1. Medical Imaging Dr. Mohammad Dawood Department of Computer Science University of Münster Germany

2. 2 Medical Imaging, SS-2014 Dr. Mohammad Dawood Recap

3. 3 Medical Imaging, SS-2014 Dr. Mohammad Dawood α decay β - decay β + decay Gamma scintigraphyPETSinogram

4. 4 Medical Imaging, SS-2014 Dr. Mohammad Dawood Ultrasound / Sonography

5. 5 Medical Imaging, SS-2014 Dr. Mohammad Dawood The frequency range of sound above 20kHz is known as ultrasound Sound spectrum

6. 6 Medical Imaging, SS-2014 Dr. Mohammad Dawood Sound wave propagation

7. 7 Medical Imaging, SS-2014 Dr. Mohammad Dawood Ultrasound

8. 8 Medical Imaging, SS-2014 Dr. Mohammad Dawood Ultrasound

9. 9 Medical Imaging, SS-2014 Dr. Mohammad Dawood Ultrasound - is produced through the conversion of electrical energy into mechanical energy - is detected by the reverse process, by converting mechanical energy into electrical energy. - The transducer is a device that is both a transmitter and receiver of the ultrasound signal and it serves a dual role in pulse echo imaging.

10. 10 Medical Imaging, SS-2014 Dr. Mohammad Dawood Inge Edler und Helmut Hertz (1954)

11. 11 Medical Imaging, SS-2014 Dr. Mohammad Dawood Ultrasound

12. 12 Medical Imaging, SS-2014 Dr. Mohammad Dawood ReflexionScatterTransmission Ultrasound

13. 13 Medical Imaging, SS-2014 Dr. Mohammad Dawood Frequency Depth Resolution Ultrasound

14. 14 Medical Imaging, SS-2014 Dr. Mohammad Dawood Ultrasound

15. 15 Medical Imaging, SS-2014 Dr. Mohammad Dawood Ultrasound

16. 16 Medical Imaging, SS-2014 Dr. Mohammad Dawood Medium Speed of sound  m/s  Air331 Water1483 Tissue1540-1595 Liver1549 Blood1570 Glycerin1923 Bones (Compact)3600

17. 17 Medical Imaging, SS-2014 Dr. Mohammad Dawood

18. 18 Medical Imaging, SS-2014 Dr. Mohammad Dawood Ultrasound - A mode (amplitude) - B mode (brightness) - M mode (moving)

19. 19 Medical Imaging, SS-2014 Dr. Mohammad Dawood Ultrasound - no functional information - fast - cheap - no radiation - portable - no injection -Bone / gas -Obesity -Operator dependence

20. 20 Medical Imaging, SS-2014 Dr. Mohammad Dawood Image Reconstruction

21. 21 Medical Imaging, SS-2014 Dr. Mohammad Dawood Reconstruction Tomography

22. 22 Medical Imaging, SS-2014 Dr. Mohammad Dawood Reconstruction Law of Attenuation

23. 23 Medical Imaging, SS-2014 Dr. Mohammad Dawood Reconstruction Parallel projections of a plane

24. 24 Medical Imaging, SS-2014 Dr. Mohammad Dawood x y r s θ n Reconstruction Radon Transformation f

25. 25 Medical Imaging, SS-2014 Dr. Mohammad Dawood Reconstruction Radon Transformation (Line Integrals at different angles)

26. 26 Medical Imaging, SS-2014 Dr. Mohammad Dawood Reconstruction Radon Transformations

27. 27 Medical Imaging, SS-2014 Dr. Mohammad Dawood Reconstruction Radon Transformation32 128 512

28. 28 Medical Imaging, SS-2014 Dr. Mohammad Dawood Reconstruction Inverse Radon Transformation H: Hilbert transform

29. 29 Medical Imaging, SS-2014 Dr. Mohammad Dawood Reconstruction Inverse Radon Transformation Problems with Missing data and Noise!

30. 30 Medical Imaging, SS-2014 Dr. Mohammad Dawood Reconstruction Filtered Back Projection

31. 31 Medical Imaging, SS-2014 Dr. Mohammad Dawood AB DC A+B C+D 1 A+D B+C 3 2 B A+C D Reconstruction Projections A B+D C 4

32. 32 Medical Imaging, SS-2014 Dr. Mohammad Dawood ?? ?? Reconstruction Back projections A+B C+D 1 A+B C+D 2 B A+C D 2A+B +C A+2B C+2D A+2C +D A+D B+C 3 3A+B +C+D A+3B +C A+C+ 3D A+B+ 3C+D A B+D C 4 4A+B +C+D A+4B +C+D A+B+ C+4D A+B+ 4C+D

33. 33 Medical Imaging, SS-2014 Dr. Mohammad Dawood 4A+B +C+D A+4B +C+D A+B+ C+4D A+B+ 4C+D Reconstruction Back projections 3A3B 3D3C - (A+B+C+D) =/ (n-1) = AB DC

34. 34 Medical Imaging, SS-2014 Dr. Mohammad Dawood Reconstruction Filtered Back Projection

35. 35 Medical Imaging, SS-2014 Dr. Mohammad Dawood 1=Ram-Lak (ramp), 2=Shepp-Logan, 3=Cosine, and 4=Hamming Reconstruction FBP: Commonly used filters

36. 36 Medical Imaging, SS-2014 Dr. Mohammad Dawood Projections Backproject Filter 1D Filter 2D Backproject Image Reconstruction Filtered Back Projection 2D/3D filtering is costly

37. 37 Medical Imaging, SS-2014 Dr. Mohammad Dawood Reconstruction Fourier slice theorem Take a two-dimensional function f(r), project it onto a line, and do a Fourier transform of that projection Take that same function, but do a two-dimensional Fourier transform first, and then slice it through its origin parallel to the projection line

38. 38 Medical Imaging, SS-2014 Dr. Mohammad Dawood

39. 39 Medical Imaging, SS-2014 Dr. Mohammad Dawood

40. 40 Medical Imaging, SS-2014 Dr. Mohammad Dawood Reconstruction Iterative Reconstruction Kaczmarz Method (=ART: Algebraic Reconstruction Technique) 1. Start by setting x(0) = 0 2. Compute the forward projection 3. Update the current estimate 4. Iterate steps 2,3 until the difference between new forward projection, computed in 2, and the old one is below tolerance

41. 41 Medical Imaging, SS-2014 Dr. Mohammad Dawood