Digital Signal Processing Reference
In-Depth Information
2
2
φ
() |
Cgf
=−
| | |
−
κ
(13)
κ
κ
where
is the noise of imaging system. According to the work of [14],
is set
to
. In order to calculate (11) for getting the approximate solution of
C,
the
Newton iteration method is used. The approximate equation of (13) is shown as
2
4||
σ
||
X
2
φ
()
CCCC
+
φ
'
( (
−
) 0
=
(14)
k
+
1
k
φ
φ
()
()
C
CC
=−
(15)
k
+
1
k
'
C
k
denotes the number of iterations.
is the derivative of
.The condition of
'
φ
()
C
φ
()
C
stopping iterations is
or the maximum number of iterations is 200.
The proposed method can be summarized as follow:
φ
6
() 10
C
≤
−
1. Compute the SSIM of the reference patches and their neighboring versions.
2. If the value of SSIM belonged to some corresponding patches are more than 0.4,
then apply the improved NLM method to process these patches.
3. If no corresponding patches satisfy the rule about SSIM, then apply the DT-CWT on
the log-transformed patches.
4. Estimate the parameter of SNIG and GGD model, then obtain the MAP estimate
from (6).
5. Perform an exponential transformation of the result from Step 4.
6. Compute (12) and update the regularization parameter
C.
If the terminating
condition is met, the restoration is accomplished, Otherwise iterating the process
from Step1 to Step 6.
4
Experiment Results
To investigate the effectiveness of the proposed image denoising methods, we
compare the denoised results of traditional NLM [5], BM3D [15] and BLS-GSM [16]
with SNIG-NLM.
Suppose the noiseless image is available, and its noisy version is produced by
adding zero-mean white Gaussian noise with
δ
=20. The test image is grayscale
n
Lena with the size
512
×
512
. Figure 1 shows the original image and various
denoised versions.
Among these methods, BM3D is the most effective algorithm for denoising, which
relies on the structure of blocks. Its denoising result is prior to other existing methods
in terms of both visual quality and PSNR. Comparing with the results of BLS-GSM
and NLM, the great majority of texture and geometric structure are still clear with
fewer nicks in Figure 2 (e) and (f). So the result of NLM-SNIG shown in Figure 2 (f)
is close to BM3D in preserving details and keeping smooth within the homogeneous
area.
