. Author manuscript; available in PMC: 2014 Mar 30.

Published in final edited form as: IEEE Trans Image Process. 2012 Sep 20;22(8):3192–3203. doi: 10.1109/TIP.2012.2216278

TABLE I.

Reinterpretation of current nonlocal schemes

Current methods		Re-interpretation
Reference	Current algorithm J_w(f) and w(x, y)	Penalty function ϕ(x)	Weight function ψ(x)
H₁ [11], [14]	(6) and (2)	(l − exp (− x²/2σ²))	exp (−x²/2σ²)
Peyre et al., [15]	(8) and (9)	(1 − e ^{− x/σ})	$\frac{\exp (- x ∕ σ)}{2 σ x}$
nonlocal TV [11], [12]	(7) and (2)	$\erf (\frac{x}{σ})$	$\frac{\exp (- x^{2} ∕ σ^{2})}{\sqrt{π} σ x}$
nonlocal L1 [17]	-	$\frac{x}{σ}$	$\frac{1}{2 σ x}$