of restoring noisy images when the model parameters are not known is discussed. The underlying field, x, is modeled as a noncausal Markov random field (MRF), namely, either a multilevel logistic (MLL) or a Gaussian MRF, and is corrupted by additive independently identically distributed (i.i.d.) Gaussian noise. The application is a restoration/segmentation of regions of interest in an image obtained from histologies of brain sections, which suggests an MLL modeling since the regions are spatially smooth. The presented algorithm maximizes the joint likelihood of the observations, y, and x given the unknown parameters. The parameters of the noise and the random field are estimated separately through a maximum likelihood technique given the current estimate of x, and the underlying field is estimated through a maximum a posteriori method. In the case of images modeled by MLL MRFs, the result of the restoration is actually a segmentation since the collection of all pixels with the same level defines a region. The results show that the algorithm successfully segments the region of interest even when the signal-to-noise ratio is low