Poissonian Image Deconvolution via Sparse and Redundant Representations and Framelet Regularization

Algorithm 1

Poissonian image deconvolution via sparse and redundant representations and framelet regularization.

Initialize: Initialization: 𝑢⁰=𝑔, 𝑑⁰₁=𝐻𝑔, 𝑑⁰₂=𝑊𝑔, 𝑑⁰₃=𝑔, 𝐷=DCT, and

    𝑏⁰₁=𝑏⁰₂=𝑏⁰₃. Set iter_𝑂∶=0, iter_𝐼∶=0.

for  iter_𝑂=0to𝑁_𝑂  do

  while  stopping criterions is not satisfied  do

   Step 1. Update 𝑢^(𝑘+1) using (30);

   Step 2. Update 𝑑₁^(𝑘+1) using (32);

   Step 3. Update 𝑑₂^(𝑘+1) using (34);

   Step 4. Update 𝑑₃^(𝑘+1) using (37);

   Step 5. Update sparse representation coefficients {𝛼_𝑖𝑗} using (6);

   Step 6. Update the Bregman auxiliary variables 𝑏₁^(𝑘+1),𝑏₂^(𝑘+1),𝑏₃^(𝑘+1);

   iter_𝐼=iter_𝐼+1;

  end

   Step 7. Update Dictionary 𝐷;

end