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(a)
(b)
Fig. 1.
Noisy (a) and compressed (b) Frisco images
effect is provided due to the specific normalization of the sub-band images before
their compression and due to the larger size of the groups composed. Besides,
we consider in more detail how the coder parameters are set.
2 Lossy Compression of One-Channel Image
The lossy compression of one-channel noisy images has certain peculiarities.
One of them is the noise filtering effect [24]. This effect is positive in the sense
of improving the image quality and enhancing its classification [25] but only
under the condition that the compression ratio (coder parameters) is adjusted
to the noise type and statistics. Consider a simple example. The mixed additive
and signal dependent i.i.d. Gaussian noise has been added to the gray-scale test
image Frisco (Fig. 1 a)) where the additive noise with the variance
σ
2
=64was
predominant (the variance of the signal dependent noise
σ
2
=
kI
tr
ij
,
k
=0
.
1,
I
tr
ij
denotes a true value of
ij
-th pixel).
The noisy image has been subject to the lossy compression by the DCT based
coder AGU [26] controlled by the quantization step (
QS
).
QS
was set equal to
βσ
with
β
from 0.5 to 6. Two curves have been obtained (Fig. 2),
PSNR
or
(
QS
)
and
PSNR
nf
(
QS
) where the former is determined for the decompressed and the
original (noise added) images and the latter one for the decompressed and the
noise-free images. The curve
PSNR
or
(
QS
) is monotonous.
PSNR
or
decreases
with the larger
QS
.Thecurve
PSNR
nf
(
QS
) exhibits a maximum that is ob-
served for
QS
=4
.
5
σ
= 36. Two equal values of
PSNR
nf
(e.g., equal to 32dB)
take place for
QS
1
=3
.
5
σ
=28and
QS
2
=6
σ
= 48. In the first case, a less e-
cient noise suppression but a better edge-detail preservation are observed (Fig.
1 b)) and vice versa. Thus, setting
QS
2
≈
4
.
5
σ
can be a good choice.
In practice, the standard deviation
σ
can be unknown in advance. Then its
value
σ
should be estimated for an image to be compressed and the quanti-
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