1. Signal Processing of Germanium Detector Signals
Good afternoon, I’m David Scraggs from the University of Liverpool and I’m going to give a short presentation on a possible signal processing technique that can be used prior to any signal analysis of SmartPET detector signals.
David Scraggs
University of Liverpool

2. Overview SmartPET Convolved Signals Wavelet Analysis Results
Future Work
Discussion
So just to give an overview, my talk today will focus very briefly on SmartPET signal generation which has already been covered, I’ll then emphasise a very real limitation in the form of convolved signals resulting from multiple interactions and wavelet analysis and its advantages will then be introduced as a possible technique to deal with convolved signals. Early results from wavelet analysis will then be presented along with future work and any suggestions will be welcomed.

3. SmartPET
Two orthogonal strip planar germanium detectors with a 5mm pitch
1mm position resolution with PSA
LORs’ and cone beams well defined
Compton scattering is most probable interaction above 300keV
Two charge clouds created;
Segregated strips allow PSA
Single strips do not allow PSA

4. Convolved Signals - Leading edge of real charge is dependent+ -
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+ -
Leading edge is now convolution of two
interactions, characterised by kink.

6. Convolved Signals
Discontinuity in leading edge is due to cessation of charge collection from one charge cloud
Wrong interaction position, thus, LOR or cone is false
Effect on final image is as yet unknown
If both interactions are close then event may be acceptable
Goal is to use PSA so convolved signals must be removed

7. Convolved Signals Signals are currently analysed in time domain
Discontinuity appears in time domain but analysis would be difficult due to noise
Possible approach is to analyse signals in frequency domain first
Wavelet analysis can be used to de-noise signals through frequency analysis and discrimination

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

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

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

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

12. Wavelet Analysis
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

13. Wavelet Analysis
Dilated version
of mother
Mother Wavelet:
Mexican Hat

14. Wavelet Transformation

15. Thresholding Clearly possible to alter any wavelet coefficients
Transform vector contains a range of values
Removing the least significant components removes the least significant influences on the signal
Coherent structures and signal discontinuities within the signal are identified
Magnitude thresholding; many types
Also frequency dependent thresholds

16. Reconstruction
Universal Magnitude threshold
Inverse Wavelet Transform

17. Induced Charge Am-241

18. Convolution Identification
Well distinguished convolved event

19. Convolution Identification
Wavelet transform separates out frequencies with the signal

20. 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

21. Identification Result
Cs-137 Data was sorted for convolved events (one strip firing on DC side two on AC side)
64496 Events were convolved
Method identified 32% or events as convolved
Random sample of identified and rejected pulses appear promising
Scanning table available in June for coincidence data, allowing a blind test

22. Identification Result

23. Identification Result
Identified:
Slight uniform frequency discontinuity
Not identified:
Appears smooth

24. Future Work
Coincidence data collection so that theory can be blind tested on convolved and full energy absorption signals
Remove alleged convolved events from pre-reconstruction data and quantify image quality differential