Image
Reconstruction
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Image Reconstruction - Computed Tomography - Lecture Slides, Slides of Computed Tomography
Computed Tomography is an imaging method which uses in X-Rays. This course is part of Radiology courses. This course is basic and important course for Medical students. This lecture includes: Image Reconstruction, Real Reconstruction Problem, Intensity, Raw Data, Image Data, Fourier Transform, Frequency Domain Image, Iterative Reconstruction, Adaptive Statistical Iterative Reconstruction, Resurrection of Iterative
Typology: Slides
2012/2013
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Image
Reconstruction
“It All Adds Up” Puzzle
www.education-world.com/a_lesson/italladdsup
This is what your CT Scanner must
solve!
Reconstruction:
Solve for m’s
m 11 m 12 m 13 m 14
m 21 m 22 m 23 m 24
m 31 m 32 m 33 m 34
m 41 m 42 m 43 m 44
Real Reconstruction Problem
Intensity (transmission) measured Rays transmitted through multiple pixels Find individual pixel values (question marks) from transmission data
Raw DataIntensity
(transmission)
measurements^534
Algorithm
Set of rules for getting a specific output (answer) from
a specific input
Reconstruction algorithm examples
Fourier Transform Interpolation Convolution (filtered back projection)
Fourier Transform
converts data from spatial domain to frequency
domain
breaks any signal into frequency component parts
C-major chord consists of C, E, & G notes
Fourier Transform
Sin(x) + 1/3Sin(3x)
-1.
-1.
-0.
0.000 5.000 10.000 15.000 20.
Fourier Transform
Sin(x) + 1/3 Sin (3x) + 1/5 sin (5x)
-1.
-0.
-0.
-0.
-0.
0.000 5.000 10.000 15.000 20.
Fourier Transform Reconstruction
Each set of projection data transformed to its
frequency domain
combinations of sines & cosines at various frequencies
Frequency domain image created
Frequency domain image transformed back to spatial
domain
inverse Fourier Transform
Frequency Domain Image
Lends itself to computer calculation
Easily manipulated (filtered)
edge enhancement
emphasize higher frequencies
smoothing
de-emphasize higher frequencies
Provides image quality data directly
Back Projection Reconstruction
Back Projection
for given projection, assume equal attenuation for each pixel repeat for each projection adding results
Back Projection Reconstruction
Assume actual image has 1 hot spot
(attenuator)
Each ray passing through spot will have
attenuation back-projected along entire
line
Each ray missing spot will have 0’s back-
projected along entire line
Hot Spot