Efficient and Effective Total Variation Image Super-Resolution: A Preconditioned Operator Splitting Approach

Algorithm 2

Input: 𝑠=∑_𝑘𝑀^𝑇_𝑘𝑆^𝑇𝑦_𝑘,𝑅=∑_𝑘𝑀^𝑇_𝑘𝑆^𝑇𝑆𝑀_𝑘,𝐵,tolerance𝜁_stop,𝛾∈]0,2/𝛽[, and 𝛼,𝜇>0.

Initialize: 𝑧⁰=𝐵⁻¹𝑅⁻¹𝑠,𝜆⁰=0, and 𝑛=0.

Do

 (1) Compute 𝑤^𝑛+1 according to (3.17) for fixed (𝑧^𝑛,𝜆^𝑛).

 (2) Compute 𝑧^𝑛+1 according to (3.20) for fixed (𝑤^𝑛+1,𝜆^𝑛).

 (3) Update 𝜆^𝑛+1 according to (3.15).

 (4)𝑛=𝑛+1.

Until ‖𝑧^𝑛+1−𝑧^𝑛‖/‖𝑧^𝑛+1‖≤𝜁_stop.