Image reconstrsuction in ct pdf

IMAGE RECONSTRUCTION IN MDCT
NAME – SABINA SHRESTHA
ROLL NO- 2
4TH YEAR BSC.MIT

CONTENT
• basic principle of CT
• Step of image formation of CT
• Image reconstruction in CT
• Basic principle of helical CT• Basic principle of helical CT
• Description of MDCT
• Image reconstruction in MDCT
• References

Basic principle of CT
• The internal structure of an object can be
reconstructed from multiple projections of an
object.
• An X-ray tube rotates on a special gantry• An X-ray tube rotates on a special gantry
around the patient while the detectors
measure the average linear attenuation
coefficient µ.

• Attenuation is the reduction of the intensity of an
x-ray beam as it traverses matter.
• The reduction may be caused by absorption or
by deflection (scatter) of photons from the beam
and can be affected by different factors such as
beam energy and atomic number of the absorber.
• An attenuation coefficient is a measure of the
quantity of radiation attenuation by a given
thickness of absorber.
• Linear and mass attenuation coefficients are the
coefficients used most often.

Attenuation is followed by Lambert’s law of absorption.
Where , µ=Linear attenuation coefficient
I= transmitted intensity of x-ray,I= transmitted intensity of x-ray,
Io= initial intensity of x-ray
This equation expresses the exponential relationship
between incident primary photons and transmitted
photons for a mono energetic beam with respect to the
thickness of the absorber and thus may be used to
calculate the attenuation by any thickness of material.

Steps for CT Image Formation
All CT systems use a three step process
• Scan or Data Acquisi on → Get Data• Scan or Data Acquisi on → Get Data
• Image Reconstruc on → Use Data
• Image Display → Display Data

Tube emits x-ray beam
2. Beam is shaped
3. Beam is collimated
4. Beam is attenuated
5.Transmitted x-rays are
detected and converted
to electrical signal
6. ADC converts
electrical signal to
digital data
7. Digital data is sent to
computer

Scan or data acquisition
 The scanning process begins with data acquisition.
• Data Acquisition refers to a method by which the
patient is systematically scanned by the X ray
tube and detectors to collect information for
image reconstruction.
• DAS is the heart of the ct scan, consist of• DAS is the heart of the ct scan, consist of
• Collimator and filtration system
• Detector
• analog to digital conversion
some data preprocessing for use by the
scanner reconstruction system

Basic scheme for data acquisition:
Beam geometry -size, shape, and motion of the
x-ray beam and its path
Components- physical devices thatComponents- physical devices that
shape/define the x-ray beam, measure its
transmission through the patient, and convert
info into digital data

 Measurements of the transmitted beam intensities are
made by array of detectors.
 Ray : Single transmission measurement through the
patient made by a single detector at a given moment in
time
 Projection or view : A series of rays that pass through the Projection or view : A series of rays that pass through the
patient at the same orientation
 Projection data sets are acquired at different angles
around the patient.
 CT images are derived by mathematical analysis of
projection data sets.

RAW DATA VERSUS IMAGE DATA
• All of the thousands of bits of data acquired by the
system with each scan are called raw data.
• The process of using the raw data to create an image is
called image reconstruction.
• Once raw data have been processed so that each pixel is
assigned a Hounsﬁeld unit value, an image can beassigned a Hounsﬁeld unit value, an image can be
created; the data included in the image are now referred
to as image data .
• The reconstruction that is automatically produced during
scanning is often called prospective reconstruction.
• The same raw data may be used later to generate new
images. This process is referred to as retrospective
reconstruction

SINOGRAM
The data acquired for one CT slice can be
displayed before reconstruction. This type of
display is called a sinogram.
Rays are plotted horizontally and views areRays are plotted horizontally and views are
shown on the vertical axis.
During the 360-degree CT acquisition of a
particular object, the position of the ray
corresponding to that object varies sinusoidally
as a function of the view angle.

• The number of rays used to reconstruct a CT
image has a profound influence on the radial
component of spatial resolution, and the number
of views affects the circumferential component
of the resolution

Image Reconstruction
A mathematical process that converts the scan
data for the individuals into numerical or
image data.
A mathematical algorithm takes the multiple
projection data(raw data) & reconstructs the
CT image(image data).

In CT a cross-sectional layer of the body is
divided into many tiny blocks.
Each block(voxel)is assigned a no. proportional to
the degree that the block attenuated the X-ray
beam.
Voxel composition, thickness & quality of theVoxel composition, thickness & quality of the
beam determine the degree of attenuation.
Basic equation:
• N = N0e-µx

CT NUMBER
The relative attenuation coefficient is normally expressed in
“Hounsfield Unit” which are also known as a “CT
Number”. Therefore each tissue element (Voxel) is
assigned by a ‘CT Number’.
The relation b/w linear attenuation coefficient & CT
Number is given by: -
CT Number (HU) = K x (µ - µ )/µCT Number (HU) = K x (µt - µw)/µw
Where, K = 1000 a constant factor which determines the
contrast scale, µt & µw are linear coefficient of Tissue
Element & Water.
‘Note’: - The CT Number (HU Value) generated by a CT
scanner are approximate & depend on the kVp & filtration.

Correction-CT
1. For Heterochromatic nature of beam.
2. Weighting factor to compensate the
difference between the size & shape of thedifference between the size & shape of the
scanning beam & the picture matrix.
• As heterochromatic radiation passes through
an absorber, filtration increases its mean
energy.

0.19
70 KeV
Monochromatic
A. For Heterochromatic nature of beam.
0.19
70 KeV (mean)
120 KVp
Heterochromatic
75 KeV (mean)
Thickness (cm of water)
µ cm-1

• Correction for weighting factor
WF=1 WF<1

• In CT, reconstruction algorithms are used by
the computer to solve the many mathematical
equations necessary for information from the
detector array to be converted to informationdetector array to be converted to information
suitable for image display.

• There are 3 mathematical methods of image
reconstructions are as follows: -
• Simple Back projection Reconstruction
• Iterative method• Iterative method
• Analytical method
1) Filtered back projection
2) Fourier filtering

Simple Back projection Reconstruction
‫٭‬ It is also known as the “Summation Method” or
the “Linear Supposition Method”.
‫٭‬ In this method, each x-ray transmission path
through the body is divided into equallythrough the body is divided into equally
spaced elements & each element is assumed to
contribute equally to the total attenuation along
the x-ray path.

Continued
‫٭‬ By summing the attenuation for each element over all
x-ray paths that intersect the element at different
angular orientations, a final summed attenuation
coefficient is determined for each element.
‫٭‬ When this coefficient is combined with the summed
coefficients for all other elements in the anatomiccoefficients for all other elements in the anatomic
section scanned by the x-ray beam, a composite image
of attenuation coefficients is obtained
 The phenomenon which results in a blurred image of
the actual object when simple back projection is used
.A filtering step is therefore added to correct this
blurring, in a process known as filtered back projection.

Iterative method
 Successive approximation method to obtain an image of
attenuation coefficients from the measured intensities.
 Assumption that all points in the matrix have same value
 Compared with the measured values.
 Makes correction unit values come with in acceptable
range.range.
 Used by the first EMI brain scanner.
 Contains 3 correction factors:
1. Ray by ray correction
2. Simultaneous reconstruction
3. Point by point corrections

Ray- by-ray Correction: One ray sum is calculated and corrected, and these
corrections are incorporated into future ray sums, with the process being
repeated for every ray in each iteration.

Simultaneous Reconstruction: All projections
for the entire matrix are calculated at the
beginning of the iteration, and all corrections
are made simultaneous for each iteration.
Point-by- point Correction: The calculationsPoint-by- point Correction: The calculations
and corrections are made for all rays passing
through one point, and these corrections are
used in ensuring calculations, again with the
process being repeated for every point.

Current Commercial scanner uses this method
A mathematical technique known as convolution
or filtering
Technique employs a spatial filter for remove
blurring artifacts.blurring artifacts.
2 types of method
1) Filtered back projection
2) Fourier filtering

Filtered back projection
• Similar to back projection except the image is filtered
or modified to exactly counter balance the density
which causes blurring in simple back projection
The Mathematical filtering step involve convolving
the projection data with a convolution “KERNEL”the projection data with a convolution “KERNEL”
Faster as compare than iterative
Both are accurate if projection data is complete.
.

Filtered back projection
Convolution filter refers to a mathematical filtering
of the data designed to change the appearance of
the image.
A high frequency convolution filter suppress high
frequency signals, causing the image to have afrequency signals, causing the image to have a
smooth appearance and possible improvement in
contrast resolution.
A low frequency convolution filter suppresses
low frequency signal , resulting in edge
enhancement & improvement of spatial resolution

Steps of Filtered back projection
• All projection profiles are obtained
• The logarithm of data is obtained
• Logarithmic values are multiplied by digital
filterfilter
• Filtered profiles are back projected
• The filtered projections are summed and the
negative and positive components are
cancelled

Convolution
• Definition: - It is a mathematical filtering process of
projected data by the mathematical filter (Kernel) to
reduce the blurring effect of the projections.
• Depending on the manufacturer, this feature may be
called algorithm, convolution filter, FC filter, or simply
filter.filter.
• Current scanners offer several algorithm choices that
are designed to reconstruct optimal images depending
on tissue type.
• Filter functions can only be applied to raw data (not
image data). Changing the window setting merely
changes the way the image is viewed. Changing the
reconstruction algorithm will change the way the raw
data are manipulated to reconstruct the image

• The appropriate reconstruction algorithm depends on
which parts of the data should be enhanced or
suppressed to optimize the image for diagnosis. Some
will “smooth” the data more heavily, by reducing the
difference between adjacent pixels. This can help to
reduce the appearance of artifacts (such as those that
result from dental ﬁllings) but do so at the cost of
reduced spatial resolution.reduced spatial resolution.
• For example, smooth kernels are usually used in brain
exams or liver tumor assessment to reduce image
noise and enhance low contrast detectability, whereas
sharper kernels are usually used in exams to assess
bony structures due to the clinical requirement of
better spatial resolution.

• Conversely, some filters accentuate the difference between
neighboring pixels to optimize spatial resolution, but must
make sacrifices in low-contrast resolution.
• These latter filters are most often used when there are
great extremes of tissue density and when optimal low-
contrast resolution is not necessary. An example is images
of the internal auditory canal in which the tiny bones of theof the internal auditory canal in which the tiny bones of the
inner ear are displayed; the tissue densities of interest are
limited to bone or air, with high inherent tissue contrast so
the image can be reconstructed for spatial rather than
contrast fidelity .
• These types of high-contrast reconstruction algorithms are
often called bone or detail filters.

Temporal bone (a, b) and liver (c, d) images reconstructed with soft (a, c) and sharp kernels (b, d)

Some GE Reconstruction
algorithms
• Soft
• Standard
• Detail
Siemens
Reconstruction Kernel
B10-B90 for Body
H10 - H90 for Head
U30 - U90 Ultra High• Detail
• Lung
• Bone
• Edge
• Bone Plus
U30 - U90 Ultra High
Resolution
T20 -T81 Topogram
Lower number smoother
Higher number sharper

Fourier analysis
‫٭‬ The basis of Fourier analysis is that any function
of time or space can be represented by sum of
various frequencies & amplitudes of Sine &
Cosine waves.
‫٭‬ The Fourier transform(FT) is used to convert a‫٭‬ The Fourier transform(FT) is used to convert a
function expressed in the spatial domain
(millimeters)into the spatial frequency domain
(cycles per millimeter; the inverse Fourier
transform (FT-I) is used to convert back. Also
used in MRI.

Basic principle of helical scan
• In helical CT, the patient table translates
through the gantry while the x-ray tube and
detector rotates continuously around the
patient, creating a volume of data.patient, creating a volume of data.
• Once a volume of data is collected, an image
can be reconstructed at any point along the
effective path traced by the x-ray tube.

SCAN MODES DEFINED
1 Step-and-Shoot Scanning
• In this method 1) the x-ray tube rotated 360° around the patient
to acquire data for a single slice, 2) the motion of the x-ray tube
was halted while the patient was advanced on the CT table to the
location appropriate to collect data for the next slice, and 3) steps
one and two were repeated until the desired area was covered.one and two were repeated until the desired area was covered.
• The step-and-shoot method was necessary because the rotation
of the x-ray tube entwined the system cables, limiting rotation to
360°. Consequently, gantry motion had to be stopped before the
next slice could be taken, this time with the x-ray tube moving in
the opposite direction so that the cables would unwind. Although
the terms are imprecise, this method is commonly referred to as
axial scanning, conventional scanning, or serial scanning

Helical (Spiral) Scanning
• Many technical developments of the 1990s
allowed for the development of a continuous
acquisition scanning mode most often called
spiral or helical scanning. Key among the
advances was the development of a system thatadvances was the development of a system that
eliminated the cables and thereby enabled
continuous rotation of the gantry. This, in
combination with other improvements, allowed
for uninterrupted data acquisition that traces a
helical path around the patient.

Multidetector Row CT Scanning
• The ﬁrst helical scanners emitted x-rays that were
detected by a single row of detectors, yielding
one slice per gantry rotation. This technology was
expanded on in 1992 when scanners were
introduced that contained two rows of detectors,introduced that contained two rows of detectors,
capturing data for two slices per gantry rotation.
Further improvements equipped scanners with
multiple rows of detectors, allowing data for
many slices to be acquired with each gantry
rotation.

Single detector row vs Multidetector

DATAACQUISITION GEOMETRY
• As the number of detectors in a multi-row detector
array increases, the beam becomes wider to cover the
2D detector array.
• Larger no. Of rows in the detector array will result in• Larger no. Of rows in the detector array will result in
a wider beam in z-axis direction (cone beam).
• Special cone beam recon algorithms have been
developed.
– 3D filtered back projection reconstruction.
– Adaptive Multiple Plane Reconstruction (AMPR)

Reconstruction Of spiral CT
Reconstruction Of spiral CT image is the same as
that for conventional CT except for interpolation.
Interpolation is the computation of an unknown
value using known values on either side.value using known values on either side.
A transverse planar image can be reconstruction at
any position along the axis of the pt. i.e. z- axis.
Data interpolation is performed by a special
computer programme called an interpolation
algorithm.

Interpolation(Helical)
 Helical CT scanning produces a data set in which the
x-ray source has traveled in a helical trajectory
around the patient but CT reconstruction algorithms
assume that the x-ray source has negotiated a
circular.
 To compensate for these differences in the To compensate for these differences in the
acquisition geometry, before the actual CT
reconstruction the helical data set is interpolated
into a series of planar image data sets
 Helical scanning allows the production of additional
overlapping images with no additional dose to the
patient

Z-AXIS
KNOWN
DATA
KNOWN
DATA
INTERPOLATED
DATA

Interpolation
Interpolation
Algorithm
Interpolation
Estimation of the value b/w
two known values.
Extrapolation
Estimation of the value beyond
Range of known values.

• 3600 LINEAR INTERPOLATION:
– The plane of reconstructed image interpolated from data acquired
in one revolution apart
• Blurring in the reformatted image
– Thicker slice than 1800 interpolation.
• Less noiser image than 1800 interpolation..
– 20% less noise than conventional CT.– 20% less noise than conventional CT.
• Allows scanning at lower pitch than 1800 interpolation.
– Broadens sensitivity profile
x
y
z

• 1800 LINEAR INTERPOLATION:
– Interpolation of the value separated by180º,half a revolution of the
x-ray tube
• Results in improved Z-axis resolution and greatly improved
reformatted image.
– It results thinner slice than 3600 interpolation
• It results more noiser image than 3600 interpolation.
– 20% higher noise than conventional CT.– 20% higher noise than conventional CT.
• Allows scanning at higher pitch.
– Less Broadens sensitivity profile.
z
x
y

Quality 3600 1800
Z- Axis Resolution Low High
SSP Broaden Narrow
Spatial Resolution Low High
Noise High Low
Pitch Allow Scanning
Pitch> 1
Allow Scanning
Pitch ≤ 1

The Cone-Angle Problem in
Multi–Detector Row CT
• Two-dimensional image-reconstruction approaches
used in commercially available single-section CT
scanners require all measurement rays that contribute
to an image to run in a plane perpendicular to the
patient’s longitudinal axis.patient’s longitudinal axis.
• In multi–detector row CT systems, this requirement is
violated.
• The measurement rays are tilted by the so called cone
angle with respect to the center plane. The cone angle
is largest for the sections at the outer edges of the
detector, and it increases as the number of detector
rows increases, if their width is kept constant.

The Cone-Angle Problem in
Multi–Detector Row CT
• As a first approximation, the cone angle is neglected in
multi–detector row CT reconstruction approaches: The
measurement rays are treated as if they traveled
perpendicular to the z-axis, and modified two-dimensional
image-reconstruction algorithms are used.
• The data are then inconsistent, however, and produce
cone-beam artifacts at high-contrast objects such as bones.cone-beam artifacts at high-contrast objects such as bones.
It has been demonstrated that cone-beam artifacts can be
tolerated if the maximum number of simultaneously
acquired sections does not markedly exceed four .
• As a consequence, the image-reconstruction approaches of
all commercially available four-section CT systems and of
some systems with even more sections neglect the cone
angle of the measurement rays.

MDCT RECONSTRUCTION APPROACHES THAT NEGLECT
CONE-BEAM GEOMETRY
1 .Multi–Detector Row 180° and 360°
Linear Interpolation
2. Z-Filter Approaches

Z-Filter Approaches
• In a z-filter multi–detector row spiral
reconstruction , the spiral interpolation for
each projection angle is no longer restricted to
the two rays closest to the image plane.
• Instead, all direct and complementary rays
within a selectable distance from the image
plane contribute to the image.

Continued
• A z-filter approach implemented in Siemens
CT scanners, is the adaptive axial interpolation
algorithm (AAI).
• Another, Multislice cone-beam tomography(• Another, Multislice cone-beam tomography(
MUSCOT) algorithm used by Toshiba. Z
filtering allows the system to trade off z-axis
resolution (the SSP) with image noise(which
directly correlates with required dose).

Continued
• The intrinsic resolution of a multi–detector row
spiral scan is determined by the choice of
collimation (e.g., four sections at 1.0 or 2.5 mm).
Z filtering makes it possible to reconstruct imagesZ filtering makes it possible to reconstruct images
retrospectively with different section widths
from the same raw CT data set. Only section
widths equal to or larger than the section width
of one active detector row can be obtained.

MDCT RECONSTRUCTION APPROACHES THAT ACOUNTS
CONE-BEAM GEOMETRY
• For CT scanners with 16 or more detector
rows, modified reconstruction approaches
that account for the cone-beam
geometry of the measurement rays havegeometry of the measurement rays have
to be considered. Some manufacturers
(Toshiba, Philips) have , an approximate 3D
convolution back-projection reconstruction .

• With this approach, the measurement rays are
back projected into a 3D volume along the lines of
measurement, accounting in this way for their
cone beam geometry.
• manufacturers use variations and extensions of
nutating-section algorithms for image
reconstruction. These algorithms split the 3D
reconstruction task into a series of conventionalreconstruction task into a series of conventional
two-dimensional reconstructions on tilted
intermediate image planes, in this way benefiting
from established and very fast two-dimensional
reconstruction techniques. Representative
examples are AMPR (Siemens) and the weighted
hyperplane reconstruction (proposed by GE
Medical Systems) techniques.

Vendor Variations on Analytical
Reconstructions
• GE – 3D Weighted FBP (Tang et al, PMB, 2006)
• Philips – COBRA, nPI (Kohler et al, Med Phys,
2002; Bontus et al, TMI, 2005)
• • Siemens – AMPR (Flohr et al, Med Phys• • Siemens – AMPR (Flohr et al, Med Phys
2003) and 3D weighted FBP (Stierstorfer et al,
PMB, 2004)
• • Toshiba – TCOT, modified FDK (Taguchi et al,
Med Phys, 2003)

• IR techniques perform repetitive reconstructions applying
mathematical models to account for known imperfections in
the projection data.
• More advanced “model-based” IR (MBIR) products go
beyond statistical modeling. Both geometric (e.g. the area of
the anode, interaction of the photon beam with the voxel
and detector, anode heel effect, etc.) and physical (e.g. the
X-ray spectra, scattered photons, beam-hardening, etc.)
models can be applied.
• These models are used to predict the volumetric image. The• These models are used to predict the volumetric image. The
predicted image is forward-projected to create an artificial
raw data set that is then compared with the actual raw data
set. The predicted data are corrected on the basis of the
actual data, and this correction is back projected to create
an updated image.
• it can be performed for a fixed number of iterations, until
the difference between the predicted and actual data
reaches a predefined threshold, or until indicators of image
quality reach a specified level

Comparison between analytical and
iterative reconstruction
• Analytical reconstruction methods are fast and fairly
robust in many situations
• analytical reconstructions use the measured signal as if
all data were perfect. geometric considerations, such
as focal spot size, anode heel effect, the three-as focal spot size, anode heel effect, the three-
dimensional (3D) interaction of the beam with the
voxel, and the 2D interaction of the beam with the
detector, are ignored. X-ray spectra are assumed to be
monoenergetic, and nonlinear effects along the
assumed ray, for example scatter and beam-hardening,
are not considered.

• The major advantage of statistical IR
techniques involves noise reduction without a
corresponding decrease in spatial resolution.
• enable radiation dose reduction without• enable radiation dose reduction without
sacrificing image quality.
• one of the major drawbacks of IR is the longer
reconstruction time.

REFRENCES
• Christensen’s Physics of Diagnostic Radiology –
T.S.CURRY, III
• RADIOLOGIC SCIENCE for
TECHNOLOGISTS – S.C. Bushong
• Computed Tomography For Technologists, A
comprehensive Text by Lois E Romanscomprehensive Text by Lois E Romans
• PROTOCAL FOR MULTISLICE CT 2ND EDITION
• PUBLISHESD ARTICLE
• Optimization of Image Acquisition and
Reconstruction in Multi-slice
• The Role of Iterative Reconstruction Techniques
in Cardiovascular CT

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