Using mutual information to evaluate performance of medical imaging systems

doi:10.4236/health.2010.24040

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Vol.2, No.4, 279-285 (2010) Health

doi:10.4236/health.2010.24040

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

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

21 i

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.

(x)

(y)

(x; 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:







},),()],({[),(

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

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

200

400

600

800

1000

1200

Pixel Value

Frequency

Step 5

Step 4

Step 3

Step 2

Step 1

300500 700 900

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

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

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

283

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.0E-04

0 10203040

Relat ive Exposure Level

NPS [mm

]

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

0.6

1.2

1.8

2.4

Exposure Dose [mAs]

MI (Mutual Information) [bits]

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

0.2

0.4

0.6

0.8

1.0

Spatial Frequency [cycle s/mm]

Presampling MT F

Figure 11. Presampling MTF as a function of spatial

frequency obtained with the ST and HR imaging

plates.

0 1 23 45

-8

-7

-6

-5

-4

-3

Spatial Freq ue ncy [c ycles/mm]

N PS [mm

]

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

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.

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