computed tomography diego dreossi silvia pani university of trieste and infn, trieste section
TRANSCRIPT
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Computed Tomography
Diego DreossiSilvia Pani
University of Trieste and INFN, Trieste section
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Summary
• Computed Tomography– Purpose– How does it work?
• CT reconstruction– Filtered backprojection
• Synchrotron radiation CT• MicroCT at the SYRMEP beamline• Further applications
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The goal
• To provide a three-dimensional information (depth of the structures/organs)
• To provide information about the attenuation coefficient (tissue characterization)
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From planar imaging…to CT
Source: University of Arkansas Medical Schoolhttp://anatomy.uams.edu/HTMLpages/anatomyhtml/xraythorax.html
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How does it work?• Laminar beam and laminar detector• The object/patient is rotated in front of the beam• During the rotation, planar images (projections) are
acquired at different angles• The matrix of acquired data is called SINOGRAM: each line
of the sinogram corresponds to a projection at a given angle
• A map of the attenuation coefficients is reconstructed from the sinogram by means of proper algorithms
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Image acquisition
• The line integral of the attenuation coefficient determines the attenuation along each X-ray path
0I 1
0l
dx
eI
20
l
dx
eI
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Image reconstruction: backprojection
• Purpose: obtaining the distribution function f(x,y) given a complete set of projections P(,t)
• Fourier slice theorem: the FT of a projection P(,t) corresponds to a sampling of the FT of f(x,y) along a line tilted by an angle
yP(t)
f(x,y)
t
x
X-rays
F[P(t)]
v
u
F(u,v)
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Filtered backprojection• Each pixel of the matrix
is reconstructed by summing up all projections crossing it
• But: oversampling for low frequencies!
u
v
Filtering: each transformed projection is multiplied by a function reducing the contribution of low frequencies
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Filtered backprojection
• Ramp filter (RamLak): enhancement of high frequencies noise
• Gen-Hamming, Shepp-Logan: enhancement of intermediate frequencies
• Convolution theorem convolution in the direct space as an alternative to multiplication in the Fourier space
-0.2
-0.1
0
0.1
0.2
0.3
-10 -5 0 5 10
RamLakShepp-Logangen-Hamming
amp
iezz
a (u
.a.)
pixel
0
0.1
0.2
0.3
0.4
0.5
0 0.1 0.2 0.3 0.4 0.5
rampa
Shepp-Logan
gen-Hamming
amp
iezz
a (u
.a.)
frequenza (1/step)
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The advantages of SR CT – I• Parallel beam: – an acquisition across 180 degrees provides all necessary information (lower dose – shorter acquisition
time)– simplified reconstruction algorithms
divergentbeam
parallelbeam
+180°
+180°
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The advantages of SR CT – II
• Monochromatic beam:– No beam hardening artifacts– Possibility of reconstructing true
attenuation coefficients tissue characterization
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MicroCT at the SYRMEP beamline - I
BEAM
CCDdetector
rotationalstage
sample
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0 degrees 90 degrees 140 degrees
MicroCT at the SYRMEP beamline - II• A projection = a 2048 * 300 matrix• A height h is chosen• A line at height h is extracted from each
projection and a sinogram is formed
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MicroCT at the SYRMEP beamline - III
• The sinogram is trimmed in order to have the center of rotation coincident to the center of the matrix
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MicroCT at the SYRMEP beamline - IV• The sinogram is transformed in order to
obtain line integrals of the attenuation coefficients
=-ln ( )/I0
l
dx
l
dx
eI
0
0I
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MicroCT reconstructions at the SYRMEP beamline - V
• Each line of the logarithmic sinogram is filtered
• The final image is obtained by means of a backprojection
Volume rendering
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Volume rendering
• 2-d images are stacked• The 3-d structure of the object is
visualized
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A possible application: sintered replicas of biological samples• Why?
– Tool for enhanced visualization– Used in mechanical tests to assess the bone
architecture load bearing capabilities• Tests on biological samples cannot be repeated!
• How?– Built by rapid prototyping in a relatively
homogeneous and well characterized material
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Selected laser sintering
• The object is defined by means of a CAD file
• Layer Manufacturing Technology (LMT)• Parts are manufacturing layer by layer
from polyamide powder with a CO2 laser
• Complex structures, such as the trabecular architecture, can be built