3 Speckle Noise Reduction and Enhancement for OCT Images
63
Table 3.8 Outline of the proposed OCT despeckling algorithm
Step 1:
3D Complex Wavelet Transformation of Noisy
OCT to Find ¯
y(k) and σ n .
Step 2:
Estimation of the Prior (Finding Mixture
Model Parameters in Each Subband).
2.1.3. Initialization for a(k) and σ 11 (k),σ 12 (k), σ 21 (k), σ 22 (k).
2.2. Using (3.40) to find r 1 (k), r 2 (k).
2.3. Using (3.41) to update a(k) by substituting r 1 (k), r 2 (k) from step 2.2.
2.4. Updating the parameters of prior, σ 11 (k), σ 12 (k), σ 21 (k), σ 22 (k), using (3.42) and (3.43).
2.5. Finding g i ( ¯
y(k)) from (3.32) for AWGN and (3.33) 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 (3.36) for AWGN (after
obtaining R( ¯
y(k)) using (3.37)) and Shrinkage
Function (3.38) for two-sided Rayleigh noise
(after obtaining R( ¯
y(k)) using (3.39)).
Step 4:
Inverse 3D Complex Wavelet Transformation.
E step:
r 1 (k) ←
a(k)g 1 ( ¯
y(k))
a(k)g 1 ( ¯
y(k)) + (1 − a(k))g 2 ( ¯
y(k))
, r 2 (k) ← 1 − r 1 (k)
(3.40)
M-step:
a(k) ←
1
M
j∈N(K )
r 1 ( j),
(3.41)
σ
2
1m (k) ←
j∈N(K ) r i ( j)y
2 (k)
j∈N(K ) r i ( j)
− σ
2
n , m 1, 2
(3.42)
σ
2
2m (k) ←
j∈N(K ) r i ( j)y
2
p (k)
j∈N(K ) r i ( j)
− σ
2
n , m 1, 2
(3.43)
where M shows the number of samples in window N(k),
which is centered at ¯
y(k) and σ n is estimated by σ n
median{| noisy wavelet coe f f icients in f inest scale |}/0.6745 [69].
The final OCT despeckling algorithm is concluded in Table 3.8.
As discussed in the literature [69, 70], instead of proposing isotropic window N(k),
using anisotropic window would result in better modeling and denoising results. In
this base local polynomial approximation- intersection of confidence intervals (LPAICI) method [70] can be employed to obtain the anisotropic window around each
pixel (Fig. 3.8) and this method can be extended to 3D space (Fig. 3.9).