Digital Signal Processing Reference
In-Depth Information
TABLE 10.2
PSNR (dB) Results from Several Recent Denoising Algorithms
Noisy Images
Lena
Barbara
σ
η
Denoising Methods
10
15
20
25
10
15
20
25
Orthogonal DWT
Donoho's HT (D8)
19
31.6
29.8
28.5
27.4
28.6
26.5
25.2
24.3
Wiener
(MATLAB)
32.7
31.3
30.1
29.0
28.4
27.4
26.5
25.7
HMT (D8)
6
33.9
31.8
30.4
29.5
31.9
29.4
27.8
27.1
SAWT (S8)
23
—
31.8
30.5
29.5
—
29.2
27.6
26.5
LAWMAP (D8)
21
34.3
32.4
31.0
30.0
32.6
30.2
28.6
27.4
AHMF (D8)
22
34.5
32.5
31.1
30.1
32.7
30.3
28.7
27.5
SSM (D8)
24
34.8
32.5
——32.4
30.0
—
—
LCHMM
(D8)
34.4
32.4
30.9
29.9
32.8
30.5
28.9
27.7
LCHMM
(S8)
34.5
32.5
31.2
30.1
33.1
30.8
29.2
28.0
Redundant DWT
RHMT (D8)
6
34.6
32.6
31.2
30.1
32.8
30.3
28.6
27.7
SAWT (S8)
23
—
33.0
31.9
30.6
—
30.7
28.9
27.6
SAOE
28
34.9
33.0
31.9
30.6
33.3
31.1
29.4
28.2
LCHMM-SI
(D8)
34.8
33.0
31.7
30.5
33.5
31.2
29.6
28.3
LCHMM-SI
(S8)
35.0
33.0
31.7
30.6
33.6
31.4
29.7
28.5
The peak signal-to-noise ratio (PSNR) results are shown in Table 10.2 where
several recent image denosing algorithms are compared. It is shown that
LCHMM provides the excellent denoising performance for the two images,
especially for the Barbara image where the nonstationarity property is promi-
nent. LCHMM outperforms all the other methods in most cases. We also show
the visual quality of image denoising (with D8 wavelet) in Figure 10.8 where
LCHMM and LCHMM-SI provide better visual quality with fewer artifacts
than HMT.
10.3.6
Discussions of Image Denoising
In this section, we have proposed a new wavelet-domain HMM called the
local contextual hidden Markov model (LCHMM), for statistical modeling
and image denoising. The simulation results show that LCHMM can achieve
state-of-the-art denoising performance with three major advantages, i.e., spa-
tial adaptability, nonstructured local-region modeling, and fast-model train-
ing. However, the main drawback of LCHMM is “overfitting” in terms of
the number of model parameters, which is even larger than the number of
wavelet coefficients to be modeled. This drawback may prevent LCHMM
from the wider applications. Nevertheless, here LCHMM demonstrates its
evident advantages in image estimation and restoration applications.
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