1. Signal Analysis and Processing for SmartPET D. Scraggs, A. Boston, H Boston, R Cooper, A Mather, G Turk University of Liverpool C. Hall, I. Lazarus Daresbury Laboratory T. Beveridge, J Gilliam, R. Lewis University of Monash Introduction References Wavelet Analysis Image Charge Detector 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 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. 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. 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. 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. 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. Two detectors in coincidence. The actual crystal size is 60x60x20mm. Simulation of detector showing segmented electrode configuration. Scan of detector showing counts in relation to lateral position. The granularity of the detector is clear. 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. 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’. 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 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. The results for a range of energies are shown. Real charge accompanied by image charge on adjacent strips, the magnitudes of which are related to interaction position 60keV Results 122keV Results 662keV Results [1] K. Vetter et al, NIM A452 (2000) 223, [2] I Lazarus, private communication, [3] I. Y. Lee NIM A463 (2001) 250