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Image Reconstruction

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Title: Image Reconstruction Author: HSS Last modified by: HSS Created Date: 10/22/2009 9:15:02 PM Document presentation format: On-screen Show Company – PowerPoint PPT presentation

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Title: Image Reconstruction


1
Image Reconstruction
  • Atam P Dhawan

2
Image Formation
3
Image Formation External Source
4
Image Formation Internal Source
5
Fourier Transform
6
Radon Transform
7
Radon Transform
8
Fourier Slice Theorem
  • X-y coordinate system rotated to p-q

u w cos q v w sin q
9
Fourier Slice Theorem
10
Inverse Radon Transform
11
Filtered Backprojection
The integration over the spatial frequency
variable w should be carried out from
But in practice, the projections are considered
to be bandlimited. This means that any spectral
energy beyond a spatial frequency, say W, must be
ignored.
can be computed as
in the spatial domain and is bandlimited.
is the Fourier transform of the filter kernel
function
12
in the spatial domain and is bandlimited.
is the Fourier transform of the filter kernel
function
13
(No Transcript)
14
If the projections are sampled with a time
interval of t, the projections can be represented
as
Using the Sampling theorem and the bandlimited
constraint, all spatial frequency components
beyond W are ignored such that
For the bandlimited projections with a sampling
interval of t
15
Filter Function
16
The Final Algorithm FBP
17
Iterative ART
18
PET ML Image Reconstruction
19
ML-EM Algorithm
20
Multi-Grid EM Algorithm
21
MGEM Reconstruction
22
Reconstruction in MRI
Fourier Transform Reconstruction Method
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