Optimization-based image reconstruction in x-ray computed tomography by sparsity exploitation of local continuity and nonlocal spatial self-similarity
Zhang Han-Ming, Wang Lin-Yuan, Li Lei, Yan Bin†, , Cai Ai-Long, Hu Guo-En
       

Calculation of the image NL gradient. For a target pixel x in red, all pixels in its search window (orange square) are matched with x by calculating similarity weights. For example, the similarity between pixel y and x is measured by the weight ω(x,y), and the weight is calculated and depends on an ℓ2 distance between the patches (green squares) centered on the pixels in the comparison.