Supplementary Material Emission Computed Tomography

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Supplementary Material Emission Computed
Tomography

• Thanks to those that post interesting material on
  the internet. This supplement is a collection
  from several.

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Emission Tomography
projection
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SPECTSingle Photon Emission Computed Tomography
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PETPositron Emission Tomography

• What do we want to detect in PET?
• 2 photons of 511 keV in coincidence, coming in a
  straight line from the same annihilation

TRUE coincidence
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Types of Coincidence

• True coincidence is the simultaneous detection of
  the two emissions resulting from a single decay
  event.
• Scatter coincidence is when one or both photons
  from a single event are scattered and both are
  detected.
• Random coincidence is the simultaneous detection
  of emission from more than one decay event.

Coincidences True Scatter Random
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PET radiation detection

• PET scanner
• Typical configuration
• whole-body (patient port ?60 cm axial FOV15
  cm)
• scintillator crystals coupled to photomultiplier
  tubes (PMTs)
• cylindrical geometry
• 24-32 rings of detector crystals
• hundreds of crystals/ring
• several millions of Lines Of Response (LORs)
  (only a few are shown)

• Other configurations for special-purpose
  applications
• - brain imaging
• animal PET
• mammography, other

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PET/CT

• General Electric Medical Systems

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PET data acquisition

• Organization of data
• True counts in LORs are accumulated
• In some cases, groups of nearby LORs are grouped
  into one average LOR (mashing)
• LORs are organized into projections

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PET data acquisition

• 2D and 3D acquisition modes

In the 3D mode there are no septa photons from a
larger number of incident angles are accepted,
increasing the sensitivity. Note that despite
the name, the 2D mode provides three-dimensional
reconstructed images (a collection of transaxial,
sagittal and transaxial slices), just like the 3D
mode!
2D mode ( with septa)
3D mode( no septa)
septa
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PET data acquisition

• 2D mode vs. 3D mode

2D mode ( with septa)
3D mode( no septa)
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PET data acquisition

• Organization of data
• In 3D, there are extra LORs relative to 2D

3D mode
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PET evolution spatial resolution
Image credits Crump Institute, UCLA
Image credits CTI PET Systems
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Part of the goal is to bring order to this
alphabet soup.
J. Fessler, 2002
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PET image reconstruction
Object
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PET image reconstruction
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PET image reconstruction
Sinogram
Object
?
r
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PET image reconstruction
Sinogram
Object
?
r
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PET image reconstruction
Sinogram
Object
?
r
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PET image reconstruction
Sinogram
Object
?
r
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PET image reconstruction
Sinogram
Object
?
r
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Sinogram

• Other representations can be used instead of the
  sinogram (linogram, planogram)

PET 180º (2 opposite photons)
SPECT 360º (1 photon)
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PET image reconstruction
2D Reconstruction

• 2D Reconstruction
• Each parallel slice is reconstructed
  independently (a 2D sinogram originates a 2D
  slice)
• Slices are stacked to form a 3D volume f(x,y,z)

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PET image reconstruction
2D Reconstruction

• Projection and Backprojection

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PET image reconstruction
2D Reconstruction
Backprojection
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The Importance of counts
50 000 counts
100 000 counts
200 000 counts
4.8mm
6.4mm
12.7 mm
7.9 mm
11.1mm
9.5mm
500 000 counts
1 million counts
2 million counts
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Noise In PET Images

• Noise in PET images is dominated by the counting
  statistics of the coincidence events detected.
• Noise can be reduced at the cost of image
  resolution by using an apodizing window on ramp
  filter in image reconstruction (FBP algorithm).

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PET image reconstruction

• Data corrections are necessary
• the measured projections are not the same as the
  projections assumed during image reconstruction

Object(uniformcylinder)
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Analytical methods

• Advantages
• Fast
• Simple
• Predictable, linear behaviour
• Disadvantages
• Not very flexible
• Image formation process is not modelled ? image
  properties are sub-optimal (noise, resolution)

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Iterative methods

• Advantages
• Can accurately model the image formation process
  (use with non-standard geometries, e.g. not all
  angles measured, gaps)
• Allow use of constraints and a priori information
  (non-negativity, boundaries)
• Corrections can be included in the reconstruction
  process (attenuation, scatter, etc)
• Disadvantages
• Slow
• Less predictive behaviour (noise? convergence?)

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PET Image reconstruction

• Iterative methods

Iteration 1
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PET Image reconstruction

• Iterative methods

Iteration 2
image space
projection space
projection
Current estimate
Measured projection
Update
Error projection
Errorimage
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PET Image reconstruction

• Iterative methods

Iteration N
image space
projection space
projection
Current estimate
Measured projection
Compare
(e.g. - or / )
Update
backprojection
Error projection
Errorimage
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Algorithm comparison

• 600 000 counts (including scatter)

Image credits Kris Thielemans MRC CU, London
(now IRSL www.irsl.org)
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Reconstruction of a slice from projectionsexample
myocardial perfusion, left ventricle, long axis
courtesy of Dr. K. Kouris
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Iterative reconstruction methods
conventional iterative algebraic
methods algebraic reconstruction technique (ART)
simultaneous iterative
reconstruction technique (SIRT) iterative
least-squares technique (ILST) iterative
statistical reconstruction methods
(with and without using a
priori information) gradient and conjugate
gradient (CG) algorithms maximum
likelihood expectation maximization (MLEM)
ordered-subsets expectation maximization (OSEM)
maximum a posteriori (MAP) algorithms
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algorithm (a recipe) (1) make the first
arbitrary estimate of the slice (homogeneous
image), (2) project the estimated slice into
projections analogous to those measured by the
camera (important in this step, physical
corrections can be introduced - for attenuation,
scatter, and depth-dependent collimator
resolution), (3) compare the projections of the
estimate with measured projections (subtract or
divide the corresponding projections in order to
obtain correction factors - in the form of
differences or quotients), (4) stop or continue
if the correction factors are approaching zero,
if they do not change in subsequent iterations,
or if the maximum number of iterations was
achieved, then finish otherwise (5) apply
corrections to the estimate (add the differences
to individual pixels or multiply pixel values by
correction quotients) - thus make the new
estimate of the slice, (6) go to step (2).
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Iterative reconstruction - multiplicative
corrections
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Iterative reconstruction - differences between
individual iterations
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Iterative reconstruction - multiplicative
corrections
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Filtered back-projection

• very fast
• direct inversion of the projection formula

• corrections for scatter, non-uniform attenuation
  and other physical factors are difficult
• it needs a lot of filtering - trade-off between
  blurring and noise
• quantitative imaging difficult

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Iterative reconstruction

• amplification of noise
• long calculation time

• discreteness of data included in the model
• it is easy to model and handle projection noise,
  especially when the counts are low
• it is easy to model the imaging physics such as
  geometry, non-uniform attenuation, scatter, etc.
• quantitative imaging possible

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References Groch MW, Erwin WD. SPECT in the year
2000 basic principles. J Nucl Med
Techol 2000 28233-244, http//www.snm.org. Groch
MW, Erwin WD. Single-photon emission computed
tomography in the year 2001 instrumentation and
quality control.
J Nucl Med Technol 2001 209-15,
http//www.snm.org. Bruyant PP. Analytic and
iterative reconstruction algorithms in SPECT.
J Nucl Med 2002 431343-1358, http//www.snm.org.
Zeng GL. Image reconstruction - a tutorial.
Computerized Med
Imaging and Graphics 2001 25(2)97-103,
http//www.elsevier.com/locate/compmedimag. Vanden
berghe S et al. Iterative reconstruction
algorithms in nuclear medicine. Computerized Med
Imaging and Graphics 2001 25(2)105-111,
http//www.elsevier.com/locate/compmedimag.
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