Image restoration using a kNN-variant of the mean-shift

The image restoration problem is addressed in the variational framework. The focus was set on denoising. The statistics of natural images are consistent with the Markov random field principles. Therefore, a restoration process should preserve the correlation between adjacent pixels. The proposed approach minimizes the conditional entropy of a pixel knowing its neighborhood. The conditional aspect helps preserving local image structures such as edges and textures. The statistical properties of the degraded image are estimated using a novel, adaptive weighted k-th nearest neighbor (kNN) strategy. The derived gradient descent procedure is mainly based on mean- shift computations in this framework.