1. Signal Processing of Germanium Detector Signals David Scraggs University of Liverpool UNTF 2006

2. Overview SmartPET Convolved Signals Wavelet Analysis Results Future Work Questions?

3. SmartPET PSA assumes one charge cloud is created Compton scattering is most probable interaction above 200keV Two charge clouds in single strip possible! PETSPECT

4. Convolved Signals + - Leading edge of real charge is dependent on position at which the charge carriers are Formed. PSA gives position of interaction and LOR or cone is well defined

5. Convolved Signals + - Leading edge is now convolution of two interactions, characterised by kink.

6. Discontinuity in leading edge is due to cessation of charge collection from one charge cloud Average interaction position Goal is to use PSA so convolved signals must be removed Signals currently analysed in time domain; not sensitive to discontinuities! Analyse signals in frequency domain Convolved Signals Convolved Signals

7. Discontinuities difficult to discriminate in time domain Slight frequency changes are evident in frequency domain Fourier Transform can be used to measure frequency components Frequency Analysis

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

9. Wavelet window function; Transform coefficient is integral of a convolution between the signal and wavelet; Wavelet Analysis

10. A mother wavelet is chosen to serve as a function for all windows in the process Mother wavelet is simply Functions must satisfy certain criteria Second derivative of a Gaussian Compressed or dilated version Wavelet Analysis

11. Mother Wavelet: Mexican Hat Dilated version of mother

12. Wavelet Transformation

13. Thresholding Clearly possible to alter any wavelet coefficients Transform vector contains a range of values Least significant components relate to the least significant influences in the signal Coherent structures and signal discontinuities within the signal are identified Can reconstruct original signal from transform Many types of threshold Can de-noise signals

14. Reconstruction Inverse Wavelet Transform

15. Convolution Identification Well distinguished convolved event

16. Convolution Identification Wavelet transform separates out frequencies with the signal scale Element No. Wavelet Coefficient

17. Convolution Identification Signal discontinuity seen clearly at scale 2 Two very good matches; noise also present but very small effect at this frequency, threshold out Element No. Wavelet Coefficient

18. Identification Result Cs-137 Data was filtered for convolved events 64496 Events were convolved Method identified 32% or 20419 events as convolved A random sample of identified and non identified signals shows promising results

19. Identification Result Identified ConvolvedNot identified Random sample of pulse train

20. Identification Result Identified: –Slight frequency discontinuity near top of signal Not identified: –Appears smooth; could result from two interactions close in depth

21. Future Work Coincidence data collection so that theory can be blind tested Remove identified convolved events from pre- reconstruction data and quantify image quality differential SmartPET Detector NaI