Transcript posterV1 - University of Liverpool

Signal Analysis and Processing for SmartPET
D. Scraggs, A. Boston, H Boston, R Cooper, A Mather, G Turk
C. Hall, I. Lazarus
T. Beveridge, J Gilliam, R. Lewis
University of Liverpool
Daresbury Laboratory
University of Monash
Introduction
Detector
Scintillation detector arrays are currently used in nuclear medicine.
However, given the superior radiometric properties of germanium a
natural progression is to assess the suitability of its use with the core
objective of improving spatial resolution and image quality.
SmartPET will utilise double sided germanium orthogonal strip planar
detectors with a 5mm pitch. Thus forming a chequered arrangement in
a single plane with a granularity of 5mm. The shape of the charge
pulses formed at the collecting electrodes allows the use of pulse
shape analysis [1]. By utilising digital electronics [2] the position
resolution of the detector can be significantly improved.
Simulation of
detector
showing
segmented
electrode
configuration.
Two detectors in coincidence. The
actual crystal size is 60x60x20mm.
Induced charge [ref detector section] on neighbouring electrodes will
inevitably be only a small fraction of real charge magnitudes, requiring
the analysis of small amplitude pulses. In response, image charge
magnitudes have been investigated as has the suitability of wavelet
analysis applied to de-noising signals.
Scan of detector
showing counts
in relation to
lateral position.
The granularity of
the detector is
clear.
Real charge accompanied by
image charge on adjacent strips,
the magnitudes of which are
related to interaction position
Image Charge
Radiation interaction results in a charge cloud
which is collected on the nearest electrode,
the movement of this cloud results in an
electromagnetic field [3] that is felt by all
electrodes resulting in image charges. Image
charge magnitude is a function of incident
energy and interaction position. Therefore, the
comparison of image charge magnitudes from
electrodes adjacent to the collecting electrode
has the potential to give a very accurate
position of interaction.
A plot of image charge magnitudes against
real
charge
magnitudes
shows
the
dependence of image magnitude on incident
energy and interaction position.
The mean maximum image charge for the DC
electrode face is 0.20 of the real charge and
0.17 for the AC side. This is the maximum
value and lower magnitudes are more
probable, whereas the noise in the system is
constant and has a maximum value of
approximately 10keV.
The graph shows a maximum gradient which is
indicative of surface interactions of low incident
energy close to the electrodes. Higher energy
interactions occurring deeper within the detector
and thus further from electrodes show small
image charge magnitudes. The maximum
gradients for each electrode have been
determined and mean maximum image charge
magnitudes have been calculated for each
detector face.
In past experiments it has proved to be
very difficult to identify small amplitude
image charges due to the presence of
noise. In consideration of the expected
magnitudes for SmartPET a new technique
for de-noising should be investigated.
Wavelet Analysis
Wavelet analysis is similar to Fourier analysis,
the signal is multiplied by a function of a
certain frequency, and the integral taken. A
large coefficient relates to a good match
between the signal and the frequency of the
multiplying function.
 t 
*
 xt  
 s
s
1

 ( , s) 
x

dt

A mother wavelet is chosen and the signal is
multiplied by dilated and shifted versions of
the mother. The selection of scale and
translation is discrete, usually on a dyadic grid.
Thus a 3-D map of the signal is formed which
shows the wavelet coefficients of the signal at
a particular scale and location.
The multiplying function by which the signal (x)
is multiplied by is called the wavelet, which is
a small oscillatory wave. The equation shows
that the transform is a function of two
variables; tau and s, translation and scale
respectively, which are controlled throughout
the transformation. The inverse outside the
integral is for energy normalisation.
After transformation the signal is represented
in the frequency domain. Reconstruction of the
transform is possible If a set of orthonormal
wavelet vectors have been used for the
transform. For example, take a signal composed of
typical SmartPET pulse ‘instantaneous frequencies’.
60keV Results
122keV Results
The transform clearly shows the two
frequencies of the original signal, the 10MHz
is closely packed, whilst the 1MHz is well
resolved in frequency but not in time.
Thresholding can now be used to removed
frequency
characteristics
and
the
reconstruction can be performed. Therefore, it
is possible to remove high frequency
components related to noise and perform a
noise free reconstruction.
662keV Results
The results for a range of energies are shown.
References
[1] K. Vetter et al, NIM A452 (2000) 223, [2] I Lazarus, private communication, [3] I. Y. Lee NIM
A463 (2001) 250