ACT I:… in which our heroes meet the

Fundamentals and Practicalitiesof Image Acquisition,

Reconstruction, and Processing

ACT I:… in which our heroes meet the

Fundamentals and Practicalitiesof Image Acquisition,

Reconstruction, and ProcessingJeff Siewerdsen, Ph.D.

Department of Biomedical EngineeringJohns Hopkins University

Johns Hopkins UniversitySchools of Medicine and Engineering

A medical imaging system is a device that transforms people into numbers.

M. Kessler

• How do we get the numbers?- Source-object-detector configurations

- Rad/Fluoro, CT, PET, US, and MR- Image acquisition- Image reconstruction

• What do the numbers mean?- Pixel values (“intensity”)- Mechanisms of contrast

• What are their limitations?- Spatial resolution- Noise- Artifacts- Geometric accuracy- Quantitation (voxel value)

Fundamentals and PracticalitiesFundamentals and Practicalities

Relevance to IGI:- Targeting- Localization- Segmentation- Registration- Therapy logistics

Imaging ConfigurationsImaging ConfigurationsSource Object Detector

?

Processor Display Observer

• 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 similarReconstruction, enhancement, displaySegmentation, registrationInterpretation (human or computer-assisted)

Imaging Configurations:X-Ray Projection Radiography

Imaging Configurations:X-Ray Projection Radiography

Source Object Detector Source Object Detector

Imaging Configurations:X-Ray Computed Tomography (CT)

Imaging Configurations:X-Ray Computed Tomography (CT)

Source

Object

Detector

Imaging Configurations:X-Ray Computed Tomography (CT)

Imaging Configurations:X-Ray Computed Tomography (CT)

Object

Detector

Source

Source

Imaging Configurations:Positron Emission Tomography (PET)

Imaging Configurations:Positron Emission Tomography (PET)

SourceDetector

Object

Source-DetectorTransducer

Imaging Configurations:Ultrasound Imaging

Imaging Configurations:Ultrasound Imaging

Source Detector

Imaging Configurations:Magnetic Resonance (MR) Imaging

Imaging Configurations:Magnetic Resonance (MR) Imaging

Object

B

Source

Detector

Imaging Configurations:Magnetic Resonance (MR) Imaging

Imaging Configurations:Magnetic Resonance (MR) Imaging

Object

Gz

Gy

Gx

Morphology Function

Multi-Modality Imaging

SPECT

PET

OpticalUS

MR

CT

Multi-Modality Imaging: ReviewD. W. Townsend, Multi-Modality Imaging of Structure and Function

Physics in Medicine and Biology (Vol. 53(4): 2008)

4%

5%

2%

31%

58%

Pop-QuizWhich imaging modality has the most well defined source-detector

geometry?1. Radiography

2. CT

3. PET

4. Ultrasound

5. MRI

Which imaging modality has the most well defined source-detector geometry?

(a)Radiography(b)CT(c)PET(d)Ultrasound(e)MRI

Answer

Reference: “Medical Imaging Systems”, Prentice-Hall Inc, Albert Macovski

Geometrically accurate.

Source = detector

• 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, …

Implications for Imaging in IGIImplications for Imaging in IGI

How to Get the Numbers (Signal)For Example: Photon Detectors

PhotomultiplierTube

(PMT)

Readout

X-ray Converter(Scintillator)

X-ray ImageIntensifier

(XRII)

Flat-panelDetector

(FPD)

Secondary Quanta(photons or e-)

Incident X-ray

CouplingConversion

Amplification

Digitization

Computed TomographyComputed Tomography

Readout

X-ray Converter(Scintillator)

Secondary Quanta(photons or e-)

Incident X-ray

CouplingConversion

Amplification

DigitizationSir Godfrey HounsfieldNobel Prize, 1979

Circa 1895

Projection radiographyI0

Computed Tomography

( )

( ) ( )∫=

=

∫=−

d

dyyx

dyyxIIxP

eII

0

0

,

0

,ln µ

µ

γ source

9-day acquisition 2.5-hr recon

Detector

Turntableand linear track

Hounsfield’s CT Scanner

p(ξ)How to Reconstruct the Numbers?

The Sinogram:Line integral projection p(ξ)… measured at each angle θ

� p(ξ;θ) “Sinogram”

ξ

θ

p(x;θ)

Simple Backprojection:

Trace projection data p(x;θ)through the reconstruction matrixfrom the detector (x) to the source

Simple backprojection yieldsradial density (1/r)

Therefore, a point-object isreconstructed as (1/r)

Solution: “Filter” the projection databy a “ramp filter” |r|

p(ξ;θ)

X-ray source

Filtered Backprojection

p(ξ;θ)p(ξ;θ)*RampKernel(ξ)

ξ

θ

The Filtered Sinogram:Convolve with RampKernel(ξ)

p(ξ)*RampKernel(ξ)Equivalent to Fourier product

P(f)|f|

p(ξ;θ)

X-ray source

Filtered Backprojection

p(ξ)p(ξ,θ) µ(x,y)

Filtered Backprojection Filtered Backprojection: Implementation

Projection at angle θp(ξ,θ)

Filtered Projectiong(ξ,θ)

Backproject g(ξ,θ).Add to image µ(x,y)

µ(x,y)

Loo

p ov

er a

ll vi

ews

(all

θ)

Third-Generation CT“Third Generation” CT Scanner

Fan-Beam X-ray Source1-D Detector Array

Multiple Projections, P(ξ,θ)

Helical Acquisition

Typical rotation time: 0.3 sec(3 rotations / sec)

Typical couch speed: ~5-30 mm/s

Two complete x-ray and data acquisition systems on one gantry.330 ms rotation time

(effective 83 ms scan time)

Siemens Medical Solutions – Somatom Definition

Dual-Source CT

From “Fan” to “Cone”

Conventional CT:Fan-Beam

1-D Detector RowsSlice Reconstruction

Multiple Rotations

Cone-Beam CT:Cone-Beam CollimationLarge-Area Detector3-D Volume ImagesSingle Rotation

Cone-Beam CT

Projection dataMultiple projections

over ~180o

Volume reconstructionSub-mm spatial resolution

+ soft tissue visibility

Cone-Beam Filtered Backprojection

Weight Filter2D

Interpolation

Geometry

# of voxels

# of projectionsRepeat ×

Reconstruction Volume

Pixel Values (“Intensity”)and Contrast

Some Fundamentals(really fundamental)

This is not a pipe. It is:

1 2 3 4

7%

16%

1%

76%1. whatever you believe it is.

2. an image of a pipe.

3. in French, so I don’t know.

4. too early in the morning for philosophy.

Some Fundamentals(really fundamental)

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 ProjectionsDisplayed Pixel Values• Pixel value can be anything you want!

� Window / level adjustment

In X-ray Projection Images• Raw pixel values are line integrals

• Depend on the intensity of the beam (kVp and mAs)• Subject to considerable processing (“tone scaling”)

• For example: conversion to “Log-Exposure Space”• Range 0-4000 (12-bit) representative of exposure to detector• Pixval 4000 � 100 mR, Pixval 3000 � 10 mR, etc.• Changes in pixel value corresponds to consistent change in EA

ActualPixel Value

Dis

pla

yed

Pix

el Valu

e

0

256

0 10,000

window

leve

l

See also: AAPM Task Group #116 andIEC International Standard 62494-1 (“Exposure Index…”)

Pixel Values: CT

Hounsfield Units (HU)

The CT image pixel values have units ofthe attenuation coefficient, µ (cm-1 or mm-1)

Commonly converted to a convenient scale: Hounsfield Units (HU)

HU’ = µ’ - µwater

µwater1000

Brain (8)

Fat (-100)

Liver (+85)

Breast (-50)

Water (0)

Polyeth (-60)

ContrastA “large-area transfer characteristic”Defined:

• As an absolute difference in mean pixel values:

• As a relative difference in mean pixel values:

ROI #1

ROI #2

21 µµ −=C

( ) 221

21

µµ

µµ

+

−=C

For example:C = |0.18 cm-1 – 0.20 cm-1|

= 0.02 cm-2

orC = |-100 HU – 0 HU|

= 100 HU

For example:C = |0.18 cm-1 – 0.20 cm-1|

0.19 cm-1

~ 10%

( ) ( )21

21 ,,,,xx

dyzyxdyzyx ∫∫ −>− µµµµ

Pop-QuizContrast is higher in CT than in x-

ray projections, because:

71%

10%

20% 1. CT uses a higher dose

2. Because you inject a contrast agent

3. Because

Reference: “Medical Imaging Systems”, Prentice-Hall Inc, Albert Macovski

( ) ( )21

21 ,,,,xx

dyzyxdyzyx ∫∫ −>− µµµµ

Pop-QuizContrast is higher in CT than in x-

ray projections, because:1. CT uses a higher dose

2. (b) Because you inject a contrast agent

3. (c) Because282

237

Contrast

Contrast =I1 – I2

(I1 + I2)/2

CT Radiograph

6325 25

252524182219251920 40

20214022 17 3019

Why CCT >> Crad?

CCT =63–25

(63+25)/2=86%

Crad =282–237

(282+237)/2=17%

Pixel Values: PETRadiopharmaceutical ACTIVITY Relating to Biological Process:

18F FDG Glucose metabolism11C Methionine (MET) Amino-acid transport and metabolism18F Fluoroethyltyrosine Amino-acid transport18F Fluoromethyltyrosine Amino-acid transport18F Fluorothymidine DNA synthesis (thymidine phosphorylation)11C Thymidine DNA synthesis18F Fluoromisonidazole (FMISO) Hypoxia62Cu ATSM Hypoxia15O water Perfusion15O gas Oxygen extraction rate11C Choline Choline metabolism99mTc annexin V Apoptosis99mTc hydrazine nicotinamide Apoptosis99mTc anti-EGF antibody Epidermal growth factor receptor (EGFR)123I mAb 425 / 111In mAb 425 EGFR

Y. Cao, University of Michigan

Pixel Values: PETStandard Uptake Value (SUV)• Ratio of tissue radioactivity concentration at time t: CPET(t)

… to the injected dose (MBq), normalized to body weight:

• SUVmax often used as a metric of tumor response.• Threshold in SUV often used for tumor volume measurement

(region-growing segmentation with PixelValue ≤ SUVthresh)SUVmean = average SUV within the segmented volume

• Important to measure SUV at a common, late time point for purposes of comparison

Major Drawbacks to Quantitation• Variability associated with noise, resolution, and ROI defintition• SUV as a quantitative metric is discouraged

SUV =CPET(t)D • W

Units: (g/ml)

LBNL 0.5 T MRI (circa 1988)

MR Image AcquisitionMagnetic Resonance (MR) Images:• Tissue Contrast• Physiology / Function• Metabolites• Acquisition in Arbitrary Planes

Acquisition by means of variousMR Pulse Sequences:

T1

T2 DWI

Gd Flair

MR Image Acquisition

Nuclei (e.g., protons)behave like magnetic

dipoles(Magnetic Moment)

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.

In the same manner that a spinning top precesses around a gravitational field,the dipoles precessaround the external

B0 field

ω = γ B0Larmor Frequency

Magnetic Dipoles Alignment and Precession

Bo

Mo=Mz

Apply RF pulse (B1 field)at Larmor frequencyin transverse plane

Flip Angle

α = γB1τ

Mxy

Net Longitudinal Magnetization

Transverse Magnetization

Spin Flip +Phase Coherence

MR Image AcquisitionMeasure the increase in

Longitudinal Magnetization (Mz)

MR Image Acquisition

1 2

Mz

… and the decrease inTransverse Magnetization (Mxy)

3 1 2 3

Mxy

T1 Spin-LatticeRelaxation Time

0.63

T2 Spin-SpinRelaxation Time

0.37

MR Image Signal and Contrast

T1 (

sec)

T2 (

ms)

Intrinsic Tissue Properties � Tissue Contrast

Spin-Lattice Spin-SpinT2 ContrastTra

nsv

erse

M

agnetiza

tion

Time

Longitudin

al M

agnetiza

tion

T1 Contrast

Time

Tiss

ue

ATi

ssue

B

∆∆∆∆Mo

Tissu

e A

Tissue B

∆∆∆∆Mxy

Contrast Weighting

T1 Weighting T2 Weighting

WaterLong T1 Dark T1 signalLong T2 Bright T2 signal

FatShort T1 Bright T1 signalLong T2 Gray T2 signal

Gd ContrastReduces T1 Enhanced T1 sigReduces T2 Reduced T2 sig

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 fiberPerfusion 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, neovascularity1H CSI Choline, Creatine, NAA, Lactate !!31P CSI Phospho - choline, - creatine, - ethanolamine, pH

BOLD contrast, T2* Tissue / blood oxygenation change, ion depositionBOLD contrast w carbogen & O2 Functionality of vasculature

O2 extraction and consumption Tissue oxygen consumption

19F-MRI perfluoro-15-crown-5-ether Hypoxia

Molecular targeted contrasts e.g., Anti-angiogensis

Pixel Values: MRAcquisition Method Process / Tissue Type / Metabolite

Y. Cao, University of Michigan

Artifacts

www.e-mri.org

Pixel Values and Contrast: Implications for IGI

Image Registration• Intensity-based registration

• For example:- Mean-square difference- Demons algorithm

• Non-intensity based registration• For example:

- Mutual information (MI)- Finite element models (FEM)

Proj

CT

PET

US

MR

Image 0 Image 0

Resolution-Limited

Contrast-to-Noise Limited

Image Quality:Beyond Contrast

CT Image Quality

1975

Liver

GB

Spine

Spleen

AO

Pancreas

2000

1 mm

Voxel size: 0.12 mm voxelsFull-width at half-max: ~0.42 mm

Hanning reconstruction filter

Axial image of steel wire

VoxelSize

0.2 mm

0.4 mm

0.8 mm

“ImageSize”

“1024”

“512”

“256”

FW

HM

(m

m)

Image Size

0.8 0.6 0.4 0.2

“128” “256” “512” “1024”

Voxel Size (mm)

ideal

actual

blu

r

sam

plin

g

Spatial Resolution

Full

-Wid

th H

alf-

Max

(µm

)

Reconstruction Filter Coeff. hwin

Han

ning

Ram

-Lak

www.impactscan.org

“Smooth” “Sharp”

Reduced Spatial ResolutionLower Noise

Improved SNRImproved Soft-Tissue Visibility

Improved Spatial ResolutionHigher NoiseReduced SNR

Reduced Soft-Tissue Visibility

Reconstruction Filter Modulation Transfer Function (MTF)

JJJJJJJJJJJJJJJJJJJJJJJJJJ

JJ

JJ

JJ

JJ

JJ

JJ

JJ

JJ

JJ

JJ

JJ

JJ

JJJJ

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0

Spatial Frequency (mm-1)

Steel Wire

Measured

System MTF

( ) ( )[ ] ,, yxLSFFTffMTF yx =

x (mm) y (mm)

Sig

nal (m

m-1

)

127 µm Wire in H2O

• CT image noise depends on– Dose Do

– Detector efficiency η– Voxel size

Axial axy

Slice thickness az

– Reconstruction filter

Barrett, Gordon, and Hershel (1976)

zxy

xy

o

E

aa

K

D

k

13

2

ησ =

oD

1∝σ 3

1

xya∝

za

1∝

Image Noise

∫∝cf

reconMTFdf0

2 Kxy

Noise / Resolution Tradeoff

Sm

oo

th

Sh

arp

Reconstruction Filter

Artifacts

Rings Shading

Lag

Motion

Metal

Streaks

“Cone-Beam”Truncation

Pop-QuizThe main image quality advantage

of CT over radiography is:

2%

2%

65%

29%

2% 1. Energy resolution

2. Spatial resolution

3. Contrast resolution

4. Temporal resolution

5. Speed of acquisition

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

Answer

Reference: “Computed Tomography”, McGraw-Hill, Stuart Bushong

Pop-QuizIn CT and cone-beam CT, image

noise exhibits which of the following dependencies:

1%

23%

8%

35%

33% 1. proportional to (1/Dose)

2. proportional to 1/sqrt(Slice Thickness)

3. proportional to # projections

4. proportional to scatter-to-primary ratio

5. independent of reconstruction filter

In CT and cone-beam CT, image noise exhibits which of the following dependencies:

(a) σ proportional to (1/Dose)

(b) σσσσ 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

Answer

References:“Computed Tomography”, McGraw-Hill Co., Steward BushongBarrett HH et al., “Statistical limitations in transaxial tomography,” Comput. Biol. Med. 6: 307-323 (1976).

Image Quality: Implications for IGILocalization / Targeting• Soft-tissue visibility• Spatial resolution• Geometric accuracy

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

Therapy LogisticsGeometry• Patient access• Field of view• Portability• Compatibility

Time• Speed of acquisition• Speed of reconstruction

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

Oops!Oops!

Pop-QuizWhen 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?

19%

25%

8%

8%

40% 1. A piece of wire

2. A moon rock

3. A piece of the American flag

4. A felt-tip pen

5. Spit

Answer

Thank you!

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?(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

• Natural history of CT scanners“Generations” of CTAdvanced scanner technologies

• Fundamentals of CT reconstructionFourier slice theoremFiltered backprojection

• Image quality / artifactsPhysical factorsPerformance metrics

• Radiation doseMagnitude and risk (in context)

What about CT?What about CT?

K. Kanal, University of Wisconsin

Conventionally: Gas (Xenon)

Single-slice CT only

Modern: Scintillator / Semiconductor

Well-suited to Multiple Detector Rows(MDCT)

Integrated (Hybrid) MMIMultiple modalities integrated within a single exam:

- Integrated hardware: hybrid scanners

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

OR

This is an image of:(a)A leaf(b) A starfish(c) A liver met(d) An apple

Pop-Quiz

SystemInput Output

q0(x) q1(x)

Image Acquisition

For Example: Digital Radiography

X-ray Converter(Scintillator or Photoconductor)

Active Matrix Sensor(Photodiodes and TFTs)

Area: ~(20x20) – (41x41) cm2

Pixel size: ~150µm – 400 µm

Incident FluenceBeam energy (kVp)Tube current (mA)Exposure time (tx)Dose (mGy)

For Example: Digital Radiography

Incident FluenceQuantum DetectionFraction of x-rays interacting / depositing energyBeam energy (kVp)Thickness of converterFundamental limit to SNR

Maximum DQE = η

For Example: Digital Radiography For Example: Digital Radiography

x

Incident FluenceQuantum DetectionConversion to Secondary QuantaOptical photons (scintillator)e-h pairs (photoconductor)“Gain” depends on converter:

Nquanta ~ Eo / W(E)Swank conversion “noise”Fundamental limit to DQE:

max DQE ~ η I

Spatial SpreadingBlurFor scintillators: depends on structure and thicknessFor photoconductors: almost negligible“Modulation transfer function”

MTFconverter ~ FT [LSF]

xa

For Example: Digital RadiographyIncident FluenceQuantum DetectionConversion to Secondary QuantaSpatial SpreadingCouplingConversion to e-h pairs

IntegrationIntegration by pixel aperture

MTFaperture ~ sinc[ax]System spatial resolution

MTFsystem ~ MTFconverter x MTFaperture

For Example: Digital RadiographyIncident FluenceQuantum DetectionConversion to Secondary QuantaSpatial SpreadingCouplingIntegrationSamplingSignal at discrete pixel locationsPotential for signal and noise

“aliasing”Electronic ReadoutAdditive electronic noise

Pixel components (TFT and PD)Capacitive readout linesAmplifierDigitizer

Imparts exposure dependence on DQEDegrades imaging performance at low dose

TFT

Amp

ADC

Fully 3-D Volumetric CT

Conventional CT:Fan-Beam

1-D Detector RowsSlice Reconstruction

Multiple Rotations

Cone-Beam CT:Cone-Beam CollimationLarge-Area Detector3-D Volume ImagesSingle Rotation

Cone-Beam CT

CT Image Reconstruction

The Fourier Transform of a projection of an object at a given angle

yields a slice of the Fourier Transform of the objectat the corresponding angle in the Fourier domain.

Fourier Slice Theorem

f(x,y)

y

x

v

u

FT

F(u,v)

CT Image ReconstructionFourier Slice Theorem

v

u

f(x,y)

ξξξξ

θθθθ

y

x

p(ξξξξ,θ,θ,θ,θ)

X-rays

θθθθ

F(u,v)

F F F F [p(ξξξξ,θ,θ,θ,θ)]

CT Image ReconstructionFourier Slice Theorem

v

u

f(x,y)

ξξξξ

θθθθ

y

x

p(ξξξξ,θ,θ,θ,θ)

X-rays

θθθθ

F(u,v)

F F F F [p(ξξξξ,θ,θ,θ,θ)]

CT Image ReconstructionFourier Slice Theorem

v

u

f(x,y)

ξξξξ

θθθθ

y

xp(ξξξξ,θ,θ,θ,θ)

X-rays

θθθθ

F(u,v)

F F F F [p(ξξξξ,θ,θ,θ,θ)]

CT Image Reconstruction

y

x

v

u

f(x,y) p(ξξξξ,θ,θ,θ,θ) F(u,v)

F F F F -1[F(u,v)]

Image Quality:A Very Quick Overview

• What are the pertinent IMAGE QUALITY METRICS?- Contrast resolution- Spatial resolution- Noise- Other…

• What are the ACQUISITION and RECONSTRUCTIONparameters?

- 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

Noise-Power Spectrum

f1

f2

Rothko

fC-fC

fC

-fC

fx

0

fy 0

SeuratfC-fC

0

fC

-fC

fx

0

fy

• Want to quantify:– Magnitude of fluctuations– Spatial correlations

• Noise-power spectrum (NPS)

• Note:

( )[ ] , 2

yxdFTNPS ∆≡

( )∫+

−

=Nyq

Nyq

dffNPS2σ

WA Kalender, Computed Tomography, 2nd Edition (2005)

Slip ring gantryContinuous gantry rotationContinuous couch translation

Pitch =Table increment / rotation (mm)

Beam collimation width (mm)

Pitch <1 :OverlapHigher z-resolutionHigher patient dose

Pitch >1:Non-overlapLower z-resolutionLower patient dose

Helical CT

Multi-Detector CT

• Multiple slices acquired in each revolution

• Higher speed• Reduced slice thickness

(Improved axial resolution)

GE Light Speed multi-row CT detector

4x1.25 mm

4x2.5 mm

4x3.75 mm

4x5.0 mm

Cone-Beam CT

Projection data P(u,v,θ)200 – 2000 projections

in a single rotation

Volume reconstruction µ(x,y,z)Sub-mm spatial resolution

+ soft tissue visibility

Minimum resolvableline-pair group

Metrics of spatial resolution:Minimum resolvable line-pairPoint-spread function (psf)Modulation transfer function (MTF)

Factors affecting spatial resolutionFocal spot sizeSystem geometry•X-ray focal spot size•Magnification (SDD/SAD)Detector configuration•X-ray converter•Pixel pitchRecon parameters•Recon filter•Slice thickness•Voxel sizePatient motion

Spatial Resolution Noise-Power Spectrum: in CTAxial Plane (x,y) Sagittal Plane (x,z)

S(fx, fy) S(fx, fz)