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ICGST-GVIP Journal, ISSN 1687-398X, Volume (8), Issue (V), January 2009
Wavelet Based Microcalcifications Detection in Digitized Mammograms
S. Bouyahia, J. Mbainaibeye, N. Ellouze
Ecole Nationale d’Ingenieurs de Tunis, ENIT, BP37, Tunis le Belvédère 1002 Tunis, Tunisia
sihem_bouyahia@yahoo.fr
http://www.enit.rnu.tn
Abstract • Circumscribed masses
Detection of microcalcifications in mammograms has • ill defined masses
received much attention from researchers and public • architectural distortions
health practitioners in these last years. The challenge is to The detection of microcalifications in mammograms is
quickly and accurately overcome the development of not a trivial task, as the microcalification occur in
breast cancer which affects more and more women clusters, vary in size, signal intensity and contrast, and
through the world. Microcalcifications appear in a can be located in dense tissue, making detection difficult.
mammogram as fine, granular clusters, which are often The clusters vary in size from 0.05mm to 1mm in
difficult to identify in a raw mammogram. Although, a diameter.
variety of techniques have been proposed in the literature
to enhance and automatically detect microcalcifications, A number of methods have therefore been proposed to
but no method gives full satisfaction and clinically detect microcalcifications in an automatic manner.
acceptable results. In this paper, we propose different
Among these, global and local thresholding, difference
wavelet based techniques for automatically
images techniques, statistical approaches, neural
microcalcifications detection. In a first time, we propose
networks, fuzzy logic, thresholding of wavelet
a pre-processing step to enhance the mammograms. In a
second time, we propose different wavelet based coefficients and related techniques. A more extensive
techniques; from undecimated wavelet transform to review on detection and classification methods of
multi-scale product, including the wavelet packets microcalcifications can be found in [15, 18]. This work
transform, the one-dimensional modulus maxima wavelet explores the detection of microcalcifications using
transform, and the two-dimensional to multi-scale wavelets. The utility of wavelets to detect calcifications
product. is based on the hypothesis that the microcalcifications
present in mammograms can be preserved under a
Simulations are operated on Mini-Mammographic Image transform which can localize the signal characteristics in
Analysis Society (MIAS) database and the results are the original and transform domains; consequently
presented and compared to some relative works. We have wavelet analysis becomes useful in this application
shown that the proposed approach is competitive with the because microcalcifications correspond to high frequency
best of the state of the art. The enhancement and the component of the image.
different wavelet based techniques proposed are the
major contributions of this work. The remaining of this paper is organised as follow: the
second section presents the basic of wavelet transform.
Keywords: Breast cancer, mammography, wavelets, The data collection is presented in section 3. Section 4
wavelet packets, modulus maxima, multi-scale product. describes the pre-processing step which consists on
different enhancement techniques. The different
1. Introduction microcalcifications detection methods proposed in this
Breast cancer is the leading cause of non preventable paper are presented in section 5. Section 6 focuses on the
cancer death among women. Although there is yet no different results and the discussion. Evaluation of
known cure, early detection leads to better prognosis. X- detection methods are described in section 7.
ray mammography is currently the most established
means of screening [1]. Symptoms of breast cancer
include:
2. Wavelet transform
Wavelet analysis is an extremely powerful data
• Clustered microcalcifications
representation method that allows the separation of
• Speculated (or stellate) lesions
images into frequency bands without affecting the spatial
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ICGST-GVIP Journal, ISSN 1687-398X, Volume (8), Issue (V), January 2009
locality [2]. Thus, information concerning localised high- contrast, which makes them difficult to decipher. Solving
frequency signals such as microcalcifications can be this problem requires the use of several image
extracted effectively. The wavelet transform makes use enhancement techniques. The techniques used in this
of two separate bases for analysis and synthesis. The two- work involve filtering, histogram manipulation and
dimensional wavelet transform is achieved by morphological operations. By combining several
implementing a bank of one-dimensional low-pass and different forms of image enhancement, the contrast can
high-pass analysis filters. be greatly increased, facilitating the finding of the
locations of the calcium deposits.
For one level of decomposition, the image is decomposed
into four orthogonal subbands: LL, HL, LH, and HH as A. Enhancement using Unsharp Masking filter
shown in figure 1. The Unsharp Masking improves the visual appurtenance
of the image, emphasizing its high frequency contents
and enhancing the edge and detail information. This
technique is a simple and effective method, which works
well and is widely used in many applications. In this
technique, a fraction of the high-pass filtered image is
added to the original image. This process results in an
enhanced version of the input image, as shown in figure
2.
Figure 1. Wavelet decomposition at one-level
The three "detail" images, Low-High (LH), High-Low
(HL), and High-High (HH), correspond to distinct
frequency bands. The HL subband contains horizontal
Figure 2. Block diagram of Unsharp Masking Filter
oriented features. Deductively, the LH subband contains
vertically oriented structures, and the HH subband Therefore, the linear unsharp masking algorithm obtains
contains diagonal structures. The LL subband is the low- the image O(x,y) from the input image I(x,y) through:
pass filtered version of the image and is further O ( x , y ) = I ( x, y ) + λ z ( x, y ) (1)
decomposed in the same manner, in the next octave. This
collection of sub-images forms a multiresolution
Where z(x,y) is the correction signal computed as the
representation that organises the image into a set of
output of the high-pass linear filter, λ is the enhancement
details appearing at different resolutions.
factor which controls the level of contrast enhancement
achieved at the output.
3. Database collection We used the unsharp masking filter to enhance the
Mammographic images considered in this work were
mammograms. The processed images are sharper because
chosen from the Mini-Mammographic Image Analysis
low-frequency information in the mammogram is
Society (MIAS). MIAS, which is an organization of
reduced in intensity while high-frequency details are
research groups interested in the understanding of
amplified [2]. This makes microcalcifications more
mammograms situated in UK, has produced a digital
visible in the mammograms.
mammography database [14]. The X-ray films in the
database have been carefully selected from the United A. Enhancement using contrast stretching
Kingdom National Breast Screening Program and
digitized with a Joyce-Lobel scanning microdensitometer The histogram of an image represents its relative
to a resolution of 50 µm x 50 µm, with each pixel being frequency of occurrence of gray levels. The simplest
encoded with 8 bits. The database contains left and right method of increasing the contrast in a mammogram is to
breast images from 161 patients. In total, it counts 322 adjust the mammogram histogram so that there is a
images, belonging to three types, namely normal, benign greater separation between foreground and background
and malignant. There are 208 normal, 63 benign and 51 grey level distributions. The most basic form of
malignant (abnormal) images. histogram manipulation is the histogram stretching. We
The MIAS database is used because it has complete used the histogram stretching to enhance the visibility of
information about abnormalities of each mammographic the microcalcifications in the mammograms and which
image like class of lesion, location, size. We have linearly re-maps the pixel value so that the entire range
selected those images which included from 0 to 255 is used in the mammogram. This has an
microcalcifications. end result of giving the image more contrast.
B. Enhancement using morphological operations
4. Image enhancement techniques
Many of the mammographic images have very low Morphological operations can be employed for many
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ICGST-GVIP Journal, ISSN 1687-398X, Volume (8), Issue (V), January 2009
image processing purposes, including edge detection, B. Detection of microcalcifications using wavelet packets
segmentation, and enhancement of images. The transform
simplicity of the mathematical morphology comes from In the wavelet transform, decomposition is achieved by
the fact that a large class of filters can be represented as iterative two-channel perfect reconstruction filter-bank
the combination of two simple operations on image: the operations over the low frequency band at each level.
erosion and dilation. Given this, the opening and closing From a multiresolution analysis, the two-dimensional
operations can be defined as following. The opening is subband wavelet decomposition is achieved by
erosion followed by dilation, and the closing is dilation implementing a bank of one-dimensional low-pass and
followed by erosion. These two operations are considered high-pass filters, h(x) and g(x) respectively.
as filters. The discrete wavelet packet transform is more flexible
To enhance mammograms, we used two operations: the and powerful than the standard discrete wavelet
top-hat transform defined as the difference between the transform. Its multiresolution decomposition scheme can
original image and its opening, and the bottom-hat be applied to any frequency. The low frequency
transform defined as the difference between the closing subimage and high frequency subimage corresponding to
of the original image and the original image. Operations background, microcalcifications and noise would be
of addition and subtraction of images are then carried out analyzed [7].
using top-hat and bottom-hat transforms to obtain a
In our work [2], we chose Daubechies filters because
mammographic image containing much more visible
while it has finite (compact) support, it is continuous and
microcalcifications [2].
yields better frequency resolution than the Haar wavelet
5. Detection methods and achieves better spatial resolution than other wavelets.
Several different wavelet-based approaches for the Two levels of wavelet packets decomposition are
detection of microcalcifications can be found in the performed with bi-orthogonal Daubechies wavelet.
literature [3], [4]. They all utilize the fact that Fifteen (15) maximums are extracted, one from each
microcalcifications are small, bright features, and, they, wavelet packets (from the second level) except the
therefore appear in certain levels of the wavelet approximation. A threshold is defined for each packet
decomposition of the image. using formula below:
A. Detection of microcalcifications using undecimated Ti = σ i (2 log( N i )) 1 / 2 (2)
wavelet transform
In our work [2], full resolution is maintained during the Where σi is the standard deviation of the packet i and Ni
multiresolution analysis by using redundant is the size of the packet i. A single threshold is defined as
(undecimated) wavelet transform. The wavelet transform the mean of the 15 thresholds calculated for each packet.
is operated without down-sampling and up-sampling in An adaptive thresholding is then performed by varying
respectively the analysis and synthesis computations. the value of the threshold with a logarithmic way. The
This ensures translation invariance and implies a finer process is stopped when we find the best detection of
sampling rate of the wavelet decomposition, a vital microcalcifications in the image. A post processing is
requirement during small object detection such as performed by using a high pass filtering.
microcalcifications. The redundant transform is applied
in each pixel of the image. The size of each subband is C. Detection of microcalcifications using one-
the same as the original image. dimensional Wavelet Transform Modulus Maxima
At first, three levels redundant wavelet decomposition of
We propose in this section a wavelet-based method to
the image are performed with bi-orthogonal Daubechies
perform analysis of digitized mammograms called one di
wavelet [6]. We notice that the wavelet decomposition is
mensional (1D) Wavelet Transform Modulus Maxima
performed after an enhancement step [5]. First level
(WT MM). This method gives very encouraging results
detail coefficients contain mostly noise. Detail
for the detection of singularities like microcalcifications.
coefficients in level 2 and 3 contain fine breast structure
Applications of the WTMM method to 1D signal have
and microcalcifications.
already provided insight into a wide variety of problems,
After decomposition of the image, the low-frequency
e.g. the validation of the cascade phenomenology of fully
subband is set to zero (the microcalcifications appear in
developed turbulence, the characterisation and the
the high-frequency subbands).
understanding of long-range correlation in DNA
An adaptive thresholding is performed to detect
sequences. [8], [9].
microcalcifications. The thresholds are calculated as
Singularity detection can be undertaken by describing the
following: after wavelet decomposition, we determine the
local regularity of a signal [10]. In our approach, we take
maximum value in each subband. We threshold the detail
advantage of the ability of the wavelet transform to
coefficients of each subband with the corresponding
characterize the local regularity of functions. The
threshold and we perform the reconstruction of the
mathematical background justifying this method is
image. The process is iterated by varying the thresholds
described in [11].
with logarithmic way.
The proposed method includes two mains steps. The first
one is based on the continuous wavelet transform applied
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ICGST-GVIP Journal, ISSN 1687-398X, Volume (8), Issue (V), January 2009
on each line of the mammographic image and the multi- Multi-scale product of wavelet coefficients of a function f
scale product of the coefficients of the wavelet transform is given by:
at successive scales. Each line of the image is considered p(u ) = i∏1Wf (u, s )
n
(3)
=
as signal.
The second step includes an algorithm which localises
the maxima corresponding to microcalcifications and This product, which operates the multiplication of
generates automatically a map containing wavelet transform coefficients at successive dyadic scales
microcalcifications only. reinforce maxima lines across scales and raise picks
After a pre-processing step, a continuous and one corresponding to singularities of the signal which is each
dimensional wavelet transform is perform on each line of line of the mammographic image. The product reduces
the mammographic image. We use a wavelet which has and even eliminates false picks.
one moment. It is the first derivative of a Gaussian In our work, we use three dyadic successive scales. The
function. Indeed, the wavelet decomposition of odd number of the terms of p(u) is used to preserve the
theoretical signals, like square or triangle, with wavelets sign of the singularity. Figure 4 shows the result of the
which are derivatives of a Gaussian function provides coefficients multi-scale product. Indeed, we can easily
modulus maxima lines which persist across all scales of remark that noise due to background is totally eliminated
decomposition. These lines of maxima allow to spot and and, there is only picks corresponding to the modulus
to distinguish all types of singularities. maxima of the wavelet transform.
For the mammographic image which is not a theoretical
signal but a real one, detection of singularities is also
performed by a location of maxima lines across scales of
decomposition. However, some interesting maxima
corresponding to singularities are difficult to pick up
from the image details or are present but have very low
value. This is because relevant wavelet coefficients are
embedded into non-specific background. Maxima which
are difficult to locate are also difficult to characterize by
the decade of wavelet modulus maxima [10].
Figure 3 shows continuous wavelet decomposition with
the first derivative of a Gaussian function, operated on a
line of a mammographic image. Indeed, singularities are
not clearly spotted. They are surrounded by a field of low
coefficients. This makes microcalcifications detection
and characterization a very difficult task.
Figure 4. Multi-scale product of wavelet coefficients
The first step is complete; we present in this section the
second step of our detection method which consists in an
algorithm which localises the maxima detected by the
first step and generates automatically a map containing
microcalcifications only. The algorithm localises both:
- maxima corresponding to microcalcifications
isolated in the mammography.
- maxima corresponding to the beginning and the
end of a landing of microcalcifications points in
the mammography. In fact, for some images used
in this work, microcalcifications are pressed
against others and constitute a homogeneous
surface that we call landing.
Figure 3. Decomposition of one line of To generate microcalcifications not included in the
mammographic image landing in the map, we consider the value of each
maxima localised to distinguish it from the background
To overcome this problem, we used the multi-scale of the image.
product of the one-dimensional wavelet transform To generate the landing of the microcalcifications, we
coefficients at successive dyadic scales. The algorithm proceed by:
of the multi-scale product was introduced by Sadler [12], 1- Searching a first maxima on the multi-scale product
[13]. and test its value to distinguish it from the
mammographic tissue.
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ICGST-GVIP Journal, ISSN 1687-398X, Volume (8), Issue (V), January 2009
2- Searching a second maxima on the multi-scale is operated for each of the three direction of wavelet
product and test its value to distinguish it from the decomposition (horizontal, vertical and diagonal).
mammographic tissue. 3
(5)
H L = ∏ LH
3- If the first maxima has negative value and the i =1
i
second has a positive one (landing begins with a negative 3
maxima value and ends with a positive maxima value): LH = ∏ LH
i
(6)
i =1
We test the ratio between the first and the second
3
maxima values. HH = ∏ HH (7)
i
If the maxima values are nearest: i =1
we calculate the mean of the coefficients between We use the fact that the product of significant
the two maxima localised. coefficients across scales at the location (x,y) results in a
we calculate the ratio between the mean of the significant value of Pj(x,y) only if the local maxima
coefficients and the maxima values. propagate down to the considered scale. Obviously, if the
If the ratio is small, generate the landing local maxima die at some intermediate scale, this one
between the tow maxima localised small coefficient in the product will be sufficient to
else (the ration is not small), consider the decrease the value of Pj(x,y)significantly. The key point
maxima as isolated microcalcifications. here is that the wavelet coefficients are significant only in
else (the maxima values are not nearest), consider the vicinity of an important feature while they are close
the maxima as isolated microcalcifications. to zero elsewhere.
To increase further the efficiency of the method, we have
D. Detection of microcalcifications by two-dimensional found that before computing the multiscale correlation
multi-scale product image, it is desirable to select the most significant
We present in this section another wavelet transform wavelet coefficients and to reduce the influence of non-
methodology for detection of microcalcifications. With significant noisy coefficients by applying an adaptive
this method, we can identify microcalcifications which threshold-based denoising to the wavelet coefficients.
are small calcium deposits in tissue, appearing as clusters The thresholds are calculated as following: after wavelet
of bright spots. The method is based on the à trous decomposition, we determine the maximum value in each
wavelet transform [14], which gives a multiresolution subband. We threshold the detail coefficients of each
representation of images consisting of approximation subband with the corresponding threshold and we
images which display the image with increasingly coarser perform the reconstruction of the image.
resolution as the scale itself increases, and of detail
planes which show the objects whose size is adapted to 6. Results
the resolution of the filter at each scale. The MIAS database was used, especially mammographic
However, it is very difficult to pick up the interesting images with calcifications. We present firstly the results
features corresponding to microcalcifications from the of the enhancement step and secondly we present the
analysis of one detail image only. This is because results obtained by the four proposed methods for the
relevant coefficients are embedded into non-specific detection of the microcalcifications.
background detail coefficients. Microcalcifications are Figure 5 is a mammographic image with the amplified
features in the image that are small compared to the region of the lesion and figure 6 presents the obtained
global image, but indeed relatively large when analyzed findings for the enhancement process.
locally.
To overcome the limitation of data coming from a single
image and to distinguish important wavelet coefficients
from non-relevant ones, we take advantage of the
multiresolution. We therefore design a multi-scale spatial
filtering scheme that results in wavelet coefficients that
have high values in the presence of microcalcifications
and characterize them unambiguously, whereas they have
non significant values for the background. To that goal,
we compute a correlation image Pj(x,y) which is defined
at each location (x,y) by the direct spatial multi-scale
product of the wavelet coefficients images at adjacent
scales:
j
P j = ∏ W i ( x, y ) (4) Figure 5. Mammographic image and amplified
i =1 region of the lesion
Where j is the deepest level at which the correlation is
computed. In our work, we applied three levels of
wavelet decomposition.
We notice that the multi-scale product is directional i.e. it
27
ICGST-GVIP Journal, ISSN 1687-398X, Volume (8), Issue (V), January 2009
(a) (b) (a) (b)
(c) (c) (d)
Figure 6. (a) image enhanced with unshrap masking,
(b) with contrast stretching, (c) with morphological
operations
The results of the enhancement techniques are
satisfactory, the contrast stretching, the unsharp masking
filtering and the morphological operations have enhanced
the visibility of features in the mammograms. These
results are comparable to those obtained by other authors (e) (f)
[16]. Nevertheless, by combining these different forms of
image enhancement, the contrast can be greatly Figure 8. (a) mammographic image case mdb209,
increased, facilitating the finding of the locations of the (b) detection with undecimated wavelet transform;
microcalcifications. In this paper, we propose a (c) detection with wavelet packets; (d) detection
combination of enhancement techniques. This with1D WTMM; (e) detection with 2D multi-scale
combination is an unsharp masking filtering followed by product and (f) detection with Donho thresholding
a contrast stretching. Figure 7 shows the result of the
proposed combination method.
According to the radiologist expert, the results obtained
by our proposed method are very satisfactory results.
They are also comparable to those obtained by the
universal threshold of Donoho and even improve them.
Figure 9 presents the obtained results using our proposed
method for another case of mammography.
The detection results obtained by the one-dimensional
modulus maxima wavelet transform seems to be very
(a) (b) accurate and successfully applied to assist in the
diagnosis of digitised mammograms even when
Figure 7. (a) mammographic image, (b) enhanced mammograms present very dense tissue. The results
with the combination method obtained by the two-dimensional multi-scale product are
comparable to those provided by the redundant wavelet
According to the practitioner radiologist, results obtained transform and the wavelet packets transform.
by the proposed combination are very satisfactory and
facilitate the location of the lesion in the mammograms.
The mammograms are enhanced; we present the results
of the proposed detection methods. Figure 8 presents the
obtained results usin the four proposed methods and the
result using the universal Donoho threshold as described
in [17].
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ICGST-GVIP Journal, ISSN 1687-398X, Volume (8), Issue (V), January 2009
(a) (b) (a) (b)
(c) (d) (c)
Figure 10. (a) mammographic image, (b) detection
result, (c) Region of interest
Observation result (One region of interest)
(e)
Figure 9. (a) mammographic image case mdb223,
(b) detection with undecimated wavelet transform;
(c) detection with wavelet packets; (d) detection
with1D WTMM; (e) detection with 2D multi-scale
product
(a) (b)
7. Evaluation of detection methods
The database used in this work is labeled. In fact, the
expert radiologist has mentioned for each image of the
database the center and the radius of the
microcalcifications cluster and that we call region of
interest. In this section, we present a statistical evaluation
of the results obtained by our proposed detection
methods, in relation with the labeling of the expert (c)
radiologist. The images containing microcalcifications
that we generated by the four detection methods are Figure. 11 (a) mammographic image, (b) detection
indeed observed through windows that are circles which result, (c) Region of interest
center coincides with center of the region of the interest Observation result (two regions of interest)
and which radius is determined by the labelling of the
radiologist. In fact, for some images, we can observe
more than one region of interest. Figure 10 and figure 11 Table 1 shows the comparison of detection rate between
show the result of the observation after the detection step, the previous works and our proposed methods.
applied to two images containing respectively one and
two clusters of microcalcifications. The results of
detection shown in these figures are obtained by the one-
dimensional modulus maxima wavelet transform method.
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ICGST-GVIP Journal, ISSN 1687-398X, Volume (8), Issue (V), January 2009
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ICGST-GVIP Journal, ISSN 1687-398X, Volume (8), Issue (V), January 2009
techniques. 40th Southeaster Symposium on System Dr. Mbainaibeye Jérôme
Theory , University of New Orleans, New Orleans, received the Master degree
LA, USA, March, 16-18, 2008. in Signal Processing and the
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International Journal on Graphics Vision and Image an Assistant Professor in the
Processing. 5, 2005. department of Computer
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and A. F. Frere. Analysis of Asymmetry in He is also with the Systems and Signal Processing
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20(9)953 – 964, 2001. department, University of Poitiers, France. His
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Comp. Biomed. Res., 24:273–295, 1991. Compression, Wavelet Transform and its applications.
[21] M. Y. Sallam and K. W. Bowyer. Registration and Dr Mbainaibeye Jérôme is in Post Doctoral research
difference analysis of corresponding mammogram with the Laboratoire de Système et Traitement du
images. Medical Image Analysis, 3(2):103-118,
Signal L.S.T.S, Ecole Nationale d’Ingénieurs de Tunis,
1999.
BP37, Le Belvédère, Tunis 1002, Tunisia (phone :
[22] K. Thangavel, M. Karnan. Computer Aided
+216 874 700, fax : +216 872 700.
Diagnosis in Digital Mammograms: Detection of
Microcalcifications by Meta Heuristic Algorithms.
International Journal on Graphics Vision and Image
Processing. 7, 2005.
Pr. Noureddine Ellouze
received a PhD degree in
10. Biographies 1977 from l’Institut National
Polytechnique at Paul
Dr. Sihem Bouyahia Sabatier University
received the PhD degree in (Toulouse, France), and
Electrical engineering from Electronic Engineer Diploma
ENIT (National High School from ENSEEIHT in 1968 at
of Engineers), Tunisia in the same university. In 1978,
July 2006. She is presently Dr Ellouze joined the
an Assistant Professor in the Department of Electrical
Electrical Department at the Engineering at the National School of Engineer of
High Institute of Medical Tunis (ENIT‐Tunisia), as Assistant Professor in
Techn‐ologies of Tunisia. Statistic, Electronic, Signal Processing and Computer
She is also with the Systems Architecture. In 1990, he became Professor in Signal
and Signal Processing Laborat‐ory at ENIT. Her Processing, Digital Signal Processing and Stochastic
research activities include Digital Signal Processing, Process. He has also served as Director of Electrical
Medical Image Processing, Image analysis, Wavelet Department at ENIT from 1978 to 1983, General
Transform and its applications. The Laboratoire de Manager and President of the Research Institute on
Système et Traitement du Signal L.S.T.S, Ecole Informatics and Telecommunications (IRSIT) from
Nationale d’Ingénieurs de Tunis, BP37, Le Belvédère, 1987 to 1990, President of the same Institute from
Tunis 1002, Tunisia (phone : +216 874 700, fax : +216 1990 to 1994. He is now Director of Signal Processing
872 700,e-mail : sihem_bouyahia@yahoo.fr Research Laboratory (LSTS) at ENIT and is in charge
of Control and Signal Processing Master degree at
ENIT. Pr Ellouze is IEEE fellow since 1987, he directed
multiple Master thesis and PhD thesis and published
over 200 scientific papers in journals and conference
proceedings. He is chief editor of the scientific journal
Annales Maghrébines de l’Ingénieur. His research
interests include Neural Networks and Fuzzy
Classification, Pattern Recognition, Signal Processing
and Image Processing applied in biomedical,
Multimedia, and Man Machine Communication.
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