Local Adaptivity to Variable Smoothness for Exemplar-Based Image Regularization and Representation

A novel adaptive and exemplar-based approach is proposed for image restoration (denoising) and representation. The method is based on a pointwise selection of similar image patches of fixed size in the variable neighborhood of each pixel. The main idea is to associate with each pixel the weighted sum of data points within an adaptive neighborhood. We use small image patches (e.g. 7×7 or 9×9 patches) to compute these weights since they are able to capture local geometric patterns and texels seen in images. In this paper, we mainly focus on the problem of adaptive neighborhood selection in a manner that balances the accuracy of approximation and the stochastic error, at each spatial position. The proposed pointwise estimator is then iterative and automatically adapts to the degree of underlying smoothness with minimal a priori assumptions on the function to be recovered. The method is applied to artificially corrupted real images and the performance is very close, and in some cases even surpasses, to that of the already published denoising methods. The proposed algorithm is demonstrated on real images corrupted by non-Gaussian noise and is used for applications in bio-imaging.