A Modified Iterative Alternating Direction Minimization Algorithm for Impulse Noise Removal in Images

Algorithm 1

Remove impulse noise using PANO.

Initialization:

 Input the noise contaminated image 𝐟, the PANO 𝐀_𝑗𝑗=1,…,𝐽,

 regularization parameter 𝜆, tolerance of inner loop 𝜇=10⁻³, and times of

 learning similarity is 3. Initialize 𝐮=𝐟, 𝐳=𝟎, 𝜶_𝑗=𝟎 for 𝑗=1,2,…,𝐽,𝛽=2⁴ and 𝐮_last=𝟎.

Main:

 Step 1. Obtain the initial guide image 𝐫 from median filtering [1];

 While  𝑡≤3,

     Step 2. Learn similarity 𝐀_𝑗𝑗=1,…,𝐽 in PANO from the guide image 𝐫 [27];

     While   𝛽≤2¹⁴,

       Step 3. Solve (8);

       Step 4. Solve (9);

       Step 5. Solve (10);

       Step 6. If 𝐮_last−𝐮>𝜇𝐮_last, 𝐮_last←𝐮, go to Step 3;

          otherwise, go to Step 7;

       Step 7. 𝛽←2𝛽, 𝐮←𝐮, go to Step 3.

     End While

     Step 8. 𝐫←𝐮, 𝑡←𝑡+1, 𝛽=2⁴, Go to Step 2;

 End While

Output:  𝐮