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: [e-mail], [e-mail]
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]:
 
1
,d
t
Wa xtt
a
a








 (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].

22
ee
tiCt
t 

 (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,,,
jj
n
j
hthtk nk
jknjkZ




 


1
1
1, 02
1
1, 1
2
t
ht
t









(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).

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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
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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.

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