Department of Physics and Astronomy, University of Canterbury,
Private Bag 4800, Christchurch, New Zealand
Spectral CT: Image processing
and revised Hounsfield units
Michael Clark
PHYS480 Project 2009
Supervisor: Prof. Phil Butler
Supervisor: Dr. Anthony Butler
Supervisor: Dr. Nick Cook
Abstract
We investigate several aspects of spectral Computed Tomography
(CT). We report improvements in image processing software, and
investigate the variation of Hounsfield scale in spectral CT.
Image processing software for the MARS-CT scanner was improved:
software was rewritten and documented, with major improvements
made to noise identification and removal. These improvements make
the software easier to use, and easier be adapted to new detectors. The new software allowed the reconstruction of scans from new
Medipix2 detectors with GaAs and CdTe sensor layers.
We review the published literature on Hounsfield units. We note the
weaknesses of the scale and propose amendments. We report on an
scan which show that the Hounsfield scale varys as a function of energy. Charge sharing between pixels affected the measurements. Despite this effect, the measurements indicate that the Hounsfield scale
varies with energy variation. We conclude that the current Hounsfield
scale has weaknesses in spectral CT. To overcome these weaknesses
we propose energy dependant Hounsfield units.
Contents
1 Introduction
1.1 Spectral CT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Report Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1
3
2 Background
2.1 X-rays . . . . . . . .
2.2 Beers Law . . . . . .
2.3 The K-edge . . . . .
2.4 Image Reconstruction
2.5 Medipix Detector . .
2.6 Multiple Energy CT
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3 Image Processing
3.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
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4 Hounsfield Units
4.1 The Hounsfield Scale . . . .
4.2 Method . . . . . . . . . . .
4.3 Results . . . . . . . . . . . .
4.4 A Spectral Hounsfield Scale
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5 Conclusion
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20
iii
List of Figures
1
2
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10
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13
14
Physical components of attenuation coefficients . . . . . . . . . . .
Narrow beam geometry for linear attenuation measurements . . . .
Back-projection during CT reconstruction . . . . . . . . . . . . . .
Image filtering for CT reconstruction . . . . . . . . . . . . . . . . .
Two types of beam for measuring x-ray projections . . . . . . . . .
The structure of a pixel in a Medipix2 detector . . . . . . . . . . .
Detector noise profile . . . . . . . . . . . . . . . . . . . . . . . . . .
Noise in GaAs and CdTe Medipix2 detector flat-fields . . . . . . . .
Image cleaning on a CdTe image . . . . . . . . . . . . . . . . . . . .
The Hounsfield scale - an illustration . . . . . . . . . . . . . . . . .
Hounsfield scale in terms of attenuation coefficients . . . . . . . . .
Region of interest choice . . . . . . . . . . . . . . . . . . . . . . . .
Results: Predicted and measured Hounsfield values for iodine and
solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Linear interpolation of noise on CdTe . . . . . . . . . . . . . . . . .
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calcium
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6
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17
Table of experimental Hounsfield values for iodinated contrast and CaCl2 . .
Table of experimental Hounsfield values for iodinated contrast and CaCl2 . .
24
24
19
24
List of Tables
2
4
iv
1
Introduction
In this report, we investigate the Medipix all resolution system (MARS) CT scanner, which
uses an energy sensitive Medipix detector. This spectral CT scanner measure attenuation at
many energies. This report covers an investigation that: improved image processing routines
for the MARS-CT scanner; and measures, reviews, and proposes revised Hounsfield units
(HU) for spectral CT.
Diagnosis is critical to effective and informed health care. Computed tomography using
x-rays (often referred to as CT) is one of the most common medical diagnostics and has
applications in non-medical fields. CT uses multiple x-ray projection images to reconstruct
the internal structure of an object. The advantages of x-ray CT (known as CT or CAT
scans) over simple x-ray projections include 3D information and better object differentiation.
Simple x-ray projections are 2D projections which represent the mean absorption along the
beams path. These are known as plain film x-rays in radiology, to the public they are known
them as x-rays or x-ray scans. To distinguish between x-ray photons in physics from x-ray
scans we will refer to them as plain film x-rays (see section 2.1 for more). Recently, spectral
CT scanners have been developed with the ability to measure at multiple x-ray energies; this
gives new and improved information.
1.1
Spectral CT
Diagnosis in health care is far from at saturation point: this is illustrated in a 1991 study
finding a 44% discrepancy between diagnosis and autopsy. 10-20% of these misdiagnoses
involving fatal illness [1]. This value hasnt changed significantly since then [2]. The discrepancy shows that there is room in diagnostic medicine for great advancements.
X-ray computed tomography (CT) came about in 1973 [3]. Since then it has been a gold
standard of diagnosis, with one United States hospital during 1990-1999 finding that 19%
of radiology patients undergo at least one CT scan, with the number increasing during this
period [4]. Other common diagnostic technologies are: plain film x-ray, magnetic resonance
imaging (MRI), ultrasonography (US), and positron emission tomography (PET). These
have differing iodising radiation doses, contrast medium toxicity, structure contrast, and
cost. Techniques often have different contrast in soft tissue such as the lungs, or hard tissue
structures such as bone.
Plain film x-rays are projections that measure the mean absorption of a beam through
an object. X-ray CT computes the absorption of each volume element (voxel). Plain x-ray
lacks 3D information; this means the image is often obscured with superimposed objects.
While a CT scan has much better soft tissue contrast, plain film x-ray often cannot distinguish between relevant structures unless contrast dye is used [3]. Plain x-rays are useful as
exploratory precursors to CT, but lack the diagnostic information gained from CT reconstruction.
Magnetic resonance imaging is an alternative to CT. Both have similar running costs
but MRI was found to have a lower patient throughput in 1987 [5], with the comparative
throughput changing little since. MRI is more expensive per scan, signal depends on atoms
with non-zero spin. This occurs in nuclei with an odd number of protons and/or neutrons.
1
The atoms with the strongest signal are H 1 , H 3 , and C 13 . The most common is H 1 , which
is a component of water. MRI aligns the spins with a strong magnetic field, then uses radio
pulses to perturb spin states and produce a new magnetic field. MRI images have good
differentiation in soft tissue with high water content such as the brain [6]. Since it uses nonionising radiation, it avoids the ionising radiation doses of CT and PET imaging. Contrast
dyes are sometimes used, these can lead to toxicity.
Ultrasonography is an inexpensive alternative per scan [7; 8]. It uses the echoes of high
frequency sound waves to reconstruct an image in a similar manner to sonar. Its high
frequency waves have trouble penetrating air and porous bone, but show surfaces between
soft and hard tissue well. The major advantage is that US has no ionising radiation dose,
while contrast dyes are sometimes used.
Positron emission tomography PET traces positron annihilations, from positron emitting
radionuclides. The injected radionuclides are part of a biologically active molecule, which follows a metabolic pathway. An example of a common molecule is FDG, the glucose analogue
[9]. The emitted positrons annihilate with electrons, producing gamma ray pairs in nearby
tissue. A gamma ray camera tracks the positron-electron annihilations; these are highly
correlated with the radionuclide’s path. PET measures the spatial co-ordinates of positronelectron annihilations and often uses CT to find what these co-ordinates correspond to in
the body. This is another common diagnostic technique, but not a serious alternative to CT.
Since diagnosis is far from a saturation point, hospitals often use multiple diagnostic
techniques. CT has applications in fields outside medicine such as surveying [10], materials
testing [11], and airport scanning [12].
Main limits to the use of x-ray CT are radiation dose and contrast medium toxicity.
Contrast mediums serve as an x-ray dye where they accumulate. They are used with many
techniques, such as CT, MRI, and US. These are injected into a patient, where their presence enhances x-ray absorption. Contrast mediums accumulate or are placed in medically
interesting areas to increase their contrast. For example, iodine based contrasts are often
used to map the blood vessels [13]. Contrast mediums give valuable information but often
risk toxicity to the patient. This danger prevents many patients from getting useful CT
scans [14]. Greater than 14% of the population of America, Europe, and Asia have diabetes,
which makes contrast media a great risk of toxicity[15]. Radiation exposure from x-ray CT
is significant. For example, in the United States, CT contributes approximately a third of
an average persons lifetime exposure and over two thirds of the exposure from diagnostic
medicine [16]. If radiation and contrast medium dose could be decreased, CT could be used
in more cases and more often.
Standard CT computes a material’s x-ray absorption; multiple energy CT measures also
the variation of absorption as a function of energy. The single energy bin in standard CT
limits its diagnosis and research ability. Development of energy sensitive CT scanning is
likely to be a major step in CT development. It gives more information, and so requires less
exposure and less contrast media. Spectral CT improves object differentiation by comparison
of absorption as a function of energy. The medical applications are extensive and including
improved ability for detecting fatty liver [17] and arterial calcium deposits for heart disease
[18]. Multi energy CT may also excel in CT’s wider applications such as non-destructive
materials testing [11] and surveying [10].
2
The Christchurch MARS-CT group is developing spectral CT scanners [19] using the
Medipix detector. This detector is derived from a high energy particle detector developed at
CERN [20]. The Medipix detector is a photon counting detector consisting of a semiconductor sensor bonded to a electronics layer (see section 2.5). The detector offers high resolution
in the spatial and energy domains. It has pixels with sides of 55µm, and an energy resolution
up to 1.4 keV energy windows and 1 counts per 1µs in the clinical x-ray range [20] [21].The
group has developed a small animal scanner based on this detector and is working towards
a full-body multiple energy CT scanner. In contrast, the latest clinical CT scanners only
measure two energies (see section 2.6). As well as developing a multiple energy scanner,
the group is investigating the applications of spectral CT. Applications being investigated
include detecting breast cancer [22] and identifying materials by applying statistical methods
to the energy information[19].
1.2
Report Outline
This report hopes to contribute to the field of spectral CT imaging, and the development of
a spectral CT scanner. The goals for the project which inspired this report were to develop
the image processing in the MARS-CT scanner and to investigate Hounsfield units.
Section 2 gives the background information necessary for this report. It covers: x-rays,
Beer’s law of attenuation, the K-edge, image reconstruction, and the Medipix detector. The
Hounsfield scale is introduced later (in section 4.1) since it is approached as a review of the
relevant literature, instead of background information.
In section 3, the report covers improvements to the MARS-CT image processing software. This image processing software cleans artefacts and dead pixels then normalises and
combines frames to prepare for reconstruction. Good image processing is essential for useful
CT reconstructions. Without it, any research which depends on experiments is halted. An
example, is research using new detectors. We report on the improvements in image processing software for the MARS-CT scanner. These improvements consisted of rewriting and
documenting the image processing code. The new code has improved noise removal, which
enabled research with new GaAs and CdTe detectors. In section 3.1, the need for improvement is established, the improvements reported, and the structure and function final routines
are outlined. The results of the final image processing routines are covered in section 3.2.
Section 4 reports our investigation into Hounsfield units and our interpretation of the
results. The Hounsfield scale has been the standard for CT scans since 1973 [3]. This
scale is necessary for reconstructed CT images. Since some methods of reconstruction lose
the connection to x-ray absorption, a scale is defined by using set points at water= 0 and
air= −1000. In section 4.1 the Hounsfield scale is reviewed with a focus on its weakness,
proposed revisions, and unsuitability to spectral CT. A system of units should enable its
values to be quantitatively compared [23].It is not possible to compare values if they vary by
unaccounted factors. Therefore, Hounsfield units are incomplete if they vary with energy.
In section 4.2 we cover the experimental work, which attempts to show the Hounsfield
scale varies as energy varies. The experimental scans are of various solutions at multiple
energies. In section 4.3 we compare the results of this experiment to expected results,
and the significant effects are discussed. In section 4.4 we propose an energy dependant
3
Hounsfield scale. We argue that this revision makes the Hounsfield scale more suitable to
spectral CT than the original scale or alternative revisions.
My contributions to the research in this report are explicitly stated as follows: for the
improvements to the image processing software, I understood the original processing code
and documented it. This was a major task since the original image processing code was,
in general, undocumented and unorganised. Then along with others I rewrote the image
processing code to be more effective, clear, and adaptable. For the rewriting, I wrote the
first local masking algorithm and proofread the final code. In the investigation of Hounsfield
units, my contribution included: processing, reconstructing, calculating the results, and
calculating the expected values. The experimental findings show the phenomenon of charge
sharing, which made it useful for other students investigating the phenomenon. The results
from this investigation have been submitted for publication in the Journal of Medical Imaging
and Radiation Oncology. My contribution to the submitted paper was: the production of
graphs; the bibliography; writing the processing, reconstruction, and analysis section; and
some proofreading.
2
Background
This section contains the background necessary for the following sections of this report.
Section 2.2 covers what x-ray projections measure; section 2.4 shows the process which
reconstructs the internal structure of an object in CT; section 2.5 introduces the Medipix
photon counting detector; and section 2.6 is about spectral CT.
For the markers of this report, I should disclose that my own background includes previous
experience in parts of the MARS project. I investigated reconstruction and diagnosing fatty
liver for a summer research project [24; 25].
2.1
X-rays
X-ray beams are made up of electromagnetic x-ray photons with wavelengths from 0.01nm
to 10nm. This puts them above the visible spectrum and gives them the ability to penetrate
tissue which is impenetrable in the visible spectrum. X-rays are defined as photons produced
by an electron outside the nucleus [26].
In x-ray CT the beam is usually generated with an x-ray tube. The x-ray tube uses a
vacuum tube with a high voltage. It accelerates electrons from the cathode to the anode
with high kinetic energy. The anode target is a material with a high atomic number, which
produces x-rays through bremsstrahlung or fluorescence. In this case, bremsstrahlung occurs
when electrons pass close to the positively charged nucleus of an atom. The magnetic
field produces a large acceleration, deflecting the electrons and producing x-ray emissions.
Florescence occurs if an electron knocks out an orbital electron. In this case an electron from
a higher orbital will fill the vacancy, with the electron emitting energy equal to its energy
transition. This emits fluorescence photons with a characteristic energy corresponding to
transitions between the quantised electron orbitals. X-ray beam produced is often passed
through a filter, which will remove low energy x-rays. Low energy photons never pass through
4
the target, so only increase the radiation dose.
If an x-ray tube and a detector (such as an x-ray film) are placed on opposite sides of an
object, an x-ray projection can be measured. The image shows the mean absorption along
the path of the beam. In contrast, x-ray CT uses many x-ray projections to reconstruct the
absorption at each volume element (voxel) of an object (see section 1.1).
2.2
Beers Law
Beers law relates the absorption of a beam with an attenuation coefficient. It states that
there is a logarithmic dependence between a beams transmission through a material I, its
attenuation coefficient µ, and the materials thickness dx. This can be shown as equation 1
[27].
I(x)
= e−µx
(1)
I(0)
Atomic cross sections represent the probability of a photon interacting per atom of the target
material. Attenuation coefficients can be expressed as the sum of the cross sections of underlying physical effects. In the clinical x-ray spectrum (around 1-100 keV) the cross sections of
major effects are: photoelectric effect τ , followed by Compton effect σc , and Raleigh scattering σR . Raleigh scattering is the elastic or coherent scattering of an incident photon with an
orbital electron, and Compton scattering is the inelastic interaction (incoherent scattering).
Equation 2 shows the attenuation coefficient µ as a breakdown of major effects in the clinical
x-ray spectrum for each atom N [28].
µ = (τ + σR + σc )N
(2)
Attenuation coefficients are measured in real conditions as linear attenuation coefficients.
These are linear because they are measured by narrow-beam geometry, which removes all nonlinear photon paths. This geometry uses a single collimated beam and detector to remove
scattered photons (see figure 2). In cases where scattering is significant, a correction factor
called the build up factor can be used. Build up factors vary with beam profile and target
material. This factor accounts for photons scattered to the detector along non-straight paths
(see figure 7). Linear attenuation coefficients are often referred to simply as attenuation
coefficients and from here on will be denoted as µ.
2.3
The K-edge
The K-edge is a sharp increase in attenuation. This increase happens at the binding energy of
the K-shell and shows where the photoelectric effect begins to occur. There are corresponding
and lower energy effects, which are labelled for the L-shell and M-shell and so on (these are
seen in figure 1). The term K-shell is the name for the first energy level n=1, where n is
the principle quantum number indicating the energy level. This terminology originates from
labels given by Berkla when he first observed the atomic energy levels [30]. The K-edge is
a point where there is major attenuation variation with energy. Equation 4 suggests that
major variation occurs in the Hounsfield scale. This variation prompted us to focus our scan
on the the k-edge of iodine (see section 4.2).
5
Figure 1: This shows the components of the attenuation coefficient responsible for photon absorption in iodine. In the x-ray spectrum (the keV range) photoelectric absorption
dominates the attenuation coefficient. This graph was constructed using the NIST X-COM
database [29]
Beam Source
Beam Source
x
Detector Signal I(x)
Detector Signal I(0)
Figure 2: This image shows narrow beam geometry, where the left image measures the
baseline beam intensity, and the right image measures the reduced beam for distance x of
material. The mono-energetic beam source is at the top, followed by a collimator, material,
collimator, and detector at the bottom.
6
2.4
Image Reconstruction
Computed Tomography (CT) uses reconstruction algorithms to get the internal radiodensity
of a scanned object. These are many reconstruction techniques; all use many x-ray projection
images from different angles.
The earliest reconstruction technique was the inverse radon transform. The original
transform was developed by Johann Radon and generates the projection image obtained in
the scan of an object [31]. However, this technique was computationally intensive and can
only be applied to projections measured with parallel pencil beams (figure 5). Pencil beams
are narrow beams that do not significantly diverge. To make a parallel projection many
pencil beam images are combined. A more convenient alternative is to use 2D fan-beam
or 3D cone-beam projections as these are measured with a single point source of x-rays. A
cone-beam is a beam which spreads out in a fan in 2 dimensions perpendicular to its focal
axis. For example a point source and a 2D detector. A fan-beam is a cone-beam with one
less dimension (see figure 5).
The most common form of reconstruction is Feldkamp filtered back projection. This
algorithm is fast and the reconstruction is a good approximation to the inverse radon transform [32; 33]. Other methods include: iterative reconstruction [34] and algebraic methods
[35].
Feldkamp filtered back projection overlays all projections onto the image, giving a blurred
representation of the original object. The sources of attenuation are represented by dark
spots at the apex of the radioshadows (figure 3). Back projection constructs a blurred
Capturing a single projection
of the object
Overlaying 8
detected Images
X-ray shadow detected
Object
Parallel Beam Source
Figure 3: Back-projection: on the left we have a single projection of a square object. This
is where the radioshadow cast by the object is measured. On the right projections at eight
different angles combine, giving us a blurred representation of the original objects radiodensity.
representation of the original object. By taking reconstructing projections of an object, we
7
blur the representation of the object. A sharpening filter drastically improves the blurred
back projections; filtered back projection uses this method (see figures 3 and4).
A common sharpening filter is the linear ramp filter. The way this filter works is by
transforming an image in the frequency domain. In this domain, regular information is represented by a high frequency, while high entropy information such as noise is low frequency.
If we multiply the image by a function equal to its own frequency, we reduce the noise and
increase the ordered information (figure 4).
1
Filtering transforms a blurred back projection into a higher resolution reconstruction.
This step is the same as a high pass filter in signal processing or sharpening filters in image
manipulation programs (figure 4).
-1
0
+1
Figure 4: Left is a back-projected but unfiltered image. Middle a linear frequency domain
filter with a x axis of frequency and a y axis of filter response. Right the back-projected
image after filtering is applied. This is an image of a Shep-Logan phantom constructed in
Matlab [36; 37]
2.5
Medipix Detector
The Medipix detector is a high resolution x-ray detector made using microchip fabrication
technology. It is a photon counting detector. It only counts photons that cause a signal
above an electronically calibrated threshold. The signals correspond to the photon energy,
so we can count photons in a particular energy range. Alternative methods are integration
which counts all charge signals, and weighting which counts using a weighting function [38].
This detector is a development of the detector technology originally developed for tracking
high energy particles at CERN.
The investigation in this report used the second version of the detector. The Medipix2
is energy sensitive with a high spatial and temporal resolution. This detector consists of
2552 pixels of 55 µm dimensions, giving a 14mm detector size. Medipix2 is a hybrid pixel
detector, consisting of a semiconductor sensor layer bump bonded to an electronic readout
layer. Bump bonding is a process that solders each pixel separately between layers with a
bump of solder.
The semiconductor sensor layer operates under a voltage bias to deplete it of charge
carriers. Incoming x-rays interact with the sensor layer through the photoelectric effect,
knocking off an electron. This electron has a kinetic energy made up of the photon’s energy
8
minus the electron’s binding energy. This charged photoelectron sheds its large kinetic energy
through the creation of many electron-hole pairs along its path. These new electron and hole
charge carriers are in a depletion layer under a voltage bias, so they drift towards the anode
or cathode (figure 6) [39].
Various materials can be used for the sensor layer on Medipix2 detectors, such as silicon,
gallium-arsenide, and cadmium-telluride. Different semiconductors have differing advantages. Better-known materials, such as silicon, are easier to bump bond. The stopping
power is proportional to the proton number Z of the material, hence cadmium-telluride and
gallium-arsenide have a higher stopping power and lower exposure times. Other factors include the thickness of the material and the mobility of the charge carriers. The mobility
affects the spread of the charge cloud, the signal shape, and amplitude. The thickness has a
exponential relationship with respect to stopping power (equation 1).
The noise level in Medipix2 is theoretically 3.5 keV, with contributions from electronic
noise and threshold dispersion. Noise causing phenomena particular to the detector are
charge sharing between pixels and the fluorescence of detector components. Florescence is
the phenomenon where light is absorbed and re-emitted by elements in the detector. In the
Medipix2 detector, the tin (solder bonds) and sliver (glue) give peaks at 22 keV and 25 keV
[40]. The flat-field normalisation (section 3.1) stop some part of fluorescence, but we have
some lingering effects.
Charge sharing is an effect present in counting detectors that have pixels of less than 100
µm. This phenomenon occurs when the size of the electron-hole cloud is comparable to the
pixel size. Counting detectors use a charge threshold, so the spread of this charge over many
pixels results in multiple counts or loss of counts. This has the effect of spreading any charge
impulse over lower energies and neighbouring pixels while losing some counts altogether.
This effect is present in the Medipix2 but will be not be in the next iteration of the detector.
Medipix3 will sum the simultaneous signals in neighbouring pixels to cancel charge sharing.
Charge sharing is dependent on the mean free path; so factors such as semiconductor type,
charge carrier mobility, and bias voltage may influence its magnitude (figure 7) [41].
2.6
Multiple Energy CT
Multiple energy CT scanners enable measurements of attenuation at multiple energies. This
allows us to see how the attenuation varies with energy. In contrast, the latest clinical
scanners in this field use dual energy. Dual CT uses two pairs of x-ray tubes and detectors
with each pair at a quarter rotation around the target. Dual CT doubles the radiation dose
and the hardware requirements while only obtaining two different energies. The MARS-CT
multiple energy CT uses multiple electronic thresholds. These determine which charge signals
are counted. Since charge signals correspond to the energy of a photons, the threshold allows
counting within an energy bin. Instead of two beams and two detectors, multiple energy
CT uses one beam and one detector, with separate detectors or pixel sets for distinguishing
photon energy. This allows scanning at energies which get the best image and minimise dose
[42].
9
N parallel beams detected
Fan beam det ected
X
X
Y
Y
ϑ
ϑ
Object
Object
N pencil beam sourc es
Fan beam sourc e
Figure 5: This shows projections being measured by (left) a parallel beams, (right) a
diverging fan-beam of photons. ϑ is the projection angle to the lab x and y axes. The
parallel beam is theoretically simpler but experimentally complex, while the fan-beam is the
reverse.
X-ray photon
Depleted
semiconductor
sensor
Solder bump
Pixel readout
Electronic chip
{
(a)
(b)
n+
p-
{
{
{
n-well
p-substrate
Figure 6: This figure shows a pixel in a Medipix2 detector (adapted from [39]). An incoming
photon ejects an orbital electron through the photoelectric effect (a). The electron sheds its
high kinetic energy, (b) creating electrons and ’holes’ in the semiconductor sensor layer. The
charge carriers drift in the direction of the cathode or anode, creating a charge signal. The
sensor layer (top) is in depletion mode (indicated by p- n+).
10
3
3.1
Image Processing
Method
Images from completed scans need to have a series of processing steps applied. In brief, the
it normalises for: exposure time, beam profile, and the sample container. Next, the frames
are joined and the noisy, dead, and overcounting (saturated) pixels are corrected.
When this project was started, the image processing steps were undefined. The code that
processed the images was not commented on or documented and had many obsolete or suboptimal routines. This gave a software black-box; output data was transformed in unknown
ways and it was difficult to modify. The problem with the image processing routines was
that they had accumulated by trial and error. Forming them into a cohesive structure was
a useful job. The biggest leap in this process was understanding the previous routines.
The need for documentation was increased when the silicon Medipix2 detector failed.
This detector was replaced with a prototype Medipix2 with a GaAs sensor layer and many
artefacts. Figure 8 shows the noise in a frame. At this point, the lack of working image
processing was preventing the reconstruction of scans. This prompted a group of us to work
on improving the image processing code. The aim of my work was to allow reconstruction of
the GaAs data sets and to make the routines transparent and easier to modify. The improved
image processing had seven steps: exposure normalisation, flat-fielding, stitching, masking
bad pixels, masking noisy pixels, interpolating the masked pixel, and the final formatting.
Exposure-time normalisation corrects for the different exposure times at different energy thresholds. Different exposure times are set to avoid overcounting and the noise floor.
The beam profile varies at different energies and the optimal exposure has corresponding
variation. Overcounting is a phenomenon whereby a pixel is exposed to overlapping charge
signals, it is saturated, and counts at the maximum rate.
The flat-field serves to account for the beam profile, detector profile, and the container
attenuation. The beam intensity changes for different energies and different parts of the
detector. The detector has areas of higher and lower sensitivity. A container holds samples
while scanning. This container is included in the flat-field scan so its effect is removed by
flat-fielding. It is common to have separate images for detector, beam, and casing variation.
However, this flat-field combines them all. The flat-field is measured with only the sample
casing in the scanner. After the flat-field is normalised, the projection are divided by it.
This corrects for the variations in the detector, beam, and sample case.
The 3rd part of the process is called stitching and combines the individual frames by using
a function of position. Since the objects that are imaged are often larger than the 14mm
detector, multiple images are taken at a single angle but multiple translations to construct
one projection. These images are called frames and are overlapped to make projections. The
frames are taken with overlapping target areas; because this allows us to have a smooth
transition between the frames, ignoring dead pixels, and checking for consistency.
The next step in image processing is to mask for overcounted and dead pixels. A mask
serves to mark an offending pixels location, so it can be replaced later. Dead pixels are those
which no longer count and overcounting is the case where a pixel was saturated with counts
beyond it ability to distinguish separate signals.
11
Intensity
measurement R (E’, 59.3 keV)
simulation of R (E’, 59.3 keV)
10
20
30
40
50
60
energy deposition [keV]
Figure 7: The first figure (left) shows the effect of charge sharing. This shows the correct
signal (black) and the signal with a charge sharing tail (red). When the size of the cloud of
charge carriers is comparable to the pixel size the charge spread over neighbouring pixels.
This results in signals below threshold or lower energy counts [40].
The Second figure (right) shows the response to a 59.3 keV beam. Here there is: (left) a
Compton scattering peak; (middle) florescence peaks of silver (from detector glue), and tin
(from solder bumps) at 23 and 25 keV; (right) the beam peak at 59.3 keV.
Figure 8: This shows the noise and artefacts in the detector with a GaAs sensor layer (left)
and a CdTe sensor layer (right). This is a flat-field frame which is a frame of an empty
sample case.
12
Next noise is masked. This is the most difficult area of image processing. It is critical,
since small dots in projections can cause serious artefacts in reconstruction. The new image
processing script calculates the variation on a pixel, by comparing the attenuation with the
mean attenuation in the region of neighbouring pixels. It does this by comparing the original
image to a smoothed version of itself. If a pixel is drastically changed by smoothing then it
has a high variation and is an outlier. These outliers represent noise and are masked
After masking, all the masked pixels are interpolated. Interpolation replaces pixels with
some combination of neighbouring pixels. A simple interpolation method is linear interpolation, which replaces a masked pixel with the average of neighbouring pixels (see figure 14).
The griddata interpolation function fits a 2D surface to the unmasked data points, where the
surface height gives us the replacement values [43]. Linear interpolation has the advantage
of speed but cannot deal with clusters of masked pixels. Griddata is slow and error prone
but can interpolate clusters of masked pixels.
After the images have been normalised, stitched, and cleaned; they are cropped (if necessary) and converted to the output format. If the reconstruction is done in Octopus, the
output is transposed and converted to unsigned 16bit uncompressed tiff. Conversion to
unsigned 16bit format also requires image rescaling.
These new image-processing steps were implemented in rewritten image processing code
along with documentation. Obsolete algorithms included multiplying by magic numbers,
interpolating specific rows, and infinite interpolation loops.
3.2
Results
The old image processing was undocumented and had detector specific code. This code
had accumulated over time without documentation or structure. The lack of structure was
halting progress so development was necessary.
Along with others, I understood, documented then rewrote the processing code. My
contribution was understanding and improving the commenting in the original code. This
allowed a group to rewrite and improve the code without starting again. I also developed
the first local masking and proof read the final code.
The new image processing code allowed the project to begin collecting data. It was also
easier to be adapted to new detectors, this allowed a new CdTe Medipix detector to adopted
with less debugging time. The new masking scripts improved the noise removal, an example
is in figure 9. The interpolation was improved by the adoption of the griddata function to
interpolate cluster of pixels.
4
4.1
Hounsfield Units
The Hounsfield Scale
The Hounsfield scale is standard for viewing x-ray CT reconstructions in radiology. Hounsfield
units are also referred to as CT numbers. The process of CT reconstruction usually does not
preserve a connection with the original attenuation coefficients from the x-ray projections.
13
Reconstruction gives values which can be compared within the reconstruction but not between reconstruction. To compare values between reconstructions a new scale is calibrated.
This calibration is a linear transform with two constants, similar to the Kelvin scale. The
Hounsfield scale is based on the set points of water at 0 HU and air at −1000 HU. These
values are calculated using a linear transformation from attenuation values.
The Hounsfield unit scale (or CT number scale) is also widely used in radiology because
it has distinct values corresponding to biological materials (see figure 10). Water is the most
common component of biological tissue, setting it as 0 HU makes any interesting variations
from water stand out. The scale gives distinct and memorable values for medically interesting
tissues, such as 1000 for bone. This scale was named after Sir Godfrey Hounsfield the inventor
of CT, and was based of his original scale where air= 500 and water= 0 [3].
Hounsfield units have disadvantages: they are often misused, and they do not specify the
energy they are measured at. Normal CT scanners aim to measure x-rays in the clinical CT
range (0-100 keV). Usually this means measuring the energy range of the x-ray beam. Different scanners have slightly different energy ranges making it difficult to compare Hounsfield
values quantitatively. The scale has also been used in dual energy which it is unsuited for
[44]. Another weakness of the Hounsfield scale is that two slightly different forms of the
transformation equation are often used: one which assumes that air is always zero (equation
3) [45], and another which does not (equation 4) [46] [47]. If air is non-zero the simple form
(equation 3) introduces new uncertainty, while the second form reduces to the first form
when µair = 0. When Hounsfield units are misused they become a system of units which
introduces uncertainty merely by using them. The misuse of the scale and the lack of energy
specification make an amendment to this scale necessary.
µX − µH2 O
× 1000
µH2 O
(3)
Here µ indicates the linear attenuation of the material at the energy of the beam.
µX − µH2 O
× 1000
µH2 O − µair
(4)
There are papers showing significant variation in the Hounsfield scale in some areas: with
reconstruction technique [48]; and with scanner, scanner target, and scanner geometry [49].
Other approaches have derived inconsistent values [47] or shown variations for dual energy
scanning [50].
While there hava been suggestions of unsuitability of the Hounsfield scales for energy
sensitive CT, proposals have been limited to dual energy CT. Two proposals are Brooks’
proposal [46] which derives a calibration parameter for each energy bin, and Rutherford’s
[51] which calculates an effective energy for each energy bin. These proposals are unsuited
for multiple energy CT because they require calibration and extensive calculations for each
energy bin. In multiple energy CT, the energy bins are often changed between scans, so
recalibration for each change in energy is a suboptimal solution. The lack of research into
HU variation in multiple energy CT makes it necessary to show and suggest an revision
suitable for multiple energy scanners - not merely the intermediate dual energy technology
(see section 4.4 for a proposal for spectral CT). ———————— ——————————
——————————
14
Figure 9: This shows what noise reduction a good local mask can achieve. On the left is a
uncleaned image, on the right is a image with local masking and linear interpolation. The
local mask is less effective at the edges because there are less neighbouring pixels. The linear
interpolation is not effective for clumps of noise.
The Hounsfield Scale
Air
Water
-1000 -800 -600
-100
0
-40
Fat
-20
Cortical Bone
+600 +800 +1000
0 +20 +40 +60
+100
Water
White matter
Grey matter
Congealed blood
Figure 10: This shows the Hounsfield units scale, with relevant biological material marked
15
4.2
Method
For this investigation, two scans were taken of a sample of three vials. The sample was
constructed by radiologist Mike Hurrell and contained vials of: water, iodine solution, and
calcium solution (see figure 12). The iodine solution was a commercial contrast medium
called Omnipaque 300 mg I/ml, which was 1:6 diluted with water. The calcium solution
was a near saturation solution of calcium chloride (CaCl2 ), which approximated the calcium
content of bone at around six moles/L. The vials were then taped together with regular
sellotape, and placed inside a perspex sample tube. This tube was mounted, and a scan
was performed under the operation of Mike Hurrell. The scanner was using a CdTe layered
Medipix2 detector. 303 projections were obtained at regular and complete intervals over a
complete rotation. These 303 projections consist of eight energy thresholds for six frames
per projection giving 12,726 frames
The scanner energy thresholds was calibrated by Nick Cook using an Americium-241
peak at 59.5 keV. Each projection had six ’stops’, which are overlapping measurements.
Stops are taken when the detector is not large enough to cover the whole sample. Stops are
joined to make a full projection of the sample. Each energy needs a different exposure time
to measure an optimum amount of photons between the noise floor and over-counting, which
were set by Nick Cook during the calibration (see table 4). The x-ray tube was set at 75 kV
and 150 A. A flat-field was measured of an empty sample case in the scanner.
The first scan used a Medipix detector with a GaAs sensor layer. This proved difficult to
process due to the noise in the detector and the image processing algorithms. A new scan was
rendered impossible when the scanner broke down for a sustained period. During this time I
attempted to improve the image processing to make the data usable. The image processing
was improved (see section 3.2) but this data was abandoned in favour of a superior data set
from the new detector using a CdTe sensor layer. The second scan was performed by Nick
Cook using eight energy thresholds with the other settings being identical.
The image processing was done by using Matlab 2007a [36] (see 3.1). Overlapping frames
were combined to form projections. The flat-field image was used to normalise data for the:
beam shape, container, and varying detector sensitivity. The results were also normalised
for exposure time.
The projections measured photons in energy bins ranging from a lower threshold to the
maximum x-ray tube energy(75 keV). Projections were binned by subtracting higher energy
projections from the lower, giving narrow energy bins with no overlap (see table 2 for bins).
The dead rows were linearly interpolated, and the noise was identified using a threshold of
two standard deviations from the local mean. Variation was calculated using a Gaussian
blur and the remaining noise interpolated by fitting a surface to the surrounding pixels (see
section 3.1).
Reconstruction was performed by me using Octopus 8.2 [53]. Before reconstruction a spot
filter, normalisation, and ring filter were used. The data set was reconstructed using cone
beam reconstruction with linear interpolation and a regular Fourier filter. Reconstruction
was performed using a beam-source to centre distance of 100mm and a beam-source to
detector distance of 125mm. An effective centre of rotation was determined to be 611 pixels
and the vertical centre of 270pixels (pixels of 55 µm).
16
Figure 11: The variation of the Hounsfield scale’s two constant points in attenuation space.
The Hounsfield scale sets water= 0 HU, and air= −1000 HU. There is always 1000 HU
difference between them on the Hounsfield scale. The changing attenuation between air and
water shows the changing Hounsfield scale. These values were calculated using the NIST
attenuation coefficient database [52].
(a)
(c)
(b)
(d)
Figure 12: This shows a example choice of region of interest for extracting data as is standard
in radiology. This is a reconstructed slice of 3 vials of solutions, these are cones with smaller
circles representing the tapering ends of vials. (a) = Air, (b)= Iodinated contrast (c)= Water
(d)= CaCl2 solution
17
4.3
Results
Predicted results were calculated using known mass attenuation values from the National
Institute of Standards and Technology (NIST) database [52]. The predicted values were
calculated by using weighted addition (equation 5) [28] to find the attenuation values of the
solutions. Weighted addition used the fraction of the total solution weight as the weighting
factor. The predicted attenuations were then transformed to Hounsfield units using the
reduced transformation (equation 3) and NIST values for air and water attenuation.
X
µ/ρ =
wi (µ/ρ)i
(5)
i
Here wi is the fraction of weight of the solution which is the ith component. (µ/ρ)i is the
mass attenuation (linear attenuation over density) of the ith component. Reconstructed
data was converted to Hounsfield units using values of air and water chosen using standard
regions of interest (see figure 12) over three reconstructed slices. An air region was taken as
an empty square inside the tube with a comparable size to the vials. The conversion used a
form of the Hounsfield equation which allows a non-zero value of air attenuation (equation
4). The data was then compared to theoretical values from the NIST database and plotted
using Gnumeric spreadsheet [54] (see figure 13).
Uncertainty was not taken from the variance between pixels in a vial or between reconstructed slices, as these uncertainties were unreasonably low. This was because any
significant uncertainty, affected all the pixels together. Variation would arise from effects
such as beam hardening, charge sharing, fluorescence, and other artefacts and geometrical
errors. Of these charge sharing and fluorescence seemed to be the most prominent. The
experimental results approximate predicted values but there are discrepancies. These can be
attributed to known sources of variation [40]. Sources of variation are the Compton effect,
charge sharing, beam hardening, and fluorescence photons (see figure 7)..
Beam hardening reduces the attenuation of low attenuation materials. This is because
when the beam passes through a high attenuation material the lower energy photons are
more likely to be absorbed (see figure 1) this is the same as a filter in a x-ray tube (section
2.1). The depleted beam is much less likely to be absorbed, so low attenuation materials in
the shadow of high attenuation materials have a lower absorption than expected. Charge
sharing removes counts and spreads them over lower energies (see figure 7). Fluorescence
is where light is absorbed and re-emitted by elements in the detector at particular energies
(see section 6).
The Compton effect should occur below our noise threshold, as it has been shown to
be primarily below 15 keV in a 59.3 keV beam such as ours [40]. Fluorescence and charge
sharing are significant effect in CdTe medipix2 detector [55].
We see two discrepancies in the results: the iodine HU value is higher than predicted in
the energies below 25keV, and calcium is to low below 25 keV. It is difficult to determine
which effects caused this since Hounsfield units rely on the attenuation values of water, air,
and the target material (see equation 4). The materials would each be exposed to variation.
Deconvolving the variation effects could give the correct spectrum but brings its own
uncertainties [40]. The Medipix3 detector has been developed which removes the charge
18
sharing effect by summing simultaneous neighbouring counts [56]. It is preferable to wait for
the Medipix3 detector to be operational instead of using statistical techniques to deconvolve
the Medipix2 data.
There are qualitative indications of the K-edge, since iodine shows an increase in the
Hounsfield value at 35 keV. This is not in an area affected by fluorescence, and beam hardening and charge sharing effect would not change the position of the peak (only the size).
There is also the theoretical data showing the variation of Hounsfield units. This is shown
in our predicted results, and literature review (section 4.1 and figure 11).
Figure 13: This compares the Hounsfield values for Iodine and Calcium solutions when predicted and measured. The predicted values are in bins which correspond to the experimental
bins.
4.4
A Spectral Hounsfield Scale
Hounsfield units have been shown theoretically, and indicated experimentally, to vary with
energy. The purpose of a scale is to allow its values to be quantitatively compared [23].
The Hounsfield units vary based on parameter it does not account for, so it is unsuited
for multiple energy CT. It is also argued, (see 4.1) that other revisions to the Hounsfield
scale are unsuitable for multiple energy scanners.Spectral CT often change energy bins.
These alternate revisions use intensive calculations and calibrations for each energy new
bin. Instead, we propose a small but useful addition to the Hounsfield scale which. For
19
thin energy bins this mirrors the way attenuation coefficients deal with energy variation (see
section 2.2). We propose that Hounsfield values should be denoted with the average energy
HU(average energy in keV). For example where Calcium varied from 3063 HU to 5190 HU
they might be referred to for example as 3063 HU(57 keV) and 5190 HU(27 keV).
5
Conclusion
Image processing for the MARS-CT scanner was documented and rewritten, with improvement in noise masking and removal. The Hounsfield scale was reviewed and evaluated. The
Hounsfield scale was shown to vary as a function of energy, by scanning the K-edge of an
iodine solution with eight energy bins. Variation was also shown by transforming known
attenuation values to Hounsfield units. We argue that the Hounsfield scale is unsuited for
multiple energy CT. If a scale varies by a unaccounted parameter, it loses its ability to compare values when the parameter varies. We propose an amendment to the Hounsfield scale,
which would make it more suited to multiple energy CT. Hounsfield units should specify the
average energy of the energy bin they are measured in. The average energy can be given as:
value(energy in keV), or 1000 HU(37 keV).
Acknowledgements
I want especially to thank: Phil Butler, for the opportunities and for proof reading this
document; Anthony Butler, for the advice and encouragement; Nick Cook, for his invaluable
problem solving; and Mike Hurrell for choosing me to help with his research. I enjoyed working with the MARS team, especially: Rafidah Zainon, Syen Nik, Juergen Meyers, Stephane
Dufreneix, Robert Doonsberg, and Hansjorg Zeller. Thanks for the help from anyone not
mentioned here.
References
[1] G. Slavin, N. Kirkham, JCE Underwood, JM Holt, A. Hopkins, M.B.T. Jackson, and
M.C.W.O. Windsor. The autopsy and audit. Report of the Royal College of Pathologists,
Physicians, and Surgeons of London, 1991.
[2] J. Roulson, EW Benbow, and PS Hasleton. Discrepancies between clinical and autopsy diagnosis and the value of post mortem histology; a meta-analysis and review.
Histopathology, 47(6):551, 2005.
[3] GN Hounsfield. Computerized transverse axial scanning (tomography): Part 1. Description of system. British Journal of Radiology, 46(552):1016, 1973.
[4] F.A. Mettler Jr, P.W. Wiest, J.A. Locken, and C.A. Kelsey. CT scanning: patterns of
use and dose. Journal of Radiological Protection, 20(4):353–359, 2000.
[5] RE Steiner. Magnetic resonance imaging: its impact on diagnostic radiology. American
Journal of Roentgenology, 145(5):883–893, 1985.
20
[6] MD Deck, C. Henschke, BC Lee, RD Zimmerman, RA Hyman, J. Edwards,
LA Saint Louis, PT Cahill, H. Stein, and JP Whalen. Computed tomography versus magnetic resonance imaging of the brain. A collaborative interinstitutional study.
Clinical imaging, 13(1):2, 1989.
[7] S. Winter, B. Brendel, A. Rick, M. Stockheim, K. Schmieder, H. Ermert, Z.N.V.T.
AG, and G. Bochum. Registration of bone surfaces, extracted from CT-datasets, with
3D-ultrasound. Biomedizinische Technik, 47(1):57–60, 2002.
[8] A.R. Weston, T.J. Jackson, and S. Blamey. Diagnosis of appendicitis in adults by
ultrasonography or computed tomography: a systematic review and meta-analysis. International journal of technology assessment in health care, 21(03):368–379, 2005.
[9] V. Casella, T. Ido, A.P. Wolf, J.S. Fowler, R.R. MacGegor, and T.J. Ruth. Anhydrous
F-18 labeled eslemental flurine for radiopharmaceutical preparation, 1980.
[10] F. Mees, R. Swennen, M.V. Geet, and P. Jacobs. Applications of X-ray Computed Tomography in the Geosciences. Geological Society London Special Publications, 215(1):1,
2003.
[11] L. Babout, E. Maire, JY Buffiere, and R. Fougères. Characterization by X-ray computed
tomography of decohesion, porosity growth and coalescence in model metal matrix
composites. Acta Materialia, 49(11):2055–2063, 2001.
[12] M.A. Meyers. The inside dope: cocaine, condoms, and computed tomography. Abdominal Imaging, 20(4):339–340, 1995.
[13] K. Nieman, M. Oudkerk, B.J. Rensing, P. van Ooijen, A. Munne, R.J. van Geuns, and
P.J. de Feyter. Coronary angiography with multi-slice computed tomography. The
Lancet, 357(9256):599–603, 2001.
[14] H. Katayama, K. Yamaguchi, T. Kozuka, T. Takashima, P. Seez, and K. Matsuura.
Adverse reactions to ionic and nonionic contrast media. A report from the Japanese
Committee on the Safety of Contrast Media. Radiology, 175(3):621–628, 1990.
[15] S. Wild, G. Roglic, A. Green, R. Sicree, and H. King. Global Prevalence of Diabetes
Estimates for the year 2000 and projections for 2030. Diabetes care, 27(5):1047–1053,
2004.
[16] M.K. Kalra, M.M. Maher, T.L. Toth, L.M. Hamberg, M.A. Blake, J.A. Shepard, and
S. Saini. Strategies for CT Radiation Dose Optimization 1, 2004.
[17] I.R. Kamel, J.B. Kruskal, E.A. Pomfret, M.T. Keogan, G. Warmbrand, and V. Raptopoulos. Impact of multidetector CT on donor selection and surgical planning before living adult right lobe liver transplantation. American Journal of Roentgenology,
176(1):193–200, 2001.
[18] X. Wang, J. Xu, K. Taguchi, B.E. Patt, D.J. Wagenaar, and E.C. Frey. Enhanced
discrimination of calcified and soft arterial plaques using computed tomography with a
multi-energy-window photon counting x-ray detector. Medical Imaging 2009: Physics
of Medical Imaging, 7258:72583W–72583W, 2009.
[19] P.H. Butler, A.J. Bell, A.P. Butler, N.J. Cook, L. Reinisch, J.S. Butzer, and N. Anderson. Applying CERNs detector technology to health: MARS Biomedical 3D spectro21
scopic x-ray imaging. In International Symposium on Peaceful Applications of Nuclear
Technologies, 2008.
[20] X. Llopart, M. Campbell, R. Dinapoli, D. San Segundo, and E. Pernigotti. Medipix2:
A 64-k pixel readout chip with 55-/spl mu/m square elements working in single photon
counting mode. IEEE Transactions on Nuclear Science, 49(5 Part 1):2279–2283, 2002.
[21] L. Tlustos, R. Ballabriga, M. Campbell, E. Heijne, K. Kincade, X. Llopart, and P. Stejskal. Imaging properties of the Medipix2 system exploiting single and dual energy
thresholds. IEEE Transactions on Nuclear Science, 53(1 Part 2):367–372, 2006.
[22] R. Cullens. The Potential Role of 3D X-ray Spectroscopy in the Imaging of Breast
Lesions. 2009.
[23] B.N. Taylor and C.E. Kuyatt. Guidelines for evaluating and expressing the uncertainty
of NIST measurement results. NIST Gaithersburg, MD, 1994.
[24] K.B. Berg, J.M. Carr, M.J. Clark, N.J. Cook, N.G. Anderson, N.J. Scott, A.P. Butler,
P.H. Butler, and A.P. Butler. Pilot Study to Confirm that Fat and Liver can be Distinguished by Spectroscopic Tissue Response on a Medipix-All-Resolution System-CT
(MARS-CT). AIP Conference Proceedings, 1151:106, 2009.
[25] M.J. Clark. 3D and materials reconstruction. 2008.
[26] C. Grupen, G. Cowan, S. Eidelman, and T. Stroh. Astroparticle physics. Springer
Verlag, 2005.
[27] A. Beer. Bestimmung der Absorption des rothen Lichts in farbigen Fl
”ussigkeiten. Ann. Phys. Chem, 86(2), 1852.
[28] HE Johns and JR Cunningham. The physics of radiology 4th ed. Springfield, Ill Thomas, 1983.
[29] MJ Berger, JH Hubbell, SM Seltzer, J. Chang, JS Coursey, R. Sukumar, and DS Zucker.
X-COM: Photon Cross-sections Database. NIST X-COM web-site, 1988.
[30] C.G. Barkla. Energy of Secondary R
”ontgen Radiation. Proceedings of the Physical Society of London, 19:185–204, 1903.
[31] J. Radon. On the determination of functions from their integral values along certain
manifolds. IEEE transactions on medical imaging, 5(4):170–176, 1986.
[32] LA Feldkamp, LC Davis, and JW Kress. Practical cone-beam algorithm. Journal of
the Optical Society of America A, 1(6):612–619, 1984.
[33] F. Xu and K. Mueller. Ultra-fast 3d filtered backprojection on commodity graphics
hardware. In IEEE International Symposium on Biomedical Imaging: Nano to Macro,
2004, pages 571–574, 2004.
[34] G. Wang, DL Snyder, JA O’Sullivan, and MW Vannier. Iterative deblurring for CT
metal artifact reduction. IEEE transactions on medical imaging, 15(5):657–664, 1996.
[35] AH Andersen. Algebraic reconstruction in CT from limited views. IEEE Transactions
on Medical Imaging, 8(1):50–55, 1989.
[36] M.U. Guide. The MathWorks, 1998.
[37] LA Shepp and BF Logan. The Fourier reconstruction of a head phantom. IEEE Trans
Nucl Sci, 21:21–43, 1974.
22
[38] Alessandro Fornaini. X-ray imaging and readout of a TPC with the Medipix CMOS
ASIC. PhD thesis, University of Twente, Enschede, 2005.
[39] A R Faruqi. Principles and prospects of direct high resolution electron image acquisition with cmos detectors at low energies. Journal of Physics: Condensed Matter,
21(31):314004 (9pp), 2009.
[40] T. Michel. Energy Dependent Imaging Properties of the Medipix2 X-ray Detector. In
Proceedings of the The 16th International Workshop on Vertex detectors, 2007.
[41] M. Chmeissani and B. Mikulec. Performance limits of a single photon counting pixel
system. Nuclear Inst. and Methods in Physics Research, A, 460(1):81–90, 2001.
[42] T.G. Flohr, C.H. McCollough, H. Bruder, M. Petersilka, K. Gruber, C. Süβ, M. Grasruck, K. Stierstorfer, B. Krauss, R. Raupach, et al. First performance evaluation of a
dual-source CT (DSCT) system. European radiology, 16(2):256–268, 2006.
[43] C.B. Barber, D.P. Dobkin, and H. Huhdanpaa. The quickhull algorithm for convex
hulls. ACM Transactions on Mathematical Software (TOMS), 22(4):469–483, 1996.
[44] T.R.C. Johnson, B. Krauß, M. Sedlmair, M. Grasruck, H. Bruder, D. Morhard, C. Fink,
S. Weckbach, M. Lenhard, B. Schmidt, et al. Material differentiation by dual energy
CT: initial experience. European radiology, 17(6):1510–1517, 2007.
[45] M. Mahesh. The AAPM/RSNA Physics Tutorial for Residents Search for Isotropic
Resolution in CT from Conventional through Multiple-Row Detector 1. Radiographics,
22(4):949–962, 2002.
[46] R.A. Brooks. Energy dependence of the Hounsfield number. In Institute of Electrical
and Electronics Engineers Proceedings, page 368, 1977.
[47] RT Mull. Mass estimates by computed tomography: physical density from CT numbers.
American Journal of Roentgenology, 143(5):1101–1104, 1984.
[48] EC McCullough and RL Morin. CT-number variability in thoracic geometry. Am. J.
Roentgenol., 141(1):135–140, 1983.
[49] C. Levi, JE Gray, EC McCullough, and RR Hattery. The unreliability of CT numbers
as absolute values. American Journal of Roentgenology, 139(3):443–447, 1982.
[50] D.F. Jackson and DJ Hawkes. Energy dependence in the spectral factor approach to
computed tomography. Physics in Medicine and Biology, 28:289–293, 1983.
[51] RA Rutherford, BR Pullan, and I. Isherwood. Measurement of effective atomic number
and electron density using an EMI scanner. Neuroradiology, 11(1):15–21, 1976.
[52] JH Hubbell and SM Seltzer. Tables of X-ray mass attenuation coefficients and mass
energy-absorption coefficients from 1 keV to 20 MeV for elements Z= 1 to 92 and 48
additional substances of dosimetric interest. 1995.
[53] M. Dierick, B. Masschaele, and L. Van Hoorebeke. Octopus, a fast and user-friendly
R
tomographic reconstruction package developed in LabView.
Measurement Science
and Technology, 15(7):1366–1370, 2004.
[54] J. Goldberg. Gnumeric documentation, 2003 http://www.gnome.org/projects/gnumeric.
[55] C. Fr
”ojdh, H. Graafsma, HE Nilsson, and C. Ponchut. Characterization of a pixellated CdTe
23
detector with single-photon processing readout. Nuclear Inst. and Methods in Physics
Research, A, 563(1F):128–132, 2007.
[56] R. Ballabriga, M. Campbell, EHM Heijne, X. Llopart, and L. Tlustos. The medipix3
prototype, a pixel readout chip working in single photon counting mode with improved
spectrometric performance. 2006.
Appendix
Energy (keV) 14.5-18
CaCl2 (HU)
4170
Iodine (HU)
1484
18-21.5
4167
1486
21.5-25
4917
1776
25-28 28-32
5190 4815
2023 2263
32-35.6
4263
3244
35.6-39.2
3787
4577
39.2-75
3063
3719
Table 2: This shows the experimental values for iodinated contrast and CaCl2 solution in
Hounsfield units. The values are arranged according to the range of the 8 energy bins.
Lower energy threshold (keV)
Exposure (s)
22
0.03
25
0.04
27
0.07
30
0.10
35
0.3
40 45
0.7 4
Table 4: This shows the experimental values for iodinated contrast and CaCl2 solution. The
values are arranged according to the range of the 8 energy bins.
Figure 14: This shows a frame before and after linear interpolation. We can see that this is
less effective for clusters of bad pixels than for single pixels.
24