1. Signal Analysis and Processing David Scraggs

2. Overview Introduction to Position Resolution Induced Charges Wavelet Transform Future Work Discussion

3. SmartPET is a Positron Emission Tomography system Lines Of Response defined through patient Position resolution is clearly important for image quality Scattered photons distort images and are rejected from image Position Resolution

4. If scattered path is well defined a LOR can also be defined Greatly increases the data within an image Gamma Ray Tracking makes use of Pulse Shape Analysis Detector geometry and electric field determine pulse shapes Raw granularity is not the limit for position resolution Position Resolution

5. SmartPET detectors in coincidence Single detector geometry, note electrode configuration Position Resolution 5mm 2 effective pixel area 144 effective pixels

6. Position Resolution Compton scattering is most probable interaction at 511keV Number of electrodes collecting charge on each face

7. Closest anode and cathode strips collect charge cloud Charge carriers do not have preferential electrodes All electrodes instantaneously see charge cloud upon liberation Results in induced charges on all strips Intuitively response is a function of translational distance Induced Charges

8. Induced Charges: Example

9. Super Traces: Across Strips

13. Magnitude is function of translational position

14. Strip AC05 20mm Depth Super Traces: Depth Scan

15. Strip AC05 20mm Depth Super Traces: Depth Scan

16. Strip AC05 20mm Depth Super Traces: Depth Scan

17. Strip AC05 20mm Depth Super Traces: Depth Scan

18. Strip AC05 20mm Depth Super Traces: Depth Scan

19. Strip AC05 20mm Depth Super Traces: Depth Scan

20. Strip AC05 20mm Depth Super Traces: Depth Scan

21. Strip AC05 20mm Depth Super Traces: Depth Scan

22. Strip AC05 20mm Depth Super Traces: Depth Scan

23. Strip AC05 20mm Depth Super Traces: Depth Scan

24. Strip AC05 20mm Depth Super Traces: Depth Scan

25. Strip AC05 20mm Depth Super Traces: Depth Scan

26. Strip AC05 20mm Depth Super Traces: Depth Scan

27. Strip AC05 20mm Depth Super Traces: Depth Scan

28. Strip AC05 20mm Depth Super Traces: Depth Scan

29. Strip AC05 20mm Depth Super Traces: Depth Scan

30. Strip AC05 20mm Depth Super Traces: Depth Scan

31. Strip AC05 20mm Depth Super Traces: Depth Scan

32. Strip AC05 20mm Depth Super Traces: Depth Scan

33. Strip AC05 20mm Depth Super Traces: Depth Scan

35. Amplitude very sensitive to translational position Negative polarities No sensitivity in charge centre of detector Constant noise level Induced charges are at maximum 20% of real Event by Event: Cs-137 Collimator Position Induced Charge Magnitude

36. Wavelet Analysis

37. Induced charges hidden in time domain Induced charges are apparent in frequency domain Fourier Transform can be used to measure frequency components Frequency Analysis

38. Fourier assumes stationary signals Detector signals are non-stationary Frequency Analysis

39. Wavelet; Transform coefficient is integral of the product of the signal and wavelet; Wavelet Analysis

40. A mother wavelet is chosen to serve as a for all windows in the process Mother wavelet is simply A number of functions can be used Second derivative of a Gaussian Compressed or dilated version Wavelet Analysis

41. Mother Wavelet: Mexican Hat Dilated version of mother

42. Wavelet Transformation

43. Thresholds Clearly possible to alter any wavelet coefficients Transform vector contains a range of values Removing the least significant components the least significant influences on the signal are removed Coherent structures within the signal are identified Known as magnitude thresholding; many types Also scale dependent thresholds; frequency

44. Reconstruction Universal Magnitude threshold Inverse Wavelet Transform

45. Induced Charge Co-57

46. Induced Charge Am-241

47. Wavelet Analysis of Noise

48. Future Work Investigate position resolution with induced charge magnitudes Investigate different wavelet techniques Investigate new threshold techniques in wavelet analysis Apply wavelet analysis online