Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising

Algorithm 2

Initialize: 𝑢⁰=𝑧,𝑑⁰_𝑥=0,𝑑⁰_𝑦=0,𝑏⁰_𝑥=0,𝑏⁰_𝑦=0.

While 𝑢^𝑘−𝑢^𝑘−1₂𝑢^𝑘₂>𝜖,

   𝑢^𝑘+1=𝐺^𝑘 by (22),

   𝑑_𝑥^𝑘+1=max(𝑠^𝑘−1𝜆∇,0)⋅^𝑥𝑢^𝑘+1+𝑏^𝑘_𝑥𝑠^𝑘,

   𝑑_𝑦^𝑘+1=max(𝑠^𝑘−1𝜆∇,0)⋅^𝑦𝑢^𝑘+1+𝑏^𝑘_𝑦𝑠^𝑘,

   𝑏_𝑥^𝑘+1=𝑏^𝑘_𝑥+(∇_𝑥𝑢^𝑘+1−𝑑_𝑥^𝑘+1),

   𝑏_𝑦^𝑘+1=𝑏^𝑘_𝑦+(∇_𝑦𝑢^𝑘+1−𝑑_𝑦^𝑘+1).

End