Download Effect of number of projections on image quality of local CT

Dentomaxillofacial Radiology (2004) 33, 361–369
q 2004 The British Institute of Radiology
http://dmfr.birjournals.org
RESEARCH
Effect of number of projections on image quality of local CT
AN van Daatselaar*, PF van der Stelt and J Weenen
Department of Oral Radiology, Academic Center for Dentistry Amsterdam (ACTA), Amsterdam, The Netherlands
Objectives: To determine the image quality of the local CT imaging procedure, in terms of
resolution, contrast, and noise as a function of the number of projections.
Methods: The contrast and resolution of the images was determined with a phantom object
consisting of three rods of different materials, as well as a phantom human head embedded in soft
tissue equivalent material. In addition, slices reconstructed from computed sinograms were used for
comparison.
Results: Sharpness, contrast and noise were determined as a function of the number of projections.
The number of projections was found to affect the contrast and the noise most, and had much less
influence on resolution.
Conclusions: Judging from the images of the phantom head and the numerical data, it seems that
the minimum number of projections needed to obtain images of useful quality in the geometry used
is about 33. Improved image quality (at any number of projections) can best be achieved through
noise suppression.
Dentomaxillofacial Radiology (2004) 33, 361–369. doi: 10.1259/dmfr/23496562
Keywords: tomography, X-ray computed; local CT; digital radiography; image reconstruction,
image quality
Introduction
Computed tomography (CT) is a frequently used technique
in medical radiology, providing detailed information by
means of cross-sectional images and volume reconstruction. However, the radiation dose involved in conventional
CT is relatively high for the diagnosis of non-lethal oral and
maxillofacial pathology, although the advent of faster
image acquisition schemes in conventional CT and the
introduction of cone beam CT modalities have lowered the
radiation dose significantly. Local CT1 – 3 is a variant of CT
that aims to reduce the radiation dose to the patient by using
a narrow X-ray beam that only covers the area of interest. As
a consequence, the field of view is reduced in size as
determined by the size of the detector and the width of the
beam. A complicating factor in local CT is the influence of
the structures surrounding the region of interest. These
structures reduce contrast and the signal to noise ratio.
A primary parameter of the imaging geometry is the
number of projections used. Clearly, reducing the number
*Correspondence to: AN van Daatselaar, Department of Oral Radiology, Academic
Center for Dentistry Amsterdam (ACTA), Louwesweg 1, 1066EA Amsterdam,
The Netherlands; E-mail: [email protected]
Received 20 August 2003; revised 9 September 2004; accepted 10 September 2004
of projections used for the reconstruction can reduce the
radiation dose to the patient. However, reducing the
number of projections will also reduce image quality
because of the sparser sampling of image data. The
problem this study addresses is how many projections are
necessary to obtain an adequate image quality for the
diagnostic question at hand.
The reduction of the number of basis projections is
relevant not only for local CT, but also for other, related,
imaging modalities. For instance, tuned aperture computed
tomography (TACTw) also generates images from a
number of basis projections and the diagnostic quality of
the images has been investigated.4
Image quality can be objectively qualified by measuring
noise, resolution and contrast.5,6 It is to be expected that a
lower number of projections would result in a lower image
quality. The objective of this study is to obtain insight into
the effects of the number of projections on noise, resolution
and contrast, related to an imaging geometry that is
suitable for local CT in dental diagnosis. In addition, an
attempt can be made to determine the minimum number of
projections that is required for the detection of specific
details in the volume of interest.
Image quality of local CT
van Daatselaar et al
362
Materials and methods
Experimental set-up
The experimental set-up used, outlined in Figure 1, is
similar to that used in previous studies.3,7 It consists of a
Heliodent X-ray source (Sirona, Bensheim, Germany), a
lead diaphragm, a rotational stage (Micro-controle, Vitrysur-Seine, France), and the Sidexis charge-coupled device
(CCD) detector (Sirona, Bensheim, Germany), all mounted
on an optical bench. The object to be studied is mounted on
the rotational stage.
The diaphragm serves to intercept as much scattered
radiation as possible and limits the beam to the size of the
detector. The CCD has 872 rows and 664 columns of
pixels, the size of which is 39 mm by 39 mm. The CCD has
12-bit resolution (it can discern 4096 levels of radiation
intensity). Using 12 bit data (instead of the more standard
8 bit) improves contrast and increases the signal to noise
ratio because the data are not rounded off to 8 bits, and
because we make use of the larger dynamical range the
12 bit data provides. An 8-bit system will only register 256
to 1 intensity ratios, whereas a 12-bit system can register
up to 4096 to 1 intensity ratios. This is especially important
because of the fact that the object is imaged from all
directions, some of them resulting in the X-ray beam
traversing through thick layers of bone and others in which
only a small amount of soft tissues is in the X-ray beam.
The X-ray source is equipped with an internal 1.5 mm
aluminium filter and has a 0.7 mm focal spot size. It was set
at 70 kV and an exposure time of 0.64 s. The source –
object distance was set at 123 cm, the object – detector
distance was as small as possible for the free rotation of the
object along the sensor. For the test object this was 1.5 cm
and for the phantom head it was 9 cm, measured from the
rotational axis to the detector. The CT series taken
consisted of 180 projections through 1808. From these
series other series with fewer projections were made by
deleting projections. This was done in such a way that the
remaining projections were still as much as possible
equally spaced.
data, before the window and level operation that transforms them to viewable 8 bit images. Therefore, these
measurements were not influenced by the window and
level operation, which is somewhat arbitrary in nature and
which causes some round-off noise when the data are
reduced to 8 bits. The contrast measurements were
performed on windowed and levelled images because
these measurements need a well defined background level
and non-negative grey values.
Test object
To ascertain image quality, a test object was made
consisting of three cylindrical posts mounted on a small
plastic disk. The posts are 5 mm in diameter and are
mounted 4.5 mm from the centre of the disk, in a
symmetrical formation (Figure 2). The three posts are
made of aluminium, Perspex and plaster. Because the sizes
and positions of the posts are well known and because they
are made from homogeneous materials, the expected crosssections are well defined. The cross-sections are well
suited for measurements and comparison with theoretical
cross-sections obtained from calculations. The reconstructed slices were 332 by 332 pixels in size. Five
consecutive slices were averaged to reduce noise. The slice
thickness was approximately 0.2 mm. No filtering other
than the ramp-filtering inherent in filtered backprojection
was used.
Computed phantom
The cross-section of the test object consists of three circles,
equal in diameter and positioned on the vertices of an
Reconstructions
The cross-sectional slices were obtained by filtered backprojection,6,8,9 using software written by one of the
authors.3 In the case of the head phantom, the filtered
backprojection as described in van Daatselaar et al3 was
combined with extrapolation of the projection data to
counter artefacts caused by the cutoff of the projection data
at the edges of the detector. The measurements on noise
and resolution were done on the raw floating point image
Figure 1
distances
Schematic diagram of the experimental set-up with typical
Dentomaxillofacial Radiology
Figure 2 Schematic drawing of the test object
Image quality of local CT
van Daatselaar et al
363
equilateral triangle. The X-ray absorption through such an
arrangement of circles (or, more generally, any arrangement of ellipses) can be easily computed. The well-known
Shepp-Logan head phantom8,10 is an example of a phantom
consisting of an arrangement of ellipses.
We developed a virtual test object to compare with the
real test object. The computed sinogram3,6 of this virtual
test object is shown in Figure 3. This sinogram is
geometrically exact, and contains no noise. The represented objects are purely homogeneous. In addition, the
absorption is strictly according to Beer’s law (exponential
attenuation), and is free of beam hardening, without
scattering. However, the number of projections is finite
and this will cause some artefacts. The reconstructed slices
were 332 by 332 pixels in size. No slices were averaged.
Because the object is mathematical, all cross-sections and
therefore all slices are exactly equal, and averaging will
produce no effect. No filtering other than ramp-filtering
was used.
regions are analysed by computing the average grey
value and standard deviation. The signal is defined as the
difference between the average value for the background
and the average value for each post. The standard
deviation of the pixel values in each post serves as a
measure for noise. In the ideal case, all pixels should
have the same value, as the posts are homogeneous. But
electronic noise and reconstruction artefacts will cause
variations that show up as noise. By comparing the
standard deviation with the average value, a signal to
noise ratio (SNR) can be computed using the following
equation:
signal
ð1Þ
SNR ¼ 10·log
noise
Head phantom
The head phantom used is a custom made head phantom,
a human skull embedded in soft tissue equivalent
material. This material gives the phantom the shape of
a normal human head. The material scatters and absorbs
the radiation in the same way as human soft tissues. The
images obtained from the phantom therefore are
comparable in image quality with the images obtained
from patients, although it does not include small errors
caused by the difficulty to completely immobilize a real
patient. The slices obtained were 400 by 400 pixels in
size. For each image used, five consecutive slices were
averaged, resulting in a slice thickness of approximately
0.2 mm.
With BS the brightness of the object and B0 the
brightness of the background. For this measurement
images scaled to (viewable) 8 bit images were used, in
order to have a well defined background level. This is
necessary because Equation 2 requires positive values,
and brightness values defined relative to zero (or black).
The transition from post to background is measured by
examining the pixels near the transition region. For each
pixel the distance to the centre and its brightness are
recorded. To this data a scaled error function is then fitted.
This function has the form
Measuring image quality
For measuring the image quality of the slices of the test
object a software tool was implemented that computes
certain statistical properties of the image and produces
graphs that can be used to assess contrast and noise.
The image is divided into regions by means of six
circles, two circular regions for each post (Figure 4). The
radius and positions of the two circles for each post are
chosen so that one falls slightly within the post, and one
slightly outside the post. If the circles are chosen as in
Figure 4, they divide the reconstruction into seven
regions, of which four are used. The inner circle for each
post defines the pixels belonging to the post, and all
pixels outside the outer circles are defined as background
pixels. The annular regions within the inner and outer
circles are not used, as they constitute the transition
region from post to background. The pixels in the four
Figure 3
Contrast C can be defined5 as
C¼
lBS 2 B0 l
B0
ð2Þ
yðxÞ ¼ a þ b erfðcx þ dÞ
with erf(x) the error function. a and b determine the left and
right limits, e.g. the object and background brightness. c
and d determine the position of the point of inflexion,
e.g. the edge of the object. c determines the width of the
transition region, e.g. the width of the blurry transition
from object to background. This non-linear four parameter
model is fitted to the data using the Leverberg-Marquardt
method.11 This method is an iterative algorithm for a leastsquares fit of a non-linear model to measured data. Nonlinear refers to the fact that the model depends non-linearly
on its parameters. In the present case, the parameters c and
d make the model non-linear.
Results
Reconstructions
Reconstructions of the real test object are presented in
Figure 5. Reconstructions using several different numbers
Computed sinogram of the virtual test object
Dentomaxillofacial Radiology
Image quality of local CT
van Daatselaar et al
364
Figure 4
A reconstructed slice of the test object, with regions indicated. The circles define the areas that are inside and outside the posts
Figure 5 Six reconstructed CT slices through test object. Left: Perspex, top: aluminium, bottom: plaster. Figures 5a – f have been reconstructed with
decreasing numbers of projections. a, 180 projections; b, 90; c, 60; d, 45; e, 30; f, 18
Dentomaxillofacial Radiology
Image quality of local CT
van Daatselaar et al
of basis projections are shown. Reconstructions of the
virtual test object are presented in Figure 6, using the same
numbers of projections as in Figure 5. Reconstructions of
the phantom head are shown in Figure 7.
Signal to noise ratios
Signal to noise ratios have been measured for the test
object using Equation 1, and are visualized in Figure 8.
The ratios have been plotted as a function of the
number of projections. Each graph shows a plot for five
averaged slices, for three averaged slices and for a slice
with no averaging. In the case of Perspex, the material
with the smallest absorption coefficient, it is clear that
for low numbers of projections, the signal is completely
lost in the noise because of the negative signal to noise
values. Compare these graphs with the images in
Figures 5 and 6. The signal to noise ratios measured
for the computed phantom are presented in Figure 9. In
the computed phantom, noise is primarily due to the
finite number of projections.
Resolution
A graph showing measured profiles is shown in Figure 10.
The graph shows three point clouds, representing the pixels
near the edge of each of the three posts. The fitted error
Figure 6
365
functions are plotted in white. Measurements of resolution
are presented in Figure 11.
Contrast
Measurements of contrast according to Equation 2 have
been made and are presented in Figure 12. For each
material the contrast is plotted as a function of the number
of projections. This has been repeated for 3 and 5 averaged
slices.
Discussion and conclusions
It is clear that for all three materials of the real test object
the SNR increases as the number of projections is
increased (Figure 8). In addition, the materials with higher
absorption coefficients have better signal to noise ratios. In
the case of Perspex, the material with the smallest
absorption coefficient, it is clear that for low numbers of
projections, the signal is completely lost in the noise, that
is, the contrast of the images is so poor that the object is not
recognizable.
The same conclusion can be drawn for the contrast:
increasing the number of projections increases the contrast
(Figure 12). In the images of the head phantom (Figure 7),
Slices reconstructed from computed data. a, 180 projections; b, 90; c, 60; d, 45; e, 30; f, 18
Dentomaxillofacial Radiology
Image quality of local CT
van Daatselaar et al
366
Figure 7 Horizontal local CT cross-sections centred at the right first lower molar of the phantom head with soft tissue equivalent material. The number
of projections used is indicated in the images
which simulate clinical images, the lower limit for the
number of projections seems to be approximately 30. With
fewer projections, all relevant anatomy is rendered
invisible. The contrast in the test object is about 0.8 for
30 projections.
The sharpness of the images of the test object are
surprisingly not very dependent on the number of
projections, except for low numbers of projections,
where the sharpness becomes meaningless because of
the dominant artefacts (Figure 11). The sharpness does
however depend on the material. The sharpnesses found
are approximately 4.3 pixels (220 mm) for aluminium,
5.4 pixels (280 mm) for plaster and 6.3 pixels (324 mm)
for Perspex.
The graphs for the computed phantom (Figure 9)
show the same trends. However, for the computed
phantom the source of the noise is clear: noise and
artefacts can only be caused by the limited number of
projections. A perfect image will only be obtained for
an infinite number of projections.
Because the head phantom is not accessible for direct
measurements, measuring noise, contrast and sharpness
is difficult. However, the head phantom can be
inspected visually. All anatomical details not on the
microscopic level have been retained in the bone.
Dentomaxillofacial Radiology
The slices show the major anatomical structures of the
teeth: root canals, lamina dura, and periodontal space
are clearly seen, as well as the cortical and trabecular
structure of the surrounding bone.
Judging from the graphs and figures, it seems that the
minimum number of projections needed to obtain images
of useful quality is about 33. With fewer than 20
projections the contrast in the reconstructions is lost and
with fewer than 33 projections the sharpness of the
reconstruction is lost. This can be seen in Figure 11
where below 33 projections the constant resolution is
overtaken by noise.
In conclusion, the number of projections affects mostly
the contrast and the noise, not the resolution. Improved
image quality (at a certain number of projections) must
therefore come from reduction of noise and improvement
of contrast. Reduction of noise can be achieved either by
using better hardware, e.g. CCD detectors with less noisy
signals, or by software noise suppression.
Acknowledgments
Special settings making the raw 12 bit image data available from
the system were supplied by Sirona.
Image quality of local CT
van Daatselaar et al
Figure 8
Figure 9
367
Graphs of the signal to noise ratio for the three materials. (a) Aluminium; (b) Perspex; (c) plaster
Noise measurements for the computed phantom
Figure 10 Graph showing the profiles of the three posts. The highest is
of aluminium, the middle graph of plaster, and the lower graph of Perspex.
The slices are based on 180 projections. The white lines are the error
functions fitted to the measured data
Dentomaxillofacial Radiology
Image quality of local CT
van Daatselaar et al
368
Figure 11
Measurements of the resolution at the edges of the posts
Figure 12
Measurements of the contrast in the reconstructions of the test object. Note the different scale for Perspex
References
1. Lewitt RM. Processing of incomplete measurement data in computed
tomography. Med Phys 1979; 6: 412 –417.
2. Smith K, Keinert F. Mathematical foundations of computed
tomography. Applied Optics 1985; 24: 3950 –3957.
Dentomaxillofacial Radiology
3. Van Daatselaar AN, Dunn SM, Spoelder HJW, Germans DM,
Renambot L, Bal HE, et al. Feasibility of local CT of dental tissues.
Dentomaxillofac Radiol 2003; 32: 173 – 180.
Image quality of local CT
van Daatselaar et al
4. Abreu M, Tyndall DA, Ludlow JB, Nortjé CJ. Influence of the number
of basis images and projection array on caries detection using tuned
aperture computed tomography (TACT). Dentomaxillofac Radiol
2002; 31: 24 –31.
5. Webb S (ed). The physics of medical imaging. Bristol: IOP Publishing
Ltd, 1990.
6. Russ JC. The image processing handbook. Boca Raton: CRC Press,
1995.
7. Van Daatselaar AN, Tyndall DA, Van der Stelt PF. Detection of
caries with local CT. Dentomaxillofac Radiol 2003; 32: 235 –241.
369
8. Kak AC, Slaney M. Algorithms for reconstruction with nondiffracting
sources. In: Principles of computerized tomographic imaging.
New York: IEEE press, 1988, pp 49 –112.
9. Parker JA. Image reconstruction in radiology. Boca Raton: CRC
Press, 1990.
10. Shepp LA, Logan BF. The Fourier reconstruction of a head section.
IEEE Trans Nucl Sci 1974; NS-21: 21 –43.
11. Press WH, Flannery BP, Teukolsky SA. Vetterling WT. Modeling of
data. In: Numerical recipes, the art of scientific computing.
Cambridge: Cambridge University Press, 1990, pp 498 –546.
Dentomaxillofacial Radiology