TV+TV² Regularization with Nonconvex Sparseness-Inducing Penalty for Image Restoration

Algorithm 1

TV+TV²+ℓ_𝑝 sparseness-inducing penalty.

Initialisation:

(1)  𝑢^𝑘+1 is given by (42) for solving Subproblem 1;

(2) 𝑣^𝑘+1 is given by (43) for solving Subproblem 2;

(3) 𝑤^𝑘+1 is given by (44) for solving Subproblem 3;

(4) 𝑐^𝑘+1 is given by (54) and (55) for solving Subproblem 3;

(5) Update on 𝑏₁: 𝑏₁^𝑘+1=𝑏^𝑘₁+∇𝑢^𝑘+1−𝑣^𝑘+1;

(6) Update on 𝑏₂: 𝑏₂^𝑘+1=𝑏^𝑘₂+∇²𝑢^𝑘+1−𝑤^𝑘+1;

(7) Update on 𝑏₃: 𝑏₃^𝑘+1=𝑏^𝑘₃+𝑆ℋ_𝑑𝑢^𝑘+1−𝑐^𝑘+1.