Seeram Chapter 7: Image Reconstruction

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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

3. It All Adds Up Puzzle

4. This is what your CT Scanner must solve!

5. Reconstruction: Solve for ms

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 0s 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

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