1. Seeram Chapter 7: Image Reconstruction

2. “It All Adds Up” Puzzle www.education-world.com/a_lesson/italladdsup17
Please
Solve 2 5 6 4 9 1 22 16 19 7 9 23 15 17 14

3. “It All Adds Up” Puzzle www.education-world.com/a_lesson/italladdsup23
Please
Solve 5 1 8 6 7 2 13 21 18 14 9 26 14 17 18

4. This is what your CT Scanner must solve!13
Slightly
harder? 22 12 10 15 16 22 11 10 17

5. Reconstruction: Solve for m’s13
m11
m12
m13
m14
m21
m22
m23
m24
m31
m32
m33
m34
m41
m42
m43
m44 22 12 10 15 16 22 11 10 17

6. Real Problem Slightly More Complex
***
100’s of 100’s of angles 14
512 values
512
values
m11
m12
m13
m14
m21
m22
m23
m24
m31
m32
m33
m34
m41
m42
m43
m44 35 13 22 9 24 13 15 22 16

7. Real Reconstruction Problem
255
199
712
Intensity (transmission) measured
Rays transmitted through multiple pixels
Find individual pixel values (question marks) from transmission data ?
534
417
364
555
501
355

8. Raw Data Intensity (transmission) measurements 255 199 712 534 417 364
501

9. Image Data
Individual pixel values (question marks) ?

10. Algorithm
Set of rules for getting a specific output (answer) from a specific input
Reconstruction algorithm examples
Fourier Transform
Interpolation
Convolution (filtered back projection)

11. C-major chord consists of C, E, & G notes
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

12. Fourier Transform
Transforms any function to sum of sine & cosine functions of various frequencies + +

13. Fourier Transform
Sin(x) + 1/3Sin(3x) +

14. Fourier Transform
Sin(x) + 1/3 Sin (3x) + 1/5 sin (5x) +

15. Fourier Transform
Sin(x) + 1/3 Sin (3x) + 1/5 sin (5x) + 1/7 Sin (7x) + + +

16. 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

17. 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

18. Back Projection Reconstruction63 ? ? ? ? ? ? ?
Reconstruction Problem
converting transmission data for individual projections into attenuation data for each pixel

19. Back Projection Reconstruction
for given projection, assume equal attenuation for each pixel
repeat for each projection adding results 63 9 9 9 9 9 9 9

20. 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 63
Hot Spot 9 9 9 9 9 9 9

21. Back Projection Reconstruction
Each ray missing spot stays blank
Each ray through spot shares some density
Location of spot appears brightest 63 9 9 9 9 9 9 9
Hot Spot

22. Back Projection Reconstruction
Streaks appears radially from spot
star artifact
Star Artifact Spokes
Hot
Spot

23. Iterative Reconstruction
Start with measured data 12 15 9
? ? ?
? ? ?
? ? ? 17 19 12
Measurements

24. Iterative Reconstruction
Make initial guess for first projections by assuming equal attenuation for each pixel in a projection
Similar to back projection 12 15 9
Measurements
? ? ?
? ? ?
? ? ? 17 19 12
Initial guess based
upon vertical projections
Measurements

25. Iterative Reconstruction
calculate difference between measured & calculated attenuation for next projection
correct all pixels equally on current projection to achieve measured attenuation BUT!!!

26. Iterative Reconstruction
changing pixels for one projection alters previously-calculated attenuation for others
corrections repeated for all projections until no significant change / improvement

27. Iteration Example 8 4 4 24 12 12 Initial guess based
Initial guess based
upon vertical projections 17 19 12
Low by 1; add .33 to each.
Make corrections
based on
horizontal
Projections data
Low by 3; add 1 to each.
High by 4; subtract 1.33 from each.

28. Iteration Example 17 19 12 9 15 12
Make corrections
based upon
Data measured on
diagonals
High by .33; subtract .17 from each.
High by 1; subtract .33 from each.
Low by .3; add .17 to each.

29. Iteration Image Reconstruction
operationally slow and cumbersome, even for computers
not used
Stay tuned! We’ll be right back after a word about filtered back-projection.

30. Filtered Back Projection*
enhancement of back projection technique
filtering function (convolution) is imposed on transmission data
small negative side lobes placed on each side of actual positive data
negative values tend to cancel star artifact
Unfiltered back projection
Filtered back projection

31. Filtered Back Projection
operationally fast
reconstruction begins upon reception of first transmission data
best filter functions found by trial & error
Most common commercial reconstruction algorithm

32. The Resurrection of Iterative Reconstruction: General Electric Adaptive Statistical Iterative Reconstruction (ASIR)
Claims & Observations
22-66% reduction in dose in abdominal scans with no change in spatial or temporal resolution
No special operator training
As fast as filtered back-projection
Jagged edge seen around liver when dose too low
Imaging problems seen in thin patients when dose too low
Algorithm creates different texture
Appears artificial
Creates a “new normal”

33. The Resurrection of Iterative Reconstruction: General Electric Adaptive Statistical Iterative Reconstruction (ASIR)
Claims & Observations
New algorithm being developed
MBIR
Still too slow for routine use.
Dual-energy CT may eliminate need for pre-contrast images.

34. The Resurrection of Iterative Reconstruction: Siemens Iterative Reconstruction in Image Space (IRIS)
Claims & Observations
Dose reduction up to 60% without quality loss
Fast reconstruction

35. The Resurrection of Iterative Reconstruction: Philips iDose
Claims & Observations
Dose reduction for coronary CT angiography more than 80% without quality loss
Reconstruction times of up to 20 images/second
Can improve image quality in typically high noise bariatric exams

36. Multi-plane reconstruction
using data from multiple axial slices it is possible to obtain
sagittal & coronal planes
oblique & 3D reconstruction
Non-spiral reconstruction
Poor appearance if slice thickness >>pixel size
multi-plane reconstructions are computer intensive
Can be slow

37. Saggital / Coronal Reconstructions
Axial
Saggital

38. 3D Reconstructions Uses pixel data from multiple slices
Algorithm identifies surfaces & volumes
Display renders surfaces & volumes
Real-time motion
auto-rotation
user-controlled multi-plane rotation

39. 3D Reconstructions

40. What Are These? *

41. Interpolation
Calculating attenuation data for specific slice from spiral raw data
Table moves continually
As tube rotates table constantly moves
Position at start of rotation
Position at start of rotation
Position of interest

42. Interpolation
Estimates value of function using known values on either side
When x = 50, y = 311
When x = 80, y = 500
What will be the value of y when x=58?
(80,500) ?
(50,311) 58

43. Interpolation ? 58 58 is 8/30ths of the way between points
“y” when x=58 will be 8/30ths of the way between 311 and 500
?=311+8/30 ( )
(80,500) ?
(50,311) 58

44. The End