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

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.

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

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

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

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

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

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

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

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

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

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

Wavelet Analysis Dilated version of mother Mother Wavelet: Mexican Hat

Wavelet Transformation

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

Reconstruction Universal Magnitude threshold Inverse Wavelet Transform

Induced Charge Am-241

Convolution Identification Well distinguished convolved event

Convolution Identification Wavelet transform separates out frequencies with the signal

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

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 20419 events as convolved Random sample of identified and rejected pulses appear promising Scanning table available in June for coincidence data, allowing a blind test

Identification Result

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

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