Send the link below via email or IMCopy
Present to your audienceStart remote presentation
- Invited audience members will follow you as you navigate and present
- People invited to a presentation do not need a Prezi account
- This link expires 10 minutes after you close the presentation
- A maximum of 30 users can follow your presentation
- Learn more about this feature in our knowledge base article
Tomography Alignment and Reconstruction
Transcript of Tomography Alignment and Reconstruction
by Andrew Scullion
What is tomography?
Consists of reconstructing an image or volume based on many projections.
Computed tomography (CT or CAT scan) using X-rays
Positron emission (PET)
Magnetic resonance imaging (MRI)
Projections are produced by instrumentation.
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.
Projections give no information about depth.
Our best guess:
This is called back projection.
More projections bring us closer to the initial volume/image.
But these back projections are blurred out!
Two possible solutions:
Weighted back projection
What about with noise?
Number of iterations
Number of iterations
This is more than just
Each back projection
Affects other projections
What's happening in Fourier space?
Contrast transfer function:
Why is this?
along p, q=0
Rotation in real space = rotation in reciprocal space
If we compensate with a filter such as:
Filtered Back Projection
What if not all projections are available?
Missing Wedge Artifacts
We simply don't have information along the direction we are looking
What if projections are not aligned?
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
Choice of bandpass
Tilt axis alignment
A uniform shift causes important problems
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:
tilt axis position
tilt axis rotation
Without fiducial markers, the alignment doesn't work very well.
Manual tracking of features is possible but
IMOD's etomo developed by the University of Colorado more easily allows manual feature track but remains a black box.
Graphical user interface for identifying and tracking features
Select next track (# )
Select previous track (# )
Show tracks (toggle)
Scroll through stack
axis of rotation
Tomography reveals features we would not have seen otherwise.
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?