Digital Signal Processing Reference
In-Depth Information
where
y
is the wavelet coefficient of observation images,
c
is the wavelet coeffi-
cient of the original image,
n
is the noise wavelet coefficient (For Gaussian distribu-
tion,
).
If the hidden state
s
corresponded with
c
is known, the minimum-mean-
square-error (MMSE) estimate of
c
can be obtained by the condition mean estimate
of a Gaussian signal in Gaussian noise as
nN
~(0, )
σ
2
i
n
2
,
σ
im
Ec y
(|
) =
θ
y
.
(5)
i
i
,
2
2
i
σσ
+
im
,
n
Through the EM training to obtain the HMT model parameters, the posterior hidden
state probability is
P(
s
| y
θ
)
given the model
θ
and the observed wavelet coeffi-
i
i
,
cient
y
i
. So
c
can be obtained as:
,
2
,
σ
y
(6)
im i
cEcy psmy
=
(|
)
θ
=
(
=
|
)
θ
×
m ,L
∈
{ }
.
i
i
i
,
i
i
,
2
2
σσ
+
im
,
n
The noise variance
σ
is obtained by a median estimate method raised by Donoho
n
[6] as follows:
median abs c
(
(
))
(7)
ij
,
σ
=
,
n
0.6745
where
j
is the scale of wavelet coefficients
i
is the wavelet coefficients number on
this scale. Finally, the denoised image is achieved by the inverse DWT of this estima-
tion of wavelet coefficients.
3
Simulation
In the experiment a 512*512 Lena image is put with white Gaussian noise of mean 0
and variance 0.01. Then, respectively denoise it used by the methods including wave-
let soft-threshold, median filter, Wiener filter and wavelet-domain HMT model. The
result shows that Wavelet-domain HMT model on account of the dependencies of
wavelet coefficients between scales has obvious advantages than other classical me-
thods in Fig. 2. It keeps the shapes of the image and its PSNR is 1~2dB higher than
other methods.
The experiment continues on a
512*512 big jacquard fabric image. As the simu-
lation results showed in Fig. 3, wavelet-domain HMT model on the fabric image also
has a much better denoising effect than those classic methods. Its PSNR is the highest
one. Yet wavelet-domain HMT needs parameter training and spends more time in the
processing of denoising, which should be improved later.
