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Identification of the nature of the noise and estimation

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IMPROVED NOISE PARAMETER
ESTIMATION AND FILTERING OF
MM-BAND SLAR IMAGES
Vladimir V. Lukin, Nikolay N. Ponomarenko, Sergey K. Abramov
Dept of Transmitters, Receivers and Signal Processing,
National Aerospace University,
17 Chkalova St, 61070, Kharkov, Ukraine,
tel. +38 057 7074841, fax +38 057 3151186,
e-mails lukin@xai.kharkov.ua, uagames@mail.ru, ask379@mail.ru
Benoit Vozel, Kacem Chehdi
University of Rennes I, 6, Rue de Kerampont,
22 305 Lannion cedex, BP 80518, FRANCE,
Tel: +33 (0)2 96 46 90 71, Fax: 33 (0)2 96 46 90 75,
e-mail Benoit.Vozel@enssat.fr
1
Presentation outline
•
•
•
•
•
•
•
Motivations for research and design
Blind (automatic) techniques for determination
of noise characteristics
Real life image analysis results
Modified filtering techniques
Simulation result analysis
Real life image filtering results
Conclusions
2
Motivations for research and design
•
•
•
•
Commonly it is supposed that noise in radar images is of multiplicative nature
and additive noise component can be neglected. However, for side look
aperture radar (SLAR) images, especially for MM-band (Ka-band) ones, it is
not true.
Although noise in SLAR images is not very intensive, image pre-filtering is
also worth performing for improving reliability of sensed surface parameter
evaluation. However, majority of image filtering (denoising) techniques are
designed for either reduction of additive Gaussian noise or for suppression of
pure multiplicative noise.
However, determination of noise type and properties from remote sensing data
at hand is not an easy task. And it is desirable to perform blind (automatic)
estimation of noise characteristics.
Fortunately, such techniques have been designed recently. In this paper we
present some results of applying them to real Ka- and X-band SLAR images
offered to us by the Institute of Radiophysics and Electronics of UNAS and the
A.I. Kalmykov Center of Earth Radiophysical Sensing.
3
Identification of the nature of the noise and estimation of its variance:
Starting from the characterization of noises on homogeneous zones obtained by refined gravitational
transform [1 ]
• for additive noise :
*
*
• from following property var h ( u  b )  var h ( b )
*
• var h ( u 0 ) is a “natural” estimator of the variance
2
• the equation of the local variance according to the local mean on homogeneous zones is: Y   b
• for multiplicative noise
• from following property
*
• var h ( u 0 ) / moy h ( u 0 )
*
*
var h ( u . n ) / moy h ( u . n ) пЂЅ var h ( n ) / moy h ( n )
2
2
2
is a “natural” estimator of the variance
• the equation of the local variance according to the local mean on homogeneous zones is: Y
пЂЅпЃіn X
2
We can define local statistics on homogeneous zones by considering a local estimation kernel
пЃ› пЃ— пЃќп‚ґ пЃ› пЃ— пЃќ
пЃ† пѓЋ пЃ›0 ,1пЃќ
Then, the local mean and local variance are given by:
moy пЃ† ( u ) i , j пЂЅ
N i, j пЂЅ пЃ† i, j
N i, j

пЂЁ i ', j ' пЂ©пѓЋпЃ—
N i, j
*
var пЃ† ( u ) i , j пЂЅ
with
1
2
N i, j пЂ­ ni, j
1
i , j , i ', j '
u i ', j '
  i , j ,i ', j ' u i ', j '  moy  ( u ) i , j 
2
2
пЂЁ i ', j ' пЂ©пѓЋпЃ—
ni, j пЂЅ пЃ† i, j
2
4
2
Pseudo-Algorithm :
• calculate local statistics while varying the size of the scanning window from 3x3 to 11x11
(to get a sufficiently significant number of samples)
• classify local statistics (mean, variance) into lists according to the number of pixels taken into
account for calculting them
(to satisfy that the samples follow all the same law so that local statistics meaning keeps
sens)
• only consider the largest list of local statistics (mean, variance)
• calculate the coefficients of approximation as well as the corresponding errors of
approximation
• decide that the noise is additive if the horizontal line generates a minimum error, or
multiplicative if the minimum error is obtained by the centered parabola
[1] В« UNSUPERVISED VARIATIONAL CLASSIFICATION THROUGH IMAGE MULTI-THRESHOLDING В»
Luc Klaine, Benoit Vozel, Kacem Chehdi, Proceedings of 13th European Signal Processing Conference (EUSIPCO),
Antalya, September 4-8 2005
5
Real life image analysis results
•
•
The experiments carried out have clearly shown that the considered Ka- and
X-band SLAR images are corrupted by an additive mixture of multiplicative
and additive noise. Both can be supposed Gaussian and, in fact, the influence
of multiplicative noise is, as expected, prevailing.
The obtained estimates of noise variances for Ka-band SLAR image (in
conventional 8-bit representation) are:
– for multiplicative noise relative variance ˆ is of the order 0.005;
– additive noise variance ˆ is about 16.
2
пЃ­
2
a
•
•
This means that for image homogeneous regions with mean intensities larger
than 50…60, multiplicative noise becomes prevailing and otherwise.
Similarly, the obtained estimates of noise variances for X-band SLAR image
are the following:
– multiplicative noise relative variance ˆ is about 0.009;
– additive noise variance ˆ is approximately equal to 64.
2
пЃ­
2
a
•
Thus, for the considered X-band SLAR image one can’t neglect additive
noise influence as well.
6
Modified filtering techniques
•
A question is how to incorporate our knowledge on noise statistics into
filtering technique? For spatially invariant DCT-based filtering there are some
analogs showing a way to follow in case of signal-dependent noise. If one
knows a dependence of image local variance on local mean for homogeneous
regions, then for each position of a sliding block one can adjust a threshold in
adaptive manner. A local DCT coefficient Wl(0;0) can serve as an estimate of
local mean Il, and Wl(0;0) is calculated for each block anyway. Then, knowing
a dependence of local variance on local mean пЃіЛ† (Il) and substituting Wl(0;0)
instead of Il it is possible to estimate пЃіЛ† for each block.
Under assumption that additive and multiplicative noise components are
mutually uncorrelated, one obtains
2
2
2
2
пЃіЛ† l пЂЅ пЃіЛ† a пЂ« пЂЁ W l пЂЁ 0; 0 пЂ© пЂ© пЃіЛ† пЃ­
Then, a proposed modification (MDCT-filter) implies that a local threshold for
each sliding block is adjusted as
T пЂЅ пЃў (пЃі пЂ« I пЃі ) пЂЅ пЃў пЂЁ пЃіЛ† пЂ« пЂЁ W пЂЁ 0; 0 пЂ© пЂ© пЃіЛ† пЂ© ,
where пЃў denotes a filter parameter commonly set equal to 2.6. Similar
approach can be used in setting thresholds for the corresponding modifications
of edge detectors for which originally a threshold is selected proportionally to
either noise variance or standard deviation.
2
l
2
•
•
l
l
2
2
2
a
l
пЃ­
1/ 2
2
2
a
l
1/ 2
2
пЃ­
7
Simulation result analysis
• The simulations have been performed for a standard test image
Barbara, Baboon, Lena, Goldhill, and Peppers corrupted by a mixture
of additive and multiplicative noises with the same parameters пЃіЛ† and пЃіЛ†
that have been observed for real life Ka-band SLAR images.
• As filtering efficiency quantitative criterion we have used PSNR
calculated for entire images.
• For comparison purposes, we have exploited DCT based filter
modifications for pure multiplicative noise (MuDCT-filter) and pure
additive noise (AdDCT-filter). In the former case, a local threshold has
been set as Tl=пЃўWl(0;0)ПѓОј. For DCT filter adjusted to pure additive
noise, a threshold has been fixed and equal to пЃўПѓa.
• Moreover, for these two DCT-filters we have varied the parameter  to
analyze the maximal attainable PSNR.
2
2
пЃ­
a
8
PSNR for different filters
( пЃіЛ† = 0.005, пЃіЛ† =16)
Filtering
2
2
пЃ­
a
MuDCT
AdDCT
MDCT
method
Image
пЃў=2.6
пЃў=2.6
пЃў=3.2
пЃў=3.9
пЃў=4.5
пЃў=2.3
пЃў=2.6
пЃў=2.9
пЃў=3.3
Barbara
34.67
28.57
30.68
31.55
31.42
33.75
34.28
34.55
34.54
Baboon
30.53
27.74
28.71
29.16
29.14
30.46
30.57
30.52
30.39
Goldhill
34.06
28.61
30.49
31.23
31.12
33.60
33.96
34.06
34.01
Lena
35.85
27.94
30.05
31.03
30.97
35.44
35.75
35.82
35.75
Peppers
34.89
28.02
29.94
30.80
30.76
34.12
34.63
34.85
34.84
9
Simulation result analysis
•
•
•
•
•
As seen, PSNR for the AdDCT-filter for any пЃў does not reach PSNR for the
proposed MDCT-filter.
For the MuDCT, the largest attainable PSNR can be approximately the same as
for the proposed MDCT-filter. However, for different images the “optimal” 
for which maximal values of PSNR for MuDCT and AdDCT-filters are
provided are considerably different.
In any case, the “optimal”  for the MuDCT and AdDCT-filters tend to be
larger than 2.6, commonly for the AdDCT-filter the “optimal”  is about 4
while for the MuDCT the “optimal”  is about 3.
The optimal пЃў values depend upon exact combination of values of пЃіЛ† and пЃіЛ† as
well as upon an image to be filtered. If one sets Tl=пЃўWl(0;0)ПѓОј or пЃўПѓa for
MuDCT and AdDCT-filters, respectively, with пЃў=2.6 as recommended, undersmoothing is observed either in image regions with either rather low or
comparatively large local means.
At the same time, MDCT-filter provides approximately the same efficiency of
noise suppression in image homogeneous regions irrespectively to Il (if
efficiency is characterized by a ratio of Пѓl2 before and after filtering.
2
2
пЃ­
a
10
Real life image filtering results
a
b
A real-life original Ka-band SLAR image (a) and the result of its
processing by the MDCT-filter (b)
11
Conclusions
•
•
•
•
•
A method for blind evaluation of additive and
multiplicative noise variance is proposed.
It is established that in SLAR images multiplicative
noise is dominant but additive noise component can not
be neglected.
A modified DCT based filter for the considered case is
designed.
It is shown that this filter can effectively remove noise
and preserve useful information in SLAR images.
The method is successfully tested for real life images.
12
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