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Seeram Chapter 7: Image Reconstruction

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**1. **CT Seeram Chapter 7:
Image Reconstruction

**2. **“It All Adds Up” Puzzle www.education-world.com/a_lesson/italladdsup

**3. **“It All Adds Up” Puzzle www.education-world.com/a_lesson/italladdsup

**4. **This is what your CT Scanner must solve!

**5. **Reconstruction: Solve for m’s

**6. **Real Problem Slightly More Complex

**7. **Real Reconstruction Problem Intensity (transmission) measured
Rays transmitted through multiple pixels
Find individual pixel values from transmission data (question marks)

**8. **Raw Data Intensity (transmission) measurements

**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. **Fourier Transform converts data from spatial domain to frequency domain
breaks any signal into frequency component parts

**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 Reconstruction Reconstruction Problem
converting transmission data for individual projections into attenuation data for each pixel

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

**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

**21. **Back Projection Reconstruction Each ray missing spot stays blank
Each ray through spot shares some density
Location of spot appears brightest

**22. **Back Projection Reconstruction Streaks appears radially from spot
star artifact

**23. **Iterative Reconstruction Start with measured data

**24. **Iterative Reconstruction Make initial guess for first projections by assuming equal attenuation for each pixel in a projection
Similar to back projection

**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

**28. **Iteration Example

**29. **Iteration Image Reconstruction operationally slow and cumbersome, even for computers
not used

**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

**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. **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

**33. **Saggital / Coronal Reconstructions

**34. **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

**35. **3D Reconstructions

**36. **What Are These?

**37. **Interpolation Calculating attenuation data for specific slice from spiral raw data
Table moves continually
As tube rotates table constantly moves

**38. **Interpolation Estimates value of function using known values on either side

**39. **Interpolation 58 is 8/30ths of the way between points
“y” when x=58 will be 8/30ths of the way between 311 and 500

**40. **The End