Fig. 1.

Illustration of the proposed nonlocal framework: We illustrate the proposed regularization functional, specified by (13), in the left box. The regularization penalty is the sum of distances between patch pairs in the image.For each pixel x, we consider the distances between the patch centered at x (specified by Px(f)) and patches centered on the neighboring pixels y ∈ N_x; N_x is a square shaped window in which the algorithm searches for similar patches. We use the robust distance metric ϕ, which saturates with the the inter-patch distance. This property make the regularization penalty insensitive to large inter-patch distances, thus minimizing the averaging between dissimilar patches. The surrogate penalty, obtained by the majorization of G(f) in illustrated the right box. The surrogate penalty is essentially a weighted sum of Euclidean distances between pixel intensities. This criterion is very similar to the classical H₁ non-local penalty. The weights γ_fn (x, y) is obtained as the sum of the similarity measures as in (20). The similarity measures between patches are computed as a monotonically decreasing non-linear function (Ψ) of the inter patch distances. This property ensures that dissimilar patch pairs result in low inter pixel weights, thus encouraging the averaging of similar pixels.