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1. Introduction
2. Overview of lecture
3. Overview of PET
4. Positron emission
5. High resolution research tomograph (HRRT)
6. The image reconstruction problem
7. How then do we make images?
8. Understanding the acquired PET data
9. PET measured data (1)
10. PET measured data (2)
11. PET measured data (3)
12. PET measured data after 6 emissions
13. PET measured data after 1000 emissions
14. PET measured data: multiple points
15. The backproject then filter method
16. Test phantom - 60K events
17. A brain - 100K events
18. 2D PET looking closer at the sinogram
19. 3D PET: 2D parallel projections
20. Rebinning methods
21. Image and sinograms are vectors
22. Object representation
23. The 5 ingredients of image reconstruction
24. From object to singoram: the system matrix
25. Creating the system matrix
26. Alternative method: filling the rows
27. Model summary (1)
28. Model summary (2)
29. What the system matrix can contain
30. Case 1: central point source
31. Case 2: off centre point source
32. Case 3: multiple point sources
33. Case 4: general distribution
34. Criteria for finding the object from the data
35. Examples of objective functions
36. Maximum Likelihood reconstruction
37. ML-EM algorithm
38. The algorithm in action: 4 iterations
39. Ordered Subsets Expectation Maximization
40. EM and it's variants: OS-EM
41. The algorithm in action: 8 iterations, 4 subsets
42. Ordinary Poisson OSEM algorithm
43. Fourier reconstruction
44. The central section theorem
45. 2D filterback projections
46. 3D filtered backprojection via 3D reprojection
47. Example ML-EM and FBP reconstruction (1)
48. Example ML-EM and FBP reconstruction (2)
49. Examples of various algorithms
50. Thank you
51. References

Topics Covered

• Overview of PET and the image reconstruction problem
• Measured data: list-mode data, sinograms and backprojected images, from point sources to more complex objects
• Line integral and convolution models, and the backproject then filter (BPF) algorithm
• 2D and 3D PET data, sinograms and rebinning methods (SSRB, MSRB and FOR)
• Object representation and the system model/matrix (creating the system matrix)
• Incorporating object motion, resolution, time-of-flight, attenuation and normalization in the system model
• Objective functions: least squares and maximum likelihood (ML), regularization
• Deriving a maximum likelihood reconstruction algorithm: Expectation Maximization ML (EM-ML) reconstruction
• Ordered subsets EM (OSEM) and ordinary Poisson OSEM
• Fourier reconstruction and filtered backprojection (FBP), for PET and CT data
• 3D FBP and the reprojection method (3D RP)
• Example FBP and ML-EM reconstructions, post-smoothing

Links

Series:

• Medical Imaging

Categories:

• Methods

Talk Citation

Publication History

• Published on April 1, 2010
• Reviewed on June 15, 2020

Financial Disclosures

• Prof. Andrew Reader has not informed HSTalks of any commercial/financial relationship that it is appropriate to disclose.