Abstract

A novel adaptive and patch-based approach is proposed for image regularization and representation. The method is unsupervised and based on a pointwise selection of small image patches of fixed size in the variable neighborhood of each pixel. The main idea is to asso- ciate with each pixel the weighted sum of data points within an adaptive neighborhood and to use image patches to take into account complex spatial interactions in images. In this paper, we consider the problem of the adaptive neighborhood selection in a manner that it balances the accuracy of the estimator and the stochastic error, at each spa- tial position. Moreover, we propose a practical algorithm with no hid- den parameter for image regularization that uses no library of image patches and no training algorithm. The method is applied to both ar- tificially corrupted and real images and the performance is very close, and in some cases even surpasses, to that of the best published denoising methods.