CARDIAC MRI STEAM IMAGES DENOISING USING
BAYES CLASSIFIER
1
A. G. Motaal1, M. A. Al-Attar1, N. F. Osman1, A. S. Fahmy1, 2
Center of Informatics Science, School of Communication and Information technology, Nile University, Cairo, Egypt
2
Systems and Biomedical Engineering Department, Faculty of Engineering, Cairo University, Cairo, Egypt
E-mail: [email protected]
Abstract- Imaging of the heart anatomy and function using
magnetic resonance imaging (MRI) is an important diagnosis
tool for heart diseases. Several techniques have been developed
to increase the contrast-to-noise ratio (CNR) between
myocardium and background. Recently, a technique that
acquires cine cardiac images with black-blood contrast has been
proposed. Although the technique produces cine sequence of
high contrast, it suffers from elevated noise which limits the
CNR. In this paper, we study the performance and efficiency of
applying a Bayes classifier to remove background noise. Real
MRI data is used to test and validate the proposed method; In
addition, a quantitative comparison is done between the
proposed method and other thresholding-based classifications
techniques.
I. INTRODUCTION
Black-blood cardiac MRI techniques provide high CNR
between the blood and the tissues by nulling blood signal.
This also has the advantage of avoiding the flow artifacts
generated by the blood. Aletras et al [1] succeeded in
proposing an acquisition technique that results in acquiring a
image of black blood, but blood signal is nulled at specific
time only in the cardiac cycle so it prohibit producing cine
sequence. Frahm et al proposed a technique that is used to
make cine sequence with black blood contrast called
STEAM[2], but it suffered from severe deformationdependent artifact[2,3]. To solve these problems Fahmy et al
proposed a modified STEAM based technique that
successfully produce cardiac cine sequence with black blood
contrast and correct the STEAM artifact [4]. Unfortunately
low CNR is the limitation of this technique. This article
proposes a method for removing the background noise in the
modified-STEAM imaging technique and thus enhancing the
myocardium CNR, The method uses a Bayes classifier to
differentiate the background from the tissues (whether
myocardium or static tissues) [5]. First, a probabilistic model
for tissue and blood signals is constructed and then used to
establish a Bayes discriminant function which is used to
identify and filter out the background signal.
II.THEORY
A. Black-blood cardiac MRI:
1) Noise-free model:
The basic idea behind the modified STEAM technique is
to acquire two black-blood STEAM image sequences with
complementary image intensity. That is, one sequence
captures static and low contracting tissues (L.T image), while
the other captures highly contracting tissues (H.T image). In
the noise-free case, given a time frame t, the signal intensities
in pixel (x,y) in the acquired images was shown to be given
by (refer to Ref. [4] for more details),
Proceedings of the 2008 IEEE, CIBEC'08
S1(x,y,t) = p(x,y) Sinc (∂ω(x,y,t)),
(1)
S2(x,y,t) = p(x,y) Sinc (1 - ∂ω(x,y,t)),
(2)
where p(x, y) is the signal component representing the nuclear
properties of the tissues at pixel (x,y) and ∂ω(x,y,t) is a
deformation-dependent term that is related to the tissue strain,
and they can be estimated from S1 and S2 as described in [6].
As shown in [4], adding the two images S1 and S2 and
multiplying the result with an appropriate weights yield an
image whose intensity does not depend on the tissue
deformation, i.e. ̂ (x, y).
2) Probabilistic model:
In order to account for the noise effect, a probabilistic
model is used to model the signal intensity of the STEAM
images. Here the well-known MRI signal model that uses
Rician and Rayleigh probability density functions [7] to
model the tissue and the background signals respectively will
be used. Using the fact that the two images S1 and S2 are
acquired independently, we can easily show that the joint
density function for their signal intensities (at the same pixel
location) can be written as mentioned in [8] as follows,
fs1,s2 (s1s2|tissue)=fs1(s1|tissue).fs2(s2|tissue)
=
S .S
.e
I0
.
.
S
S
e
.I0
.
.
.
.
.
(3.a)
fs1,s2 (s1s2|bckgnd)=fs1(s1|bkgnd).fs2(s2|bkgnd)
=
S .S
S
e
S
(3.b)
B. Identifying and removing background noise
As mentioned above, it is required to identify the
background regions in the reconstructed sequence, ̂ (x, y),
and suppress their signal. In this work, a feature vector
ν=[S1(x,y), S2(x,y)] is used to represent the information
available for each pixel (x,y) in the sequence ̂ (x, y) based on
the Bayes classifier technique [5], all feature vectors are then
classified into two classes (background and tissues) as
follows. First, a Bayes discriminant function is built using the
joint probability function in Eq. (3.a) and (3.b),
∂ =log (fs1,s2 (s1s2|tissue)) - log(fs1,s2 (s1s2|bckgnd))
(4)
Based on the above equation, the decision rule for the
classification becomes,
,
,
,
0
0
978-1-4244-2695-9/08/$25.00 ©2008 IEEE
Figure 1 shows the Block diagram of Bayyes classifier
technique.
L.T and H.T images, and thhe behavior for l1, l2 and l∞ are
shown in yellow, white, andd dashed red lines respectively.
The l1 norm can be representted by straight line, the l2 norm
can be represented by a quaddratic curve and the l∞ norm can
be represented by a rectangle.
IV. RESSULTS
A. Test and Analysis
Figure 1. Block Diagram of Bayes Technique.
III. METHODOLOGY
To validate the proposed method it was
w tested using real
MRI data. A human volunteer was imageed using the modified
STEAM technique to capture 12 time fraames for a short-axis
cross-section of his heart. At each timee frame, equations 1
and 2 were used to reconstruct a black seqquence, p(x, y). Only
2 time frames out of acquired twelve tim
me frames are shown
in Figure 2.a. To filter the backgrouund noise, first, the
standard deviation of the background noise
n
was calculated
using the maximum likelihood described in [7],
∑
=
,
є
,
,
where R is a background region of size N (shown as a white
rectangle in Figure 3); In order to idenntify the background
regions, the proposed Bayes decision rulle was applied to the
images in Figure 2.a. Simple thresholding techniques were
also used to remove the background noise. The basic idea is
to compare the length of the vector, ν, wiith a threshold and if
it is smaller than the threshold then it is considered as
background noise; otherwise, it is consiidered tissue. In this
work, three vector norms have been used
u
to measure the
length of the intensity vector, ν: l1, l2 and l∞ which are
calculated from the relation.
ln=
,
where S1 is the signal acquired from the L.T
L image while S2 is
the signal acquired from H.T image. Soo when applying the
technique we check whether the l-norm at every pixel is less
than certain threshold or not, as if it exceeeds this value it will
be an indication that this pixel is tisssue and vice versa.
Different threshold values were tested annd it was noticed that
the value equal to µ+σ, where µ and σ are the mean and
standard deviation of the background reegion in the p(x, y),
gave the best results and optimal valuees of sensitivity and
specificity for the p(x, y). Also for thee l2 norm when the
threshold value multiplied by 0.75 resultts are enhanced, and
the same for the l∞ norm when it wass multiplied by 0.65
results are enhanced at high extent. Figuure 4 shows the joint
probability density function for the backkground region in the
Proceedings of the 2008 IEEE, CIBEC'08
Figures 2.b-e show the reesult of applying the Bayes and
thresholding techniques (uusing l1, l2 and l∞ norms)
respectively on the images of
o figure 2.a. It is worth noting
that all images in Figure 2 are displayed with the same
contrast and intensity settinngs. That is, the differences
between the images are due too the effect of the noise removal
process. Numerical Analysis was
w done to represent how each
technique behaves in differennt ROI (background, static tissue
and myocardium) for the diffeerent time frames, and therefore
decide the sensitivity and specificity
s
for each technique.
Figure 5 shows the three reegions of interest and they are
represented by dotted, dashedd and solid line regions. Figure 6
shows the number of pixels considered as a background in
each technique for the differeent ROIs for all the time frames.
Also sensitivity and specificcity for all the techniques are
calculated, where they are givven by the relation,
Specificity =
Sensitivity =
where TP is the true backgrouund, FN is the false tissue, TN is
the true tissue, and FP is thhe false background. Figure 7
shows the sensitivity and Speecificity behavior with the time
for the all techniques.
B. Computation Time:
There is a need to measurre the efficiency of the different
denoising techniques based on their computation times. This
was done through applying thhe 4 different methods stated in
this paper, each method difffer from the other in the time
needed to perform the algorrithm to a set of images. The
computer specification that was
w used was 2.66GHz processor
with 2GB RAM, the techhnique that need the longest
computation time was Bayess technique while that need the
shortest time is l∞ technique. Numerically
N
each technique was
applied on 12 pictures, for the
th bayes method it took 8.287
seconds to apply the method for
f all the time frames, while for
l2 norm method it took 2.228 seconds, for the l1 norm method
it took 2.317 seconds, finally for the l∞ norm method it took
2.121 seconds. Computationaal time could be reduced to high
extent when pointers are used
u
in the program, as the
computation time reduced to 60% when pointers were used.
Table 1 shows the compuutation time for the different
methods.
Method
l∞ norm
l1 norm
l2 norm
Bayes
Com
mputation
Tim
me(sec)
0
0.1761
0
0.1780
0
0.1856
0
0.6702
Relative Time
1
1.01
1.05
3.80
Table 1 Computation time for thhe different techniques per one frame
978-1-4244-2695-9/08/$25.00 ©2008 IEEE
Figgure 2.a Two combined Images that were used to
apply the different techniques on them.
Figure 2.d
Figure 2.b
Figure 2.c
Figure 2.d
Figure 2.e
F
F
Figure
2.e
Figure 2.b) the result of applying bayes technique,, 2.c) the result of applying l1 technique 2.d) the result of applying l2 technique 2.e) the result of
applying l∞ technique
Figure 3 the region from the backround that was
w
taken to calculate the standard deviation
Figure 5 The different RO
OIs, background region (Dotted)
static tissue (Dashed), annd myocardium region (Solid)
3580
3560
3540
3520
3500
3480
3460
3440
3420
3400
Figure 4 The joint pdf for the background region in
i the L.T
and H.T images, the behavior for l1, l2 and l• are shown
s
in
solid, dashed and dotted line respectively..
Proceedings of the 2008 IEEE, CIBEC'08
Bayes
L1 norm
L2 norm
L∞ norm
Time frame
1 2 3 4 5 6 7 8 9 10 11 12
Figure 6.a shows the number
n
of pixels considered
as noise in the background region
978-1-4244-2695-9/08/$25.00 ©2008 IEEE
frame and the result after appplying region removal followed
by holes filling.
35
30
25
Bayes
20
L1 norm
15
L2 norm
10
L∞ norm
5
Time frame
0
1 2 3 4 5 6 7 8 9 10
0 11 12
Figure 8 Bayes Classifier result beefore and after applying morphological
opeerators
Figure 6.b shows the number of pixxels considered
as noise in the static tissue region
r
A
CONCLUSION
V. DISCUSSION AND
Fig 2.d
8
7
6
5
4
3
2
1
0
Bayes
L1 norm
L2 norm
L∞ norm
Time frame
1 2 3 4 5 6 7 8 9 10 11 12
Figure 6.c shows the number of pixels coonsidered
as noise in the contracting tissue reggion
In this work, we examinedd the performance of the Bayes
classifier in removing backgground noise from black blood
cardiac MRI images. Althoughh the technique provides optimal
results in terms of sensitivity and specificity, the computation
time is more than three folds that of other simpler classifiers
T later techniques successfully
such as l-norms classifiers. The
remove the background noise with comparable performance to
that of the Bayes classifierr. Therefore, we propose that
suboptimal classifiers can be used to remove the noise if the
processing time is crucial to thee application.
ACKNOW
WLEDGMENT
This work is supported by NIH
N
grant (HL072704) and PDP
grant from ITIDA agency, Ministry
M
of Communication and
Information technology, Egypt.
100
98
Bayes
96
REFERENCES
L1 norm
94
L2 norm
92
L∞ norm
90
Time frame
1 2 3 4 5 6 7 8 9 10 11
1 12
Figure 7.a shows the sensitivity behavvior for each
technique within the time fram
mes.
100
99
Bayes
98
L1 norm
97
L2 norm
96
L∞ norm
95
Time frame
1 2 3 4 5 6 7 8 9 10 11 12
Figure 7.b shows the specificity beehavior for each
technique within the time frames.
C. Further Processing
The results of the Bayes method can be
b enhanced more by
applying morphological operators like region
r
removing and
holes filling. Figure 8 shows Bayes classifier result for a time
Proceedings of the 2008 IEEE, CIBEC'08
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