An Efficient Variational Method for Image Restoration

Algorithm 1

The split Bregman scheme for subproblem (22).

(1) initialization: 𝜆,𝛼₁,𝛼₂,𝑢,𝑓⁰=0,𝑑⁰=𝑏⁰=0,𝑖=0;

(2) iteration:

   compute 𝑓^𝑖+1 by using formula (27)

   𝑑^𝑖+1=max∇𝑓^𝑖+1+𝑏^𝑖∇𝑓,0^𝑖+1+𝑏^𝑖∇𝑓^𝑖+1+𝑏^𝑖, with the convention 00⋅0=0

   𝑏^𝑖+1=𝑏^𝑖+∇𝑓^𝑖+1−𝑑^𝑖+1

   stop or set 𝑖=𝑖+1