Gamma-ray compton spectrum analysis to enhance medical imaging using wavelet transformation

doi:10.4236/ns.2011.311123

Paper Menu >>

Journal Menu >>

Vol.3, No.11, 963-970 (2011) Natural Science

http://dx.doi.org/10.4236/ns.2011.311123

Gamma-ray compton spectrum analysis to enhance

medical imaging using wavelet transformation

Ali Pazirandeh*, Saman Ebrahimi

Nuclear Engineering Department, Science and Research Branch, Islamic Azad University, Tehran, Iran;

*Corresponding Author: [email protected], [email protected]

Received 20 July 2011; revised 25 August 2011; accepted 7 September 2011.

ABSTRACT

Cs-137 radioactive source with 661.7 keV gamma-

ray energy and Am-241 with 59.5 keV gamma-ray

energy were used to study the body structure of

materials by examining transmitted gamma-ray

spectrum using a scintillation detector, NaI(Tl).

Due to specific characteristic properties of the

medium, the passing Compton broad scattering

spectrum contains valuable information. It is

possible to mark and to specify the Compton

spectrum caused by atomic specifications of Al,

Cu, bone, muscle, and lipid as interactive mate-

rials. Wavelet transforms and other multi-scale

analysis functions have been used for compact

signal and image representations in de-noising,

compression and feature detection processing

problems for about twenty years. Comparing the

transmitted spectra through muscle, bone and a

tumor-like (fat) and analyzing each spectrum by

wavelet analysis, the differences of the medium

were shown. This study is devoted to use of

wavelet transform for feature extraction associ-

ated with gamma spectrum, which corresponds

to image pixel, and their classification in com-

parison with the Haar and Rbio3.1 transforms.

Keywords: Wavelet; Haar; Rbio3.1; Compton

Scattering; MATLAB; Al; Cu; Muscle; Bone; Lipid;

Am-241; Cs-137

1. INTRODUCTION

The aim of this study is to present an effective and re-

liable technique to analyze the spectrum of the photo-

peak region and the broad Compton scattering spectrum

of Cs-137 and Am-241 passing gamma-rays, which were

recorded by a 3"*3" NaI(Tl) scintillator crystal housed in

an aluminum cylinder coupled with a photomultiplier

tube (PMT). In order to extract more valuable data from

transmitted gamma-ray, we propose a new wavelet-

based approach for analysis and classification of spec-

trum samples with small peaks of broad Compton scat-

tering. The main idea of this method is to analyze the

given spectrum with a continuous 1D wavelet transform

(CWT) and to form an image approximation with higher

contrast.

This is regarded as a nondestructive testing (NDT)

technique. With the help of multiple scatterings caused

by different material atoms, voids, cracks and other de-

formations in the energy spectrum are formed, which are

capable of being analyzed to indicate discontinuities and

defects [1]. The frequencies of each peak could be used

to determine the size of the structure or the location of

the boundaries [2].

The amount of spectrum variation, relative to when

there is no barrier, is proportional to the atomic structure

and electron density of materials such as bone and mus-

cle. Wavelet analysis was applied to explain the atomic

specifications of muscle, bone and metal sheets. In gen-

eral, any structural disorder may be reflected in the scat-

tered or transmitted gamma-ray spectra, which could be

determined effectively by wavelet transformation.

The Cs-137 661.7 keV gamma-ray spectrum passed

through aluminum and copper sheets, having the same

surface densities, and also Am-241 59.5 keV spectrum

passed through animal bone and muscle showed differ-

ent structure in their shapes. In such cases, wavelets are

powerful tools for characterizing and extracting features

because the differences among the spectra are displayed

in a specific place and frequency variations. However

these differences are seen by eyes in most cases but our

purpose is to recognize these differences by the com-

puter for comparison and further deduction. The analysis

must be independent of amplitude, which means there is

an independency between analysis and exposure dura-

tion and counting. In fact this is a benefit of using wave-

let analysis.

A. Pazirandeh et al. / Natural Science 3 (2011) 963-970

964

2. DATA ACQUISITION

Gamma-ray spectra were obtained using a 3"*3" Na

(Tl) scintillator crystal coupled with a photomultiplier

tube (PMT) and a multichannel analyzer (MCA). After

data acquisition, it converted to Excel format and then

imported to MATLAB software as a matrix. Having used

an MCA 8k internal ADC, the original matrices have

2000 up to 8000 elements depending on setup for MCA.

In this study, the transmitted spectra had a matrix size of

150 and 300 after manipulation. As mentioned earlier it

depended on setup for MCA. In each spectrum, the

x-axis indicates the number of channels corresponding to

the energy bands which are classified by MCA and the

y-axis shows the counts for each channel. There is no

unique setup for MCA device but in each experiment,

data acquisition must be formed in the same conditions

for different barriers, such as Al, Cu, bone and fat to

achieve comparable data. If higher resolution is used, it

makes lower count of individual channel and makes

more noise on registered spectrum. However, because of

the scale nature of wavelet transform, it is not very im-

portant for our analysis but more count in each channel

makes more quantitative differences. In fact, using the

specific scale we denoise the spectrum by ignoring and

discarding unwanted frequency data.

3. WAVELET

The classical Fourier transformation portrays a signal

record as superposition of infinite sinusoidal waveforms

of assorted frequencies representing an orthogonal basis.

Due to the fixed frequency basis used, the Fourier de-

composition is suitable for signal analysis having rela-

tively stationary frequency characteristics through entire

length. On the other hand, the wavelet transformation

uses a specific sets of basis which are localized both in

the original (i. e. , time) and the transformed (i.e., fre-

quency) domains. Hence the wavelet transformation is

more suitable for analyzing non-stationary signal records,

such as those with discontinuities or sudden (i.e., local)

changes. Wavelet analysis is capable of revealing as-

pects of data such as trends, breakdown points, discon-

tinuities in higher derivatives, and self-similarity which

other signal processing methods are neglecting. One

major advantage afforded by wavelets is the ability to

perform local analysis where a localized area of a larger

signal is analyzed.

A wavelet is a waveform of effectively limited dura-

tion that has an average value of zero. The continuous

Wavelet Transformation (CWT) of X(t) signal is [3]:

 

Wa xtt

















 (1)

where ψ(t) is the mother wavelet function, a is a positive

number, which defines the scale and τ is any real number

defines the shift. The 1a is a normalization factor

that makes each wavelet unitary. Presented by researcher,

some wavelet functions such as Morlet in Eq.2 have

gained a broad applications [3].



tiCt





 (2)

It is possible to generate a customized wavelet for a

specific application [4]. In this research we focused our

studies on relatively symmetric peaks, therefore it is

suitable to use wavelets which have symmetric wave-

form. After examining various wavelets and compare

results, we used Haar and Rbio3.1 wavelets that have

best results for our study. These wavelets are shown in

Figure 1.

The Haar wavelet is in fact a step function and db1

wavelet is also of the same shape. There are discussions

by other researchers [5]. The orthogonal set of Haar

wavelets hi(t) is a group of square waves with magnitude

of ±1 in some intervals and zeros outside the interval [5,

6]. In general,







12,2,

0, 02,,,

hthtk nk

jknjkZ









 





1, 02

1, 1

















(a)

(b)

Figure 1. (a) Haar wavelet (h1(t)), (b) Rbio3.1 wavelet.

A. Pazirandeh et al. / Natural Science 3 (2011) 963-970

965965

Each Haar wavelet contains one and just one square

wave, and is zero outside the square. Just these zeros

make Haar wavelets to be local and very useful in solving

singular systems of time invariant and time varying case.

[6]

Rbio.3.1 is a Biorthogonal family wavelet which is

shown in Figure 1(b).

4. MEASUREMENTS

In this study aluminum and copper sheets with surface

density 2.67 g/cm2 were used. The transmitted spectra

are shown in Figure 2. As mentioned before, the x-axis

indicates the number of channels corresponding to the

energy bands which are classified by MCA and the

y-axis shows the counts for each channel. The difference

between the two spectra is presented in Figure 2.

Using Haar wavelet analysis the difference between

these two spectra are seen explicitly by comparing Fig-

ures 3 and 4 which is displayed in the bottom left of

Figure 3. The top is original gamma spectrum and bottom

is the Haar wavelet coefficients, which are plotted for

aluminum.

Figures 3 and 4 are Ca,b coefficients—coloration

mode provided by MATLAB Wavelet Toolbox. C is the

wavelet coefficient and its value is shown in color. As in

Eq.1 “a” represents the scale and corresponds to the

y-axis and “b” defines the shift or position correspond-

ing to the x-axis. This method of MATLAB analysis is

concerned with continuous wavelet transform (CWT)

and data from MCA are discrete. It could not make mis-

take because even for CWT, computer use the digital

data for the calculation and on the other hand, the nature

of the energy spectrum is continuous.

As Figure 2 shows, there is a clear difference between

the spectra in the low energy region. Considering the

number of channels that this peak is expanded over, the

scale number 6 is a suitable wavelet coefficient for

comparison. As mentioned before, it can vary according

to the configuration of MCA, but for a defined condition

it is stable. The difference between magnified images of

this scale is seen in Figures 5 and 6.

At this scale and position, the difference between the

obtained coefficients makes it easier to characterize the

signals. In general it is possible to use some scales for

more valid results.

In the case of muscle and bone we used 59.5 keV

gamma-ray of Am-241 source to study the atomic speci-

fications. The reason for using this source is its appro-

priate energy for in vitro tissue study and its particular

shape of Compton spectrum. The comparison between

the main and the passed spectra of Am-241 through

muscle is shown in Figure 7.

In practice we are interested in recognizing whether

Figure 2. Comparison of passed spectra through within alu-

minum (blue) and copper (orange).

Figure 3. The original gamma spectrum and Haar wavelet

coefficients plot for aluminum.

Figure 4. The original gamma spectrum and Haar wavelet

coefficients plot for copper.

Figure 5. Haar wavelet coefficients in frequency of 1.66 for

Al.

A. Pazirandeh et al. / Natural Science 3 (2011) 963-970

966

Figure 6. Haar wavelet coefficients in frequency of 1.66 for

Cu.

the spectrum is for muscle or muscle and bone together.

The passed spectra are shown in Figure 8.

In addition to obvious differences in transmitted spec-

tra for the two cases, after scaling the counts and com-

paring their shapes, two main differences are seen be-

tween the two spectra. There are two peaks in the muscle

Compton spectrum, which are not visible in the bone

transmitted spectrum. We can use these differences to

characterize the signals.

Using Haar wavelet function, the differences between

the two spectra are clearly observed by comparison as

shown in Figures 9 and 10.

The mentioned differences can be used to characterize

each spectrum to extract its features. By comparing

Figures 9 and 10, the shift shown by the upper arrow is

an obvious difference which extends on a broad range of

scale. This difference in higher scales corresponds to

low frequency which is shown in Figures 11 and 12. In

other words, the differences in a general view are attrib-

uted to two Compton spectra shapes. For a more reliable

comparison we can use several scales and also more

differences.

Changing the order of materials and putting muscle in

front of bone and also letting muscle to cover bone in all

Figure 7. Comparison of two Am-241 spectra with (brown) and without muscle (black).

Figure 8. Comparison of two spectra; muscle (brown) and muscle and bone together (blue).

A. Pazirandeh et al. / Natural Science 3 (2011) 963-970

967967

Figure 9. Wavelet coefficient plot for transmitted spectrum

through muscle.

Figure 10. Wavelet coefficient plot for transmitted spectrum

through bone and muscle.

directions, despite the differences in the shape of the

spectrum specially in count value, the result of the

analysis remains the same and valid.

In the case of muscle and lipid, Figure 13 shows the

comparison between transmitted spectra.

In this case instead of using Haar wavelet we used

rbio3.1 wavelet, which is more suitable. The correspond-

ing wavelet coefficients plots and their differences are

shown in Figures 14 and 15.

By using appropriate scales to mark these two signals

the results are given in Figures 16-21.

The difference related to the above arrow is detectable

in a wider domain.

Therefore, even the slight difference between muscle

and lipid signals is identifiable. This difference remains

the same as long as the setting conditions of detector in

different samples do not change. It should be pointed out

that in our recent experiment, the animal samples with

close surface densities and thicknesses of about 2 cm

were used. Thus, the mentioned difference between the

lipid and the muscle is recognizable unless the thickness

of the lipid is small.

5. DISCUSSION

Considering the difference between transmitted Comp-

ton spectrum through aluminum and copper sheets, one

can conclude that by examining local wavelet analysis it

is possible to recognize the objects’ properties. In fact

using this analyzing method with the wavelet technique,

the difference between the two spectra leads to positive

and/or negative wavelet coefficients, independent of

Figure 11. Haar wavelet coefficients in scale number 64 for

muscle.

Figure 12. Haar wavelet coefficients in scale number 64 for

muscle and bone together.

Figure 13. Comparison of transmitted spectra for muscle (brown) and lipid (green).

A. Pazirandeh et al. / Natural Science 3 (2011) 963-970

968

Figure 14. Rbio3.1 wavelet coefficients plot for lipid trans-

mitted spectrum.

Figure 15. Rbio3.1 wavelet coefficients plot for muscle trans-

mitted spectrum.

Figure 16. Wavelet coefficients plot at scale 6 for lipid trans-

mitted spectrum.

Figure 17. Wavelet coefficients plot at scale 6 for muscle

transmitted spectrum.

Figure 18. Wavelet coefficients plot at scale 16 for lipid

transmitted spectrum.

Figure 19. Wavelet coefficients plot at scale 16 for muscle

transmitted spectrum.

Figure 20. Wavelet coefficients plot at scale 32 for lipid

transmitted spectrum.

Figure 21. Wavelet coefficients diagram at scale 32 for muscle

transmitted spectrum.

count rate or signal amplitude which then could be

translated in True or False notation. For example, in the

case of aluminum and copper, as in our experimental

condition, the change in spectrum shape was placed on

channels 7 to 13, see Figure 22. Applying wavelet

analysis and obtaining wavelet coefficients in scale 6 for

the mentioned sample spectra, total number of 2819 for

aluminum and –2330 for copper were obtained which

represents a clear difference. Figure 22 shows difference

between wavelet coefficients which is related to Figure 2.

As mentioned before, surface density of either barrier

is equal and it can be observed that the material charac-

terizations are more distinctly differentiated in Compton

spectrum region as compared to the main photo peak

region.

For other materials, the difference spectrum shape will

be formed differently which can be used to mark the

passing spectra. Choosing an appropriate source for this

job is crucial.

6. CONCLUSIONS

Applying such an analysis in medical imaging, more

information is exploitable. Thus, in addition to meas-

urement variations of total count formed by different

barrier materials, which are done by photographic films

or detectors, passing gamma ray will be studied in more

detail on its Compton scattering related aspects. This

topic helps us to achieve improved images. For example,

we can differentiate between two spectra passing

through the skeleton and muscle with the same surface

density while having attenuation in close proximity to

each other.

It is expected that diagnosing some tumors with spe-

cific atomic structure would be possible using a suitable

source and detector by this method. Nowadays, the

genesis of small scintillation detectors would increase

the possibility of using this method in radiology. Presently,

A. Pazirandeh et al. / Natural Science 3 (2011) 963-970

969969

Figure 22. Comparison of wavelet coefficients for aluminum (blue) and copper (orange).

Figure 23. Raster-scan imaging with spectra in transmission geometry.

such an analysis for passing spectrum to achieve addi-

tional information about a material located between the

source and the detector would result in a higher contrast

as mentioned before. In fact by this method amplitude

and phase/frequency imaging are formed. The target

image is obtained by analyzing the transmitted spectra.

Using a radioisotope emitting some peaks on its broad

band Compton scattering, corresponding to x-ray with

different energies, map out the atomic structural of the

target. This is characterized by material properties such

as refractive index, absorption coefficient, and thickness.

This technique is comparable to imaging with broadband

THz pulses, which implements THz imaging by THz

time-domain spectroscopy (THz-TDS) system [7]. It is

useful for imaging by equipment like to DEXA as in the

bone density measurement. In addition, Krug et al. 2007,

have shown that the Trabecular bone structure and bone

density contribute to the strength of bone and are crucial

in the study of osteoporosis. Wavelets can characterize

and quantify the texture in a bone image [8].

This technique of imaging is inherently associated

with versatile visualization schemes because a sample

image contains much more information than a typical 2D

image containing the same number of pixels. Each pixel

of an image contains a whole spectrum in the energy

domain. The excessive information provides many dif-

ferent display options for a sample image. In particular,

it contains spectroscopic information.

A straightforward implementation of this technique of

imaging is accomplished by raster-scanning of a target at

the focal plane of a spectroscopy system. Figure 23

sketches the scheme of this technique of imaging in

transmission geometry. The target image is obtained by

analyzing the transmitted spectra.

A. Pazirandeh et al. / Natural Science 3 (2011) 963-970

970

REFERENCES

[1] Xianga, J.W., Chenb, X.F., Moa, Q.Y. and Heb, Z.J.

(2007) Identification of crack in a rotor system based on

wavelet finite element method. The State Key Laboratory

for Manufacturing Systems Engineering, Xi’an.

[2] Chang, C.-C. and Chen, L.-W. (2005) Detection of the

location and size of cracks in the multiple cracked beam

by spatial wavelet based approach. Mechanical Systems

and Signal Processing, 19, 139-155.

doi:10.1016/j.ymssp.2003.11.001

[3] Yeh, P.-L. and Liu, P.-L. (2008) Application of the wave-

let transform and the enhanced Fourier spectrum in the

impact echo test. NDT&E International, 41, 382-394.

doi:10.1016/j.ndteint.2008.01.002

[4] Krug, R., Carballido-Gamio, J., Burgardi, A.J., Haase, S.,

Sedat, J.W., Moss, W.C. and Majumdar, S. (2007) Wave-

let-based characterization of verbecular bone structure from

magnetic resonance images at 3 T compared with mi-

cro-computed tomography measurements. Magnetic Reso-

nance Imaging, 25, 392-398.

doi:10.1016/j.mri.2006.09.020

[5] Sullivan, C.J., Garner, S.E., Blagoev, K.B. and Weiss,

D.L. (2007) Generation of customized wavelets for the

analysis of γ-ray spectra. Nuclear Instruments and

Methods in Physics Research Section A: Accelerators,

Spectrometers, Detectors and Associated Equipment, 579,

275-278. doi:10.1016/j.nima.2007.04.055

[6] Hariharan, G. and Kannan, K. (2009) Haar wavelet

method for solving Cahn-Allen Equation. Applied Mathe-

matical Sciences, 3, 2523-2533.

[7] Lee, Y.-S. (2009) Principles of terahertz science and

technology. Springer, Berlin, 1, 261-262.

[8] Nandhakumar, S., Selladurai, V., Muthukumaran, V. and

Sekar, S. (2010) Haar wavelet approach to time varying

model robot arm control problem. International Journal

of Academic Research, 2.