Vol.2, No.4, 279-285 (2010) Health
doi:10.4236/health.2010.24040
Copyright © 2010 SciRes. Openly accessible at http://www.scirp.org/journal/HEALTH/
Using mutual information to evaluate performance of
medical imaging systems
Eri Matsuyama1, Du-Yih Tsai1*, Yongbum Lee1, Katsuyuki Kojima2
1Department of Radiological Technology , Graduate School of Health Sciences, Niigata University , Niigata, Japan; tsai@clg.niigata-u.ac.jp
2Department of Information Networks, Faculty of Administration and Informatics, University of Hama matsu, Hamamatsu, Japan
Received 6 December 2009; revised 6 January 2010; accepted 14 January 2010.
ABSTRACT
Information on physical image quality of medi-
cal images is important for imaging system
assessment in order to promote and stimulate
the development of state-of-the-art imaging sys-
tems. In this paper, we present a method for
evaluating physical performance of medical
imaging systems. In this method, mutual infor-
mation (MI) which is a concept from information
theory was used to measure combined proper-
ties of image noise and resolution of an imaging
system. In our study, the MI was used as a
measure to express the amount of information
that an output image contains about an input
object. The more the MI value provides, the
better the image quality is. To validate the pro-
posed method, computer simulations were per-
formed to investigate the effects of noise and
resolution degradation on the MI, followed by
measuring and comparing the performance of
two imaging systems. Our simulation and ex-
perimental results confirmed that the combined
effect of deteriorated blur and noise on the im-
ages can be measured and analyzed using the
MI metric. The results demonstrate the potential
usefulness of the proposed method for evalu-
ating physical quality of medical imaging sys-
tems.
Keywords: Image Quality; Medical Imaging; Mutual
Information
1. INTRODUCTION
An important criterion for accepting an y type of medical
imaging system is the quality of the images produced by
the imaging systems. The most fundamental quality-
related factors in medical imaging systems are contrast,
spatial resolution and noise. It is customary to describe
contrast by the characteristic curve of the system, spatial
resolution by the modulation transfer function (MTF),
and noise by the noise power spectrum (NPS, also re-
ferred to as the Wiener spectrum) [1,2]. One of the cur-
rent dilemmas in digital radiography is the extent to
which these parameters such as, resolution and noise
affect physical or clinical image quality. An imaging
system may only be superior in one metric while being
inferior to another in the other metric.
In this study we present an information-entropy-based
approach for evaluating overall image quality (including
image noise and spatial resolution in this study) in
medical imaging systems. The approach uses mutual
information (MI ) in infor mation theor y [3,4 ] as an image
quality criterion. Differing from the MTF and NPS
measures, this information-entropy-based metric is de-
scribed in the spatial domain. The concept of MI has
been applied in medical imaging processing, in particu-
lar for image registration tasks and computer-assisted
detection schemes [5-7]. However, the application of MI
as an overall quality metric has been rather limited so far
[8,9]. The primary motivation behind this study was to
use the MI to express the amount of information that an
output image contains about an input object (subject).
The basic idea is that when the amount of the uncertainty
associated with an object before and after imaging is
reduced, the difference of the uncertainty is equal to the
value of MI. The more the MI valu e provides, the better
the image quality is. Therefore, we can quantitatively
evaluate the overall quality of an image by measuring
the MI. The present work is an extension of the afore-
mentioned studies [8,9]. The focus of this paper is to
investigate and characterize the combined effect of noise
and blur on the images obtained from medical imaging
systems using the proposed metric. The advantages of
our proposed method are: 1) simplicity of computation,
2) simplicity of experimentation, and 3) combined as-
sessment of image noise and resolution.
In the present study, simulation studies were first car-
ried out to investigate the relatio nship between noise and
the MI, as well as that between spatial resolutio n and the
MI. To validate the proposed method, two experiments
were then performed. The first experiment was con-
E. Matsuyama et al. / Health 2 (2010) 279-285
Copyright © 2010 SciRes. Openly accessible at http://www.scirp.org/journal/HEALTH/
280
ducted for verifying the effect of noise on the MI value.
The sec ond exper iment w as carri ed out for an alyzing th e
effect of image blurring on the MI value. Furthermore,
in order to compare the proposed method with the con-
ventionally used metrics, the presampling MTF an d NPS
were also calculated and discussed. In addition, two im-
aging plates, a high resolution (HR) type detector and a
standard resolution (ST) type detector, for computed
radiography were used for verification of the potential
usefulness of the MI metric. The verification was made
by showing two real images with detailed discussion.
Results show that the proposed method is simple to im-
plement, and has potential usefulness for evaluation of
overall image quality.
2. MUTUAL INFORMATION
Mutual information (MI) is a basic concept in informa-
tion theory. It has been introduced for the registration of
multimodality medical images. The definition of the
term has been presented in various ways in the literature
[10]. We will briefly describe the MI used for measure-
ment of image quality.
Given events s1,….. sn occu rring with probabilities p1,
p2, …….pn, the Shannon entropy H is defined as
.log),....,( 2
1
21 i
n
iin pppppH
 (1)
Considering x and y as two random variables corre-
sponding to an in put variable and an output variab le, the
entropy for the input and that for the output are denoted
as H(x) and H(y), respectively. For this case, the MI can
be defined as
,),()()(
)()()()();(
yxHyHxH
yHyHxHxHyxMI xy

 (2)
where H(x,y) is the joint entropy, and Hx(y) and Hy(x) are
conditional entropies. The relationship among these en-
tropies is shown in Figure 1.
H
y
(x)
H
x
(y)
MI
(x; y)
H
(x; y)
H
(
x
)
H
(
y
)
Figure 1. Relationship among H(x), H(y),
H(x,y), Hx(y), Hy(x), and MI(x;y).
Consider an experiment in which every input has a
unique output belonging to one of the various output
categories. In this study, for simplicity, the inputs may be
considered to be a set of subjects (for example, a test
sample object with steps of various thickness, while the
outputs may be their corresponding images varying in
optical density or gray level. A method of occurrence-
frequency-based computation is employed in the present
study for calculating the entropies of input, output, and
their joint entropies [11]. With this orderly system, the
amount of MI is easily computed. The MI conveys the
amount of information that output y has about input x.
3. METHODS AND MATERIALS
3.1. Computer Simulation
A simulation was designed and its framework is as fol-
lows. In mathematical terms, a simulation image g(x,y)
is the convolution of a uniformly-distributed signal (an
object) f(x,y) and the blurring function B. If the noise
u(x,y) is also taken into consideration, the resulting im-
age may be represented by the following formula:

5
1
},),()],({[),(
k
WyxuByxfkyxg (3)
wher e th e s ymb ol
represents the convo lution operatio n,
B is a blurring function, and k is an integer representing
the number of steps of the simulated image. In this
simulation study, the input image f(x,y) is a five-step
wedge with a specific intensity or pixel value on each
step. The term of W is a weighting coefficient used to
adjust the extent of noise, and u(x,y) is a zero-mean
Gaussian noise with a standard deviati o n of 0.5.
Two simulations were performed separately. The first
simulation was carried out to investigate the relationship
between image noise and the MI. We employed sig-
nal-to-noise ratio (SNR) to describe the extent of noise
level. The signal and noise used for SNR calculation
were [f(x,y)]
B and u(x,y) × W, respectively, as given in
(3). As a blurring function, we used a neighborhood av-
eraging filter with a size of m × m (m is an odd integer).
The extent of blurring was adjusted by varying the filter
size. The reason for choosing neighborhood averaging
filter was due to its commonality and simplicity of op-
eration. The second simulation was conducted to inves-
tigate the relationship between the blurring (spatial reso-
lution) and the MI.
An image of a simulated step wedge is shown in Fig-
ure 2(a). Five regions of interests (ROIs) indicated with
rectangles near the boundaries of two adjacent steps
were chosen for calculation of the MI. The five steps of
the step-wedge image are numbered from the right side
as step 5, step 4, …, and step 1. The right band without a
rectangular box is the background of the image. The
corresponding pixel-value distributions measured from
E. Matsuyama et al. / Health 2 (2010) 279-285
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281
the ROIs are given in Figure 2(b). The area of each ROI
used in this study was 50 × 200 pixels. As a result, a
total of 10 × 103 data for each step was obtained. As
shown in Figure 2(a), the number of inputs is five, and
the number of outputs is the range of gray levels shown
on the horizontal axis of the pixel-value distributions
(see Figure 2(b)).
3.2. Experiments
An acrylic step wedge 0-1-2-3-4-5 mm in thickness was
used as a test sample object for experiments. The speci-
fied exposure factors were kept at 42 kV and 10 mA, and
the focus-imaging distance was taken as 185 cm, but the
exposure time was varied from 0.1 sec to 0.4 sec. A tube
voltage of 50 kV was also employed for comparison. An
imaging plate (standard resolution type, ST, Fuji Film
Japan, Inc.) was used as a detector to record X-ray in-
tensities.
In this study, two experiments were performed. The
first experiment was conducted for verifying the effect
of noise properties on the measured MI value, and the
second experiment was performed for analyzing the
effect of resolution (blur) properties on the MI value.
The experiments were carried out by varying of expo-
sure levels and by use of various effective focal spot
sizes of the X-ray tube, respectively. The latter experi-
ment was achieved by shifting of the step wedge away
from the center of the X-ray beam area toward the
cathode end when imaging was performed. The effec-
tive foca l spot size ch anges with po sition in the field. I t
becomes larger for points toward the cathode end of the
field [12]. The increase in the effective focal spot size
results in the degradation of resolution (blur). In addi-
tion, a high resolution type imaging plate HR for com-
puted radiography was also used for evaluation and
comparison. Moreover, two real images (the distal fe-
mur and the tarsal bone) were shown and compared for
experimental validation of the advantages of the pro-
posed method.
4. RESULTS AND DIS CUSSION
Simulations were performed to investigate individual
effects of noise and spatial resolution on MI. Figure 3
illustrates the MI as a function of SNR for various levels
of blurring at image contrast of 20. The results indicate
that MI value increases with the increase of SNR (de-
crease in noise level). Figure 4 shows the MI as a func-
tion of filter size of blurring function for various levels
of SNR at image contrast of 20. The results indicate that
MI value decreases when filter size of the blurring func-
tion increases (degradation of resolution). It was noted
that the decline of the MI value is relatively small. It
means that the effect of the level of blur on the MI is not
so obvious in comparison to noise.
(a)
300500 700 900
0
200
400
600
800
1000
1200
Pixel Value
Frequency
Step 5
Step 4
Step 3
Step 2
Step 1
300500 700 900
0
200
400
600
800
1000
1200
Pixel Value
Frequency
Step 5
Step 4
Step 3
Step 2
Step 1
(b)
Figure 2. (a) Computer-generated step wedge. A region of
interest (ROI) shown with a rectangle at each step of the
step wedge was chosen for entropy computation. (b) The
corresponding pixel-value distributions measured from the
ROIs shown in (a).
30 35 40 45 50
1.4
1.6
1.8
2.0
2.2
2.4
Signal -to-Noise Ratio [d B]
MI (Mutual Inform atio n) [bi t s]
FS1
FS7
FS11
FS21
FS31
FS41
FS61
FS 1
FS 61
Figure 3. Relationship between the SNR and the MI for vari-
ous levels of blur at an image contrast of 20.
E. Matsuyama et al. / Health 2 (2010) 279-285
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282
020 40 60
1.8
1.9
2.0
2.1
2.2
2.3
2.4
F ilt er Size of B lurring Function
MI (Mutual Informati o n) [bi ts]
SNR35 SNR38SNR40 SNR4 2
Co ntras t 20
Figure 4. Relationship between the filter size of blurring
function and the MI for various levels of SNR at an image
contrast of 20.
Figure 5 illustrates the MI value as a function of the
relative exposure level for tube vo ltages of 42 kV and 50
kV. The result shows that the MI value increases with the
increase in the exposure level. The increase of the MI
value is considered to be mainly due to the decrease of
noise. Figure 6 illustrates the NPS of the imaging sys-
tem used in this study as a fun ction of the relative expo-
sure level at 42 kV for spatial frequencies of 0.5, 1.0,
and 1.5 cycles/mm. The figure indicates that the NPS
decreases with increasing exposure levels.
Figure 7 shows the presampling MTF as a function of
spatial frequency for three effective focal spot sizes,
obtained by shifting of the step wedge 15 cm and 30 cm
away from the center of the X-ray beam area toward the
cathode end. The MTF was measured with an angled-
edge method. Theoretically, the amount of geometric
blurring increases when the size of effective focal spot
increases. As shown in Figure 7, the MTF was degraded
with the increase of the effective focal spot size. Figure
8 provides the one-dimensional NPS as a function of
relative exposure for the three effective focal spot sizes
at spatial frequency of 0.5 cycle/mm. The difference of
NPSs is moderately small. Figure 9 is a plot of the MI
values for the three effective focal spot sizes. The meas-
ured results show th at the MI value beco mes lower when
the off-center distance is greater. In other words, the MI
value decreases when the effective focal spot size in-
creases. This means that the MI value decreases when
blur is deteriorated. It is noted that the decrease of the
MI is mainly due to the image blurring resulting from
the increase of the effective focal spot size. Therefore,
the MI is also closely correlated with the resolution (blur)
of imaging systems.
Figure 10 shows the relation between the exposure
dose and the MI for the images obtained with ST and
HR imaging plates. The results illustrate that the MI in-
creases with the increase of exposure dose. The rise of
1.5
2.0
2.5
3.0
0204060
Relative Ex
p
osure Level
MI (Mutu a l Inf ormat io n)
[
bits]
42 kV
50 kV
Figure 5. Mutual information as a function of relative
exposure level for tube voltages of 42 kV and 50 kV.
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1.0E-04
0 10203040
Relat ive Exposure Level
NPS [mm2]
0.5 cycle/mm
1.0 cycle/mm
1.5 cycle/mm
42 kV
Figure 6. Noise power spectra (NPS) as a function of rela-
tive exposure level for three spatial frequencies at 42 kV.
0.0
0.5
1.0
01234
Spatial Fr equency [ c y c les /mm]
Presampling MTF
center
off center 15 c m
off center 30 c m
42 kV
Figure 7. Presampling MTF as a function of spatial fre-
quency for three effective focal spot sizes, obtained by
shifting of the step wedge 15 cm and 30 cm away from
the center of the X-ray beam area toward the cathode end.
E. Matsuyama et al. / Health 2 (2010) 279-285
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283
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1.0E-04
0 10203040
Relat ive Exposure Level
NPS [mm
2
]
cent e r
off cen t er 15 c m
off cen t er 30 c m
0.5 cycle/mm
42 kV
Figure 8. Noise power spectra (NPS) as a function of
relative exposure level for three effective focal spot
sizes for 42 kV at the spatial frequency of 0.5 cy-
cle/mm.
1.0
1.5
2.0
0 1020304050
Relative Exposure Level
MI (Mutual Information) [bits]
cen ter
off center 15 cm
off center 30 cm
42 kV
Figure 9. Mutual information as a function of relative
exposure level for three different exposure positions of
the step wedge at 42 kV.
05 10 15 20 25 30
0
0.6
1.2
1.8
2.4
Exposure Dose [mAs]
MI (Mutual Information) [bits]
ST
HR
Figure 10. Mutual information as a function of rela-
tive exposure level for ST and HR imaging plates.
MI is considered due to the decrease of noise resulting
from the increase of radiation dose. As shown in the fig-
ure, the MI value for the ST plate is higher than that for
the HR plate at the same exposure dose. This can be ex-
plained by the fact that combined effects of the blur and
noise lead to a higher MI value for the ST plate. Figure
11 shows the presampling MTFs of the ST and HR im-
aging plates. The MTF of HR imaging plate is higher
than that of ST imaging plate. This means that the spatial
resolution (blur) of HR plate is higher than that of ST
plate. Figure 12 illustrates the NPS of the ST and HR
imaging plates used in this study. The results show that
the NPS of the HR imaging plate is higher than that of
the ST plate. This means that ST imaging plate has better
noise proper ties.
0 1 23 45
0
0.2
0.4
0.6
0.8
1.0
Spatial Frequency [cycle s/mm]
Presampling MT F
HR
ST
Figure 11. Presampling MTF as a function of spatial
frequency obtained with the ST and HR imaging
plates.
0 1 23 45
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
Spatial Freq ue ncy [c ycles/mm]
N PS [mm
2
]
HR
ST
Figure 12. NPS as a function of spatial frequency ob-
tained with the ST (standard resolution) and HR (high
resolution) imaging plates.
E. Matsuyama et al. / Health 2 (2010) 279-285
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284
Figure 13. Real images of the distal femur acquired with ST
(top row) and HR (bottom row) imaging plates.
Figure 14. Real images of the tarsal bone acquired with ST
(top row) and HR (bottom row) imaging plates.
In Figures 13 and 14, we display the real images of
the distal femur (Figure 13) and tarsal bone (Figure 14)
acquired with ST and HR imaging plates under the same
exposure conditions. In the two figures, the left column
illustrates the original images; while on the right are the
magnified images of the white rectangles indicated in the
original images. It is seen from the magnified images
(Figure 13) that the patellofemoral joint (with a white
circle) obtained with the HR plate shows better resolu-
tion as compared to ST plate. Similarly, the magnified
images of Figure 14 (the cuneiform and navicular re-
gions indicated by a white arrow) obtained with HR
plate shows better resolution as compared to ST plate.
The experimental validation provides confirming evi-
dence for the MTF results presented in Figure 11. As
regarding image noise, it can be seen from the magnified
images of Figures 13 and 14 that the images acquired
with HR plates show higher noise levels. The perceptual
results correctly reflect the outcome of the NPS shown
in Figure 12.
5. CONCLUSIONS
In this study, we have presented a method for evaluating
physical performance of medical imaging systems. In
this method, mutual information was used to measure
combined properties of image noise and resolution of an
imaging system. To validate the proposed method, com-
puter simulations were first performed to investigate the
effects of noise and resolution degradation on mutual
information. Then experiments were conducted to meas-
ure the physical performance of an imaging plate in
terms of the proposed metric. Our simulation and ex-
perimental results confirmed that the combined effect of
deteriorated blur and noise on the images can be meas-
ured and analyzed using the mutual-information metric.
The method is expected to be useful for evaluating over-
all image quality of medical imaging systems.
REFERENCES
[1] Fujita, H., Doi, K. and Giger, M.L. (1985) Investigation
of basic imaging properties in digital radiography. 6.
MTFs of II-TV digital imaging systems. Medical Physics,
12, 713-720.
[2] Giger, M.L., Doi, K. and Fujita, H. (1986) Investigation
of basic imaging properties in digital radiography. 7.
Noise Wiener spectra of II-TV digital imaging systems.
Medical Physics, 13, 131-138.
[3] Shannon, C.E. (1948) Mathematical theory of communi-
cation. Bell System Technical Journal, 27, 379-423, 623-
656.
[4] Shannon, C.E. and Weaver, W. (1949) The mathematical
theory of communication. The University of Illinois
Press, Urbana.
[5] Skerl, D., Likar, B. and Pernus, F. (2006) A protocol for
evaluation of similarity measures for rigid registration.
IEEE Transactions on Medical Imaging, 25, 779-791.
[6] Pluim, J.P.W., Maintz, J.B.A. and Viergever, M.A. (2003)
Mutual-information-based registration of medical images:
A survey. IEEE Transactions on Medical Imaging, 22,
986-1004.
[7] Tourassi, G.D., Harrawood, B., Singh, S. and Lo, J.Y.
(2007) Information-theoretic CAD system in mammog-
raphy: Entropy-based indexing for computational effi-
ciency and robust performance. Medical Physics, 34,
3193-3204.
E. Matsuyama et al. / Health 2 (2010) 279-285
Copyright © 2010 SciRes. Openly accessible at http://www.scirp.org/journal/HEALTH/
285
[8] Lee, Y., Tsai, D.Y. and Matsuyama, E. (2007) A simula-
tion study of radiographic image quality measurement
based on transmitted information. Japanese Journal of
Radiological Technology, 63, 341-344.
[9] Tsai, D.Y., Lee, Y. and Matsuyama, E. (2008) Informa-
tion-entropy measure for evaluation of image. Journal of
Digital Imaging, 21, 338-347.
[10] Cover, T.M. and Thomas, J.A. (1991) Elements of infor-
mation theory. Wiley-Interscience, New York.
[11] Attneave, F. (1967) Applications of information theory to
psychology. Holt, Rinehart and Winston, New York.
[12] Sprawls, P.Jr. (1995) Physical principles of medical im-
aging. Medical Physics Publis hing, Wisconsin.