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Tomography Alignment and Reconstruction

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by

Andrew Scullion

on 20 July 2015

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Transcript of Tomography Alignment and Reconstruction

Tomography Alignment and Reconstruction
by Andrew Scullion
What is tomography?
Consists of reconstructing an image or volume based on many projections.
Medical field:
Computed tomography (CT or CAT scan) using X-rays
Positron emission (PET)
Magnetic resonance imaging (MRI)
Materials science:
Electron tomography
X-ray tomography
Basic Principles
Projections are produced by instrumentation.
Projection
Integral of density along a direction.

Produces a lower dimensional distribution with less information. (3D->2D or 2D->1D)
Projections can be visualized as a sinogram.
Back Projection
Projections give no information about depth.
=
Our best guess:
This is called back projection.
More projections bring us closer to the initial volume/image.
Every 8°
Every 2°
But these back projections are blurred out!
Two possible solutions:
Weighted back projection
SIRT
-
=
+
=
1
2
3
4
5
6
7
8
9
10
20
Original
What about with noise?
1
4
9
16
25
36
49
64
81
100
900
Number of iterations
Number of iterations
This is more than just
Each back projection
Affects other projections
What's happening in Fourier space?
1
4
18
36
1
4
18
36
Contrast transfer function:
Why is this?
Fourier transform:
1D
2D
along p, q=0
Projection!
Coordinate transformation
Rotation in real space = rotation in reciprocal space
If we compensate with a filter such as:
Filtered Back Projection
1
40
180
360
1
4
18
36
What if not all projections are available?
Missing Wedge Artifacts
We simply don't have information along the direction we are looking
-45:45
-65:65
What if projections are not aligned?
Alignment
Arti
facts
To some extent, this can be solved using cross-correlation
Not too sensitive to noise
Bandpass filters help with this process
Good for coarse alignment
With some
minor
problems:
Slow deviations
Choice of bandpass
And one
major
problem:
Tilt axis alignment
A uniform shift causes important problems
"Banana" Artifact
(not Banahner)
How do we solve this type of misalignment?
Gold particles can be used as fiducial markers
FEI's Inspect3D detects these automatically and adjusts for:
image shifts
tilt axis position
tilt axis rotation
magnification changes
Without fiducial markers, the alignment doesn't work very well.
Manual tracking of features is possible but
very
tedious.
IMOD's etomo developed by the University of Colorado more easily allows manual feature track but remains a black box.
Enter MATLAB
Controls:
Graphical user interface for identifying and tracking features
A
+
Shift
D
D
W
Add
track
Delete
point
Delete
entire track
Select next track (# )
S
Select previous track (# )
I
Increase Gamma
K
Decrease Gamma
T
Show tracks (toggle)
Scroll through stack
axis of rotation
Repeat
Tomography reveals features we would not have seen otherwise.
gamma=2
gamma=1
Used to reconstruct a tomogram.
This blurring is an important problem.

How do we solve it?
Simultaneous iterative reconstruction tomography (SIRT)
Why does back projection fill lines in Fourier space?
What's happening to low frequencies?
Full transcript