Salt and Pepper Noise Removal with Noise Detection and a Patch-Based Sparse Representation

Algorithm 1

PANO-based salt and pepper noise removal with noise detection.

Initialization: Input the noise contaminated image 𝐲, the PANO 𝐀_𝑗𝑗=1,…,𝐽, regularization parameter 𝜆 and tolerance of

inner loop 𝜇=10⁻³. Initialize 𝐱=𝐲, 𝐳=𝟎, 𝜶_𝑗=𝟎 for 𝑗=1,2,…,𝐽, 𝛽=2⁴ and 𝐱_last=𝟎.

Main:

   While  𝛽≤2¹⁴,

 Step  1. solve (7) to get 𝜶_𝑗;

 Step  2. solve (9) to get 𝐳;

 Step  3. solve (13) to get 𝐱;

 Step  4. If 𝐱_last−𝐱>𝜇𝐱_last, go to Step  1;

      otherwise, go to Step  5;

 Step  5. 𝛽←2𝛽, 𝐱←𝐱, go to Step  1.

  End While

Output: 𝐱