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

Overview SmartPET Convolved Signals Wavelet Analysis Results Future Work Questions?

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

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

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

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

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

Wavelet window 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

Mother Wavelet: Mexican Hat Dilated version of mother

Wavelet Transformation

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

Reconstruction Inverse Wavelet Transform

Convolution Identification Well distinguished convolved event

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

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

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

Identification Result Identified ConvolvedNot identified Random sample of pulse train

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

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