Wavelet Bayes Adaptive Image Denoising

The class of natural images that we encounter in our daily life is only a small subset of the set of all possible images. This subset is called an image manifold. The Adaptive Digital Image Processing applications are becoming increasingly important and they all start with a mathematical representation of the image. In Bayesian restoration methods, the image manifold is encoded in the form of prior knowledge that express the probabilities that specified combinations of pixel intensities can be experiential in an image. Because image spaces are high-dimensional, one often isolates the manifolds by decomposing images into their components and by fitting probabilistic models on it. The construction of a Bayesian network involves prior knowledge of the probability relationships between the variables of interest. Learning approaches are widely used to construct Bayesian networks that best represent the joint probabilities of training data. In practice, an optimization process based on a heuristic search technique is used to find the best structure over the space of all possible networks. However, the approach is computationally intractable because it must explore several combinations of dependent variables to derive an optimal Bayesian network. The difficulty is resolved in this paper by representing the data in wavelet domains and restricting the space of possible networks by using certain techniques, such as the “maximal weighted spanning tree”. With the use of biorthogonal wavelets, the perceptual quality of the reconstructed image has been improved. Three wavelet properties - sparsity, cluster, and motion can be oppressed to reduce the computational complexity of learning a Bayesian network.