Cross-Field Joint Image Restoration via Scale Map Supplementary File

They can be written in vector forms respectively as E1(s, I) = (s − PxCxI) Ax(s − PxCxI) + (s − PyCyI) Ay(s − PyCyI), (4) E2(I) = (I − I0) B(I − I0), (5) where s, I and I0 are vector representations of s, I and I0. Cx and Cy are discrete backward difference matrices that are used to compute image gradients in the xand ydirections. Px, Py , Ax, Ay and B are diagonal matrices, whose i-th diagonal elements are defined as (Px)ii = pi,x, (Ax)ii = φ(si − pi,x∇xIi), (Py)ii = pi,y, (Ay)ii = φ(si − pi,y∇yIi), Bii = φ(Ii − I0,i).