Optical Coherence Tomography Noise Reduction Using Anisotropic Local Bivariate Gaussian Mixture Prior in 3D Complex Wavelet Domain

Algorithm 1

Outline of the proposed denoising algorithm.

Summarization of the proposed denoising algorithm

Step 1.  Complex Wavelet Transformation of Noisy Image to Find 𝑦(𝑘) and 𝜎_𝑛.

Step 2.   Estimation of the Prior (Finding Mixture Model Parameters in Each Subband).

 2.1.   Initialization  for  a(k)   and   𝜎₁₁(𝑘),𝜎₁₂(𝑘),𝜎₂₁(𝑘),𝜎₂₂(𝑘).

 2.2.   Using   (34)   to   find   𝑟₁(𝑘),𝑟₂(𝑘).

 2.3.   Using  (37)   to  update  a(k)   by  substituting   𝑟₁(𝑘),𝑟₂(𝑘)    from Step 2.2.

 2.4.   Updating  the  parameters  of  prior,    𝜎₁₁(𝑘),𝜎₁₂(𝑘),𝜎₂₁(𝑘),𝜎₂₂(𝑘),   using  (36)   and  (37).

 2.5.   Finding   𝑔_𝑖(𝑦(𝑘))    from  (27)   for  AWGN  and  (28)   for  two-sided  Rayleigh  noise  using  updated

       value  in  Step   2.3.

 2.6.   Iteration Step 2.2 to 2.4 until parameter convergence.

Step 3.   Substituting the Final Parameters in Step 2 in Shrinkage Function (30) for AWGN

      (after obtaining 𝑅(𝑦(𝑘)) using (31)) and Shrinkage Function (32) for two-sided Rayleigh

      noise (after obtaining 𝑅(𝑦(𝑘)) using (33)).

Step 4.   Inverse Complex Wavelet Transformation.