Image denoising using locally learned dictionaries

In this paper we discuss a novel patch-based framework for image denoising through local geometric representations of an image. We learn local data adaptive bases that best capture the underlying geometric information from noisy image patches. To do so we first identify regions of similar structure in the given image and group them together. This is done by the use of meaningful features in the form of local kernels that capture similarities between pixels in a neighborhood. We then learn an informative basis (called a dictionary) for each cluster that best describes the patches in the cluster. Such a data representation can be achieved by performing a simple principal component analysis (PCA) on the member patches of each cluster. The number of principal components to consider in a particular cluster is dictated by the underlying geometry captured by the cluster and the strength of the corrupting noise. Once a dictionary is defined for a cluster, each patch in the cluster is denoised by expressing it as a linear combination of the dictionary elements. The coefficients of such a linear combination for any particular patch is determined in a regression framework using the local dictionary for the cluster. Each step of our method is well motivated and is shown to minimize some cost function. We then present an iterative extension of our algorithm that results in further performance gain. We validate our method through experiments with simulated as well as real noisy images. These indicate that our method is able to produce results that are quantitatively and qualitatively comparable to those obtained by some of the recently proposed state of the art denoising techniques.