ACT I:
… in which our heroes meet the
Fundamentals and Practicalities
of Image Acquisition,
Reconstruction, and Processing
A medical imaging system is a device
that transforms people into numbers.
Jeff Siewerdsen, Ph.D.
Department of Biomedical Engineering
Johns Hopkins University
M. Kessler
Johns Hopkins University
Schools of Medicine and Engineering
Fundamentals and Practicalities
Imaging Configurations
• How do we get the numbers?
- Source-object-detector configurations
- Rad/Fluoro, CT, PET, US, and MR
- Image acquisition
- Image reconstruction
Source
Object
Detector
Processor
Display
Observer
?
• What do the numbers mean?
- Pixel values (“intensity”)
- Mechanisms of contrast
• What are their limitations?
-
Spatial resolution
Noise
Artifacts
Geometric accuracy
Quantitation (voxel value)
Relevance to IGI:
- Targeting
- Localization
- Segmentation
- Registration
- Therapy logistics
• Source-Obj-Det configurations vary among modalities
• Physical arrangement of source-object-detector
• Physical nature of the source (x-rays, sound, radionuclide, B-field)
• Type of detector [convert EM or Mech energy to a signal (typically e-)]
• Proc-Disp-Obs configurations are comparatively similar
Reconstruction, enhancement, display
Segmentation, registration
Interpretation (human or computer-assisted)
Imaging Configurations:
X-Ray Projection Radiography
Source
Object
Detector
Imaging Configurations:
X-Ray Computed Tomography (CT)
Imaging Configurations:
X-Ray Computed Tomography (CT)
Source
Object
Detector
Imaging Configurations:
Positron Emission Tomography (PET)
Detector
Detector
Object
Source
Object
Source
Source
Imaging Configurations:
Ultrasound Imaging
Source
Imaging Configurations:
Magnetic Resonance (MR) Imaging
Source
Object
Detector
Detector
Object
Source-Detector
Transducer
Imaging Configurations:
Magnetic Resonance (MR) Imaging
Multi-Modality Imaging
Morphology
Function
Detector
SPECT
CT
Gz
Object
Gy
Gx
Source
B
MR
US
PET
Optical
Pop-Quiz
Multi-Modality Imaging: Review
Which imaging modality has the
most well defined source-detector
geometry?
D. W. Townsend, Multi-Modality Imaging of Structure and Function
Physics in Medicine and Biology (Vol. 53(4): 2008)
58%
31%
2%
5%
4%
Answer
Which imaging modality has the most
well defined source-detector geometry?
(a)Radiography
(b)CT
Geometrically accurate.
(c)PET
(d)Ultrasound
Source = detector
(e)MRI
Reference:
“Medical Imaging Systems”, Prentice-Hall Inc, Albert Macovski
1.
2.
3.
4.
5.
Radiography
CT
PET
Ultrasound
MRI
Implications for Imaging in IGI
• Configuration and Physical Basis
• Compatibility with Tx environment
• Open geometry
• Patient access
• Utility for guidance
• Speed
• Radiation Dose
• Type of image data
• Morphology
• Function
• Contrast, Image quality
• Image artifacts
• Geometric accuracy
• Ability to segment structures
• Ability to register to other images
• Cost, workflow integration, …
How to Get the Numbers (Signal)
Computed Tomography
For Example: Photon Detectors
Photomultiplier
Tube
(PMT)
X-ray Image
Intensifier
(XRII)
Incident X-ray
Incident X-ray
X-ray Converter
(Scintillator)
X-ray Converter
(Scintillator)
Secondary Quanta
(photons or e-)
Secondary Quanta
(photons or e-)
Coupling
Conversion
Coupling
Conversion
Readout
Readout
Amplification
Amplification
Flat-panel
Detector
(FPD)
Sir Godfrey Hounsfield
Nobel Prize, 1979
Digitization
How to Reconstruct the Numbers?
Computed Tomography
Hounsfield’s
CT Scanner
Projection
radiography
Detector
p(ξ)
I0
γ source
The Sinogram:
Line integral projection p(ξ)
… measured at each angle θ
p(ξ;θ) “Sinogram”
p(x;θ)
Turntable
and linear track
9-day acquisition
2.5-hr recon
Circa 1895
θ
I = I 0e
P( x ) = ln
I0
− µ ( x , y )dy
d
I
= µ ( x, y )dy
0
Digitization
ξ
Filtered Backprojection
p(ξ;θ)
Simple Backprojection:
Trace projection data p(x;θ)
through the reconstruction matrix
from the detector (x) to the source
Filtered Backprojection
The Filtered Sinogram:
Convolve with RampKernel(ξ)
p(ξ)*RampKernel(ξ)
Equivalent to Fourier product
P(f)|f|
p(ξ;θ)
p(ξ;θ)*RampKernel(ξ)
p(ξ;θ)
Simple backprojection yields
radial density (1/r)
θ
Therefore, a point-object is
reconstructed as (1/r)
Solution: “Filter” the projection data
by a “ramp filter” |r|
X-ray source
Filtered Backprojection: Implementation
Loop over all views (all θ)
Filtered Backprojection
p(ξ,
θ)
p(ξ)
µ(x,y)
X-ray source
ξ
Projection at angle θ
p(ξ,θ)
Filtered Projection
g(ξ,θ)
Backproject g(ξ,θ).
Add to image µ(x,y)
µ(x,y)
Third-Generation CT
Dual-Source CT
“Third Generation” CT Scanner
Helical Acquisition
Fan-Beam X-ray Source
1-D Detector Array
Multiple Projections, P( ξ,θ)
Typical rotation time: 0.3 sec
(3 rotations / sec)
Typical couch speed: ~5-30 mm/s
Siemens Medical Solutions – Somatom Definition
From “Fan” to “Cone”
Conventional CT:
Fan-Beam
1-D Detector Rows
Slice Reconstruction
Multiple Rotations
Two complete x-ray and data acquisition systems on one gantry.
330 ms rotation time
(effective 83 ms scan time)
Cone-Beam CT:
Cone-Beam Collimation
Large-Area Detector
3-D Volume Images
Single Rotation
Cone-Beam CT
Projection data
Multiple projections
over ~180o
Volume reconstruction
Sub-mm spatial resolution
+ soft tissue visibility
Cone-Beam Filtered Backprojection
Geometry
2D
Interpolation
Filter
Weight
Pixel Values (“Intensity”)
and Contrast
Reconstruction
Volume
# of voxels
Repeat ×
# of projections
Some Fundamentals
Some Fundamentals
(really fundamental)
(really fundamental)
This is not a pipe. It is:
1.
2.
3.
4.
7%
76%
whatever
you
believe it is.
an image of a pipe.
in French, so I don’t
know.
too early in the
morning for 16%
philosophy.
1%
1
2
3
4
This is not a pipe.
It is:
(a)whatever you
believe it is.
(b)an image of a pipe.
(c)in French, so I don’t
know.
(d)too early in the
morning for
philosophy.
Pixel Values: X-Ray Projections
256
Displayed Pixel Values
The CT image pixel values have units of
the attenuation coefficient, µ (cm-1 or mm-1)
0
In X-ray Projection Images
level
Window / level adjustment
Displayed
Pixel Value
window
• Pixel value can be anything you want!
Pixel Values: CT
Commonly converted to a convenient scale: Hounsfield Units (HU)
HU’ = 1000
Actual
Pixel Value
0
• Raw pixel values are line integrals
10,000
µ’ - µwater
µwater
Fat (-100)
Liver (+85)
• Depend on the intensity of the beam (kVp and mAs)
• Subject to considerable processing (“tone scaling”)
Polyeth (-60)
Water (0)
• For example: conversion to “Log-Exposure Space”
• Range 0-4000 (12-bit) representative of exposure to detector
100 mR, Pixval 3000
10 mR, etc.
• Pixval 4000
• Changes in pixel value corresponds to consistent change in EA
Brain (8)
Breast (-50)
See also: AAPM Task Group #116 and
IEC International Standard 62494-1 (“Exposure Index…”)
Hounsfield Units (HU)
Contrast
Pop-Quiz
A “large-area transfer characteristic”
Defined:
• As an absolute difference in mean pixel values:
C = µ1 − µ 2
For example:
C = |0.18 cm-1 – 0.20 cm-1|
= 0.02 cm-2
or
C = |-100 HU – 0 HU|
= 100 HU
ROI #1
ROI #2
• As a relative difference in mean pixel values:
C=
µ1 − µ 2
(µ
1
)
+ µ2 2
For example:
C = |0.18 cm-1 – 0.20 cm-1|
0.19 cm-1
~ 10%
Contrast is higher in CT than in xray projections, because:
20%
10%
71%
1. CT uses a higher dose
2. Because you inject a contrast agent
3. Because
µ 1 − µ 2 > µ (x, y, z )dy − µ ( x, y , z )dy
x1
x2
Contrast
Pop-Quiz
Contrast is higher in CT than in xray projections, because:
Why CCT >> Crad?
CT
Radiograph
1. CT uses a higher dose
2. (b) Because you inject a contrast agent
3. (c) Because
µ 1 − µ 2 > µ (x, y, z )dy − µ ( x, y , z )dy
x1
19 22 40 17 30 21 25 63 25 20
282
x2
Contrast =
I1 – I2
(I1 + I2)/2
Reference:
Pixel Values: PET
ACTIVITY Relating to Biological Process:
18F
FDG
Glucose metabolism
11C
Methionine (MET)
Amino-acid transport and metabolism
18F
Fluoroethyltyrosine
Amino-acid transport
18F
Fluoromethyltyrosine
Amino-acid transport
18F
Fluorothymidine
DNA synthesis (thymidine phosphorylation)
11C
Thymidine
DNA synthesis
18F
Fluoromisonidazole (FMISO)
Hypoxia
62Cu
15O
ATSM
water
Perfusion
gas
Oxygen extraction rate
11C
Choline
Choline metabolism
99mTc
annexin V
Apoptosis
99mTc
hydrazine nicotinamide
Apoptosis
99mTc
anti-EGF antibody
Epidermal growth factor receptor (EGFR)
123I
mAb 425 / 111In mAb 425
237
63–25
=86%
(63+25)/2
282–237
=17%
(282+237)/2
Pixel Values: PET
Standard Uptake Value (SUV)
• Ratio of tissue radioactivity concentration at time t: CPET(t)
… to the injected dose (MBq), normalized to body weight:
C (t)
SUV = DPET
•W
Units: (g/ml)
• SUVmax often used as a metric of tumor response.
• Threshold in SUV often used for tumor volume measurement
(region-growing segmentation with PixelValue V SUVthresh)
SUVmean = average SUV within the segmented volume
• Important to measure SUV at a common, late time point for
purposes of comparison
Hypoxia
15O
CCT =
Crad =
“Medical Imaging Systems”, Prentice-Hall Inc, Albert Macovski
Radiopharmaceutical
20 19 25 19 22 18 24 25 25 40
Major Drawbacks to Quantitation
EGFR
Y. Cao, University of Michigan
• Variability associated with noise, resolution, and ROI defintition
• SUV as a quantitative metric is discouraged
MR Image Acquisition
MR Image Acquisition
LBNL 0.5 T MRI (circa 1988)
T1
Magnetic Resonance (MR) Images:
• Tissue Contrast
• Physiology / Function
• Metabolites
• Acquisition in Arbitrary Planes
Alignment and Precession
Magnetic Dipoles
DWI
T2
Acquisition by means of various
MR Pulse Sequences:
Nuclei (e.g., protons)
behave like magnetic
dipoles
(Magnetic Moment)
Gd
In the absence of an
external magnetic field,
the orientation of the
dipoles is random.
In the presence of an
external magnetic field the
dipoles align with direction
of the applied B0 field.
Flair
In the same manner
that a spinning top
precesses around a
gravitational field,
the dipoles precess
around the external
B0 field
ω = γ B0
Larmor Frequency
MR Image Acquisition
Net Longitudinal
Magnetization
Transverse
Magnetization
Mo=Mz
MR Image Acquisition
Measure the increase in
Longitudinal Magnetization (Mz)
Spin Flip +
Phase Coherence
… and the decrease in
Transverse Magnetization (Mxy)
Mx
y
Bo
0.63
Mxy
Mz
Apply RF pulse (B1 field)
at Larmor frequency
in transverse plane
Flip Angle
α = γB1τ
0.37
1
2
T1 Spin-Lattice
Relaxation Time
3
1
2
3
T2 Spin-Spin
Relaxation Time
MR Image Signal and Contrast
Tissue Contrast
Ti
Long T1
Long T2
Short T1
Long T2
Reduces T1
Reduces T2
Pixel Values: MR
T2 Weighting
Artifacts
Process / Tissue Type / Metabolite
FLAIR T2
Tumor, edema, …
Post Gd T1
Vascular leakage, …
ADC (diffusion coefficient)
Water diffusion, intra- and extra-cellular structure
Diffusion tensor imaging
H20 anisotropy diffusion, axonal injury, muscular fiber
Perfusion imaging
Micro-circulation in normal tissue and tumor
Blood volume imaging
CBV fraction, tumor vascular density (functional)
Permeability imaging
BBB, vascular leakage
Dynamic contrast enhancement
Gd uptake, neovascularity
1H
CSI
Choline, Creatine, NAA, Lactate !!
31P
CSI
Phospho - choline, - creatine, - ethanolamine, pH
BOLD contrast, T2*
Tissue / blood oxygenation change, ion deposition
BOLD contrast w carbogen & O2
Functionality of vasculature
O2 extraction and consumption
Tissue oxygen consumption
19F-MRI
Hypoxia
Molecular targeted contrasts
Enhanced T1 sig
Reduced T2 sig
Time
T1 Weighting
perfluoro-15-crown-5-ether
Bright T1 signal
Gray T2 signal
Gd Contrast
∆Mxy
Time
Acquisition Method
Dark T1 signal
Bright T2 signal
Fat
A
ss
ue
B
∆ Mo
Water
B
T2 (ms)
Transverse Magnetization
T2 Contrast
Spin-Spin
sue
Tis
Ti
ss
ue
A
T1 Contrast
Spin-Lattice
ue
ss
Ti
T1 (sec)
Longitudinal Magnetization
Intrinsic Tissue Properties
Contrast Weighting
e.g., Anti-angiogensis
Y. Cao, University of Michigan
www.e-mri.org
Pixel Values and Contrast:
Implications for IGI
Image 0
Image Registration
Image Quality:
Beyond Contrast
Image 0
Proj
• Intensity-based registration
• For example:
- Mean-square difference
- Demons algorithm
• Non-intensity based registration
• For example:
- Mutual information (MI)
- Finite element models (FEM)
CT
Resolution-Limited
PET
US
Contrast-to-Noise Limited
MR
Spatial Resolution
al
1 mm
ideal
Spleen
“128”
Spine
1975
2000
“256”
“512”
Image Size
“1024”
Voxel size: 0.12 mm voxels
Full-width at half-max: ~0.42 mm
Hanning reconstruction filter
0.4 mm
“512”
0.8 mm
“256”
Ram-Lak
Liver
tu
Full-Width Half-Max (µm)
AO
ac
blur
Pancreas
Voxel “Image
Size”
Size
0.2 mm “1024”
0.2
sampling
GB
FWHM (mm)
Axial image of steel wire
Voxel Size (mm)
0.8
0.6
0.4
Hanning
CT Image Quality
Reconstruction Filter Coeff. hwin
Modulation Transfer Function
(MTF)
Reconstruction Filter
“Smooth”
“Sharp”
127 µm Wire in H2O
1.0
J
J
JJ
J
J
J
Steel Wire
J
J
Signal (mm-1)
0.8
J
J
J
J
J
0.6
J
J
J
J
Improved Spatial Resolution
Higher Noise
Reduced SNR
Reduced Soft-Tissue Visibility
www.impactscan.org
Image Noise
)
m
y(
0.0
J
J
J
J
0.5
1.0
J
J
J
J
JJ
J
JJ
J J
JJ
JJ
JJJ
JJ J
JJ JJJJ
1.5
Spatial Frequency (mm -1 )
Reconstruction Filter
k E 1 K xy
Do η a 3xy a z
1
1
1
∝
∝
Do
az
a 3xy
Barrett, Gordon, and Hershel (1976)
Sharp
σ2 =
0
σ∝
J
MTF ( f x , f y ) = FT [LSF (x , y )]
Smooth
c
J
0.0
η
2
Kxy ∝ df MTFrecon
J
Noise / Resolution Tradeoff
• CT image noise depends on
– Dose Do
– Detector efficiency
– Voxel size
Axial axy
Slice thickness az
– Reconstruction
filter
f
x (m
m
m)
J
Measured
0.2
Reduced Spatial Resolution
Lower Noise
Improved SNR
Improved Soft-Tissue Visibility
System MTF
J
0.4
2.0
Pop-Quiz
Artifacts
The main image quality advantage
of CT over radiography is:
2%
Rings
Shading
Streaks
Motion
29%
65%
2%
2%
Metal
Lag
Truncation
1.
2.
3.
4.
5.
Energy resolution
Spatial resolution
Contrast resolution
Temporal resolution
Speed of acquisition
“Cone-Beam”
Answer
Pop-Quiz
In CT and cone-beam CT, image
noise exhibits which of the
following dependencies:
The main image quality advantage of CT
over radiography is:
(a)Energy resolution
(b)Spatial resolution
(c)Contrast resolution
(d)Temporal resolution
(e)Speed of acquisition
33%
35%
8%
23%
1%
Reference:
“Computed Tomography”, McGraw-Hill, Stuart Bushong
1.
2.
3.
4.
5.
proportional to (1/Dose)
proportional to 1/sqrt(Slice Thickness)
proportional to # projections
proportional to scatter-to-primary ratio
independent of reconstruction filter
Answer
Image Quality: Implications for IGI
In CT and cone-beam CT, image noise
exhibits which of the following dependencies:
Localization / Targeting
• Soft-tissue visibility
• Spatial resolution
• Geometric accuracy
σ proportional to (1/Dose)
(b) σ proportional to 1/sqrt(Slice Thickness)
(c) σ proportional to # projections
(d) σ proportional to scatter-to-primary ratio
(e) σ independent of reconstruction filter
(a)
Segmentation
• For example: intensity-based thresholding
• Contrast-to-noise ratio
• Artifacts (shading and streaks)
Registration
• Pixel value / contrast
• Intensity- or Non-intensity-based
• Consistent image information
References:
“Computed Tomography”, McGraw-Hill Co., Steward Bushong
Barrett HH et al., “Statistical limitations in transaxial tomography,” Comput. Biol.
Med. 6: 307-323 (1976).
Therapy Logistics
Pop-Quiz
Geometry
•
•
•
•
When Neil Armstrong and Buzz Aldrin re-entered the
Lunar Module, the circuit breaker that arms the ascent
engine was broken. What did they use to activate the
switch?
Patient access
Field of view
Portability
Compatibility
40%
Time
• Speed of acquisition
• Speed of reconstruction
Oops!
8%
8%
Cost
• Relative to other aspects of Tx
• “Comparative effectiveness”
Radiation Dose
• For IGRT, low in comparison to Tx dose
• In general, quantifiable benefit to therapeutic outcome
25%
19%
1. A piece of wire
2. A moon rock
3. A piece of the American flag
4. A felt-tip pen
5. Spit
Answer
When Neil Armstrong and Buzz Aldrin reentered the Lunar Module, the circuit breaker
that arms the ascent engine was broken.
What did they use to activate the switch?
(a) A piece of wire
(b) A shard of moon rock
(c) A piece of the American flag
(d) A felt-tip pen
(e) Saliva
Thank you!
What about CT?
Integrated (Hybrid) MMI
Multiple modalities integrated within a single exam:
- Integrated hardware: hybrid scanners
Modern: Scintillator / Semiconductor
Conventionally: Gas (Xenon)
• Natural history of CT scanners
“Generations” of CT
Advanced scanner technologies
• Fundamentals of CT reconstruction
Fourier slice theorem
Filtered backprojection
• Image quality / artifacts
Physical factors
Performance metrics
Well-suited to Multiple Detector Rows
Single-slice
CT only
• Radiation dose
(MDCT)
Magnitude and risk (in context)
K. Kanal, University of Wisconsin
OR
Active areas of technology development
- PET-CT… SPECT-CT
- MR-PET… MR-Ultrasound… MR-Optical
Simultaneous (or near-simultaneous) acquisition
- Improves accuracy of co-registration / co-localization
- Synergy of information (e.g., attenuation correction)
- Improves clinical space, time, and workflow requirements
Pop-Quiz
Image Acquisition
This is an image of:
(a)A leaf
(b) A starfish
(c) A liver met
(d) An apple
Output
Input
q0(x)
For Example: Digital Radiography
Active Matrix Sensor
(Photodiodes and TFTs)
cm2
Area: ~(20x20) – (41x41)
Pixel size: ~150µm – 400 µm
q1(x)
For Example: Digital Radiography
Incident Fluence
X-ray Converter
(Scintillator or Photoconductor)
System
Beam energy (kVp)
Tube current (mA)
Exposure time (tx)
Dose (mGy)
For Example: Digital Radiography
Incident Fluence
Quantum Detection
For Example: Digital Radiography
Incident Fluence
Quantum Detection
Conversion to Secondary Quanta
Fraction of x-rays interacting / depositing energy
Beam energy (kVp)
Thickness of converter
Fundamental limit to SNR
Maximum DQE =
Optical photons (scintillator)
e-h pairs (photoconductor)
“Gain” depends on converter:
η
Nquanta ~ Eo / W(E)
Swank conversion “noise”
Fundamental limit to DQE:
max DQE
~
ηI
Spatial Spreading
Blur
For scintillators: depends on structure and thickness
For photoconductors: almost negligible
“Modulation transfer function”
x
MTFconverter ~ FT [LSF]
For Example: Digital Radiography
Incident Fluence
Quantum Detection
Conversion to Secondary Quanta
Spatial Spreading
Coupling
Incident Fluence
Quantum Detection
Conversion to Secondary Quanta
Spatial Spreading
Coupling
Integration
Sampling
Conversion to e-h pairs
Integration
Integration by pixel aperture
MTFaperture ~ sinc[ax]
System spatial resolution
MTFsystem ~ MTFconverter x MTFaperture
For Example: Digital Radiography
ax
Signal at discrete pixel locations
Potential for signal and noise
“aliasing”
Electronic Readout
Additive electronic noise
Pixel components (TFT and PD)
TFT
Capacitive readout lines
Amplifier
Digitizer
Imparts exposure dependence on DQE
Degrades imaging performance at low dose
ADC
Amp
Cone-Beam CT
Fully 3-D Volumetric CT
CT Image Reconstruction
Conventional CT:
Fan-Beam
1-D Detector Rows
Slice Reconstruction
Multiple Rotations
Cone-Beam CT:
Cone-Beam Collimation
Large-Area Detector
3-D Volume Images
Single Rotation
CT Image Reconstruction
Fourier Slice Theorem
The Fourier Transform of a projection of an object at a given
angle
yields a slice of the Fourier Transform of the object
at the corresponding angle in the Fourier domain.
y
Fourier Slice Theorem
p(ξ
ξ,θ)
,θ
v
F [p(ξξ,θ)]
,θ
y
f(x,y)
θ
u
x
F(u,v)
v
ξ
FT
x
θ u
F(u,v)
f(x,y)
X-rays
CT Image Reconstruction
CT Image Reconstruction
Fourier Slice Theorem
Fourier Slice Theorem
F [p(ξξ,θ)]
,θ
y
)
p(ξ,θ
v
ξ
θ
θ u
x
F(u,v)
f(x,y)
F [p(ξξ,θ)]
,θ
y
, θ)
p(ξ
v
ξ
θ
F(u,v)
f(x,y)
X-rays
θ u
x
X-rays
CT Image Reconstruction
Image Quality:
A Very Quick Overview
y
F -1[F(u,v)]
v
x
f(x,y)
u
p(ξ
ξ,θ)
,θ
F(u,v)
• What are the pertinent IMAGE QUALITY METRICS?
- Contrast resolution
- Spatial resolution
- Noise
- Other…
• What are the ACQUISITION and RECONSTRUCTION
parameters?
- kVp, mAs
Reconstruction filter
- Time, pulse sequence
Voxel size
- Pharmaceutical agent
Slice thickness
• What are the IMPLICATIONS TO IG PROCEDURES?
- Visualization and Targeting
- Image Segmentation
- Image Registration
Helical CT
Noise-Power Spectrum
• Noise-power spectrum (NPS)
FT [∆d (x, y )]
NPS ≡
• Note: + Nyq
σ =
2
Slip ring gantry
Continuous gantry rotation
Continuous couch translation
fyfy00
2
Pitch <1 :
Overlap
Higher z-resolution
Higher patient dose
f2
-f-fCC
-f-fCC
NPS ( f )df
Rothko
fCfC
• Want to quantify:
– Magnitude of fluctuations
– Spatial correlations
f1
− Nyq
00
Seurat
ffxx
ffCC
Pitch =
Table increment / rotation (mm)
Beam collimation width (mm)
Pitch >1:
Non-overlap
Lower z-resolution
Lower patient dose
WA Kalender, Computed Tomography, 2nd Edition (2005)
Multi-Detector CT
Cone-Beam CT
• Multiple slices acquired in
each revolution
• Higher speed
• Reduced slice thickness
(Improved axial resolution)
4x
1.25 mm
4x
4x
2.5 mm 3.75 mm
4x
5.0 mm
Projection data P(u,v,θ)
200 – 2000 projections
in a single rotation
GE Light Speed multi-row CT detector
Volume reconstruction µ(x,y,z)
Sub-mm spatial resolution
+ soft tissue visibility
Spatial Resolution
Factors affecting spatial resolution
Focal spot size
System geometry
•X-ray focal spot size
•Magnification (SDD/SAD)
Detector configuration
•X-ray converter
•Pixel pitch
Recon parameters
•Recon filter
•Slice thickness
•Voxel size
Patient motion
Metrics of spatial resolution:
Minimum resolvable line-pair
Minimum resolvable
Point-spread function (psf)
line-pair group
Modulation transfer function (MTF)
Noise-Power Spectrum: in CT
Axial Plane (x,y)
S(fx, fy)
Sagittal Plane (x,z)
S(fx, fz)