New Regularization Models for Image Denoising with a Spatially Dependent Regularization Parameter

Algorithm 1

The alternating minimization method for solving Model 1.

Input:  𝑓, 𝛼, 𝑀, and 𝑟.

Output:  𝑢^𝑘.

Initialization:  𝑔⁰=0.

  while  not converged do

   Step  1. Given 𝑔^𝑘−1, computing 𝑢^𝑘 by solving

  min_𝑢∈𝑋𝐸₁𝑢,𝑔^𝑘−1=12𝑢−𝑓²_𝑋+∑_{1≤𝑖,𝑗≤𝑛}𝐾𝑔^𝑘−1∘𝑔^𝑘−1_𝑖,𝑗|𝐻𝑢|_𝑖,𝑗.    (a)

   Step  2. Given 𝑢^𝑘, computing 𝑔^𝑘 by solving

  min_𝑔∈𝑋𝐸₁𝑢^𝑘𝑀,𝑔=𝛼𝑔−𝛼⋅𝟏²_𝑋+∑_{1≤𝑖,𝑗≤𝑛}𝑔²_𝑖,𝑗𝐾𝐻𝑢^𝑘_𝑖,𝑗.      (b)

  end while