Signal Analysis and Processing David Scraggs
Overview Introduction to Position Resolution Induced Charges Wavelet Transform Future Work Discussion
SmartPET is a Positron Emission Tomography system Lines Of Response defined through patient Position resolution is clearly important for image quality Scattered photons distort images and are rejected from image Position Resolution
If scattered path is well defined a LOR can also be defined Greatly increases the data within an image Gamma Ray Tracking makes use of Pulse Shape Analysis Detector geometry and electric field determine pulse shapes Raw granularity is not the limit for position resolution Position Resolution
SmartPET detectors in coincidence Single detector geometry, note electrode configuration Position Resolution 5mm 2 effective pixel area 144 effective pixels
Position Resolution Compton scattering is most probable interaction at 511keV Number of electrodes collecting charge on each face
Closest anode and cathode strips collect charge cloud Charge carriers do not have preferential electrodes All electrodes instantaneously see charge cloud upon liberation Results in induced charges on all strips Intuitively response is a function of translational distance Induced Charges
Induced Charges: Example
Super Traces: Across Strips
Magnitude is function of translational position
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Strip AC05 20mm Depth Super Traces: Depth Scan
Amplitude very sensitive to translational position Negative polarities No sensitivity in charge centre of detector Constant noise level Induced charges are at maximum 20% of real Event by Event: Cs-137 Collimator Position Induced Charge Magnitude
Wavelet Analysis
Induced charges hidden in time domain Induced charges are apparent 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; Transform coefficient is integral of the product of the signal and wavelet; Wavelet Analysis
A mother wavelet is chosen to serve as a for all windows in the process Mother wavelet is simply A number of functions can be used Second derivative of a Gaussian Compressed or dilated version Wavelet Analysis
Mother Wavelet: Mexican Hat Dilated version of mother
Wavelet Transformation
Thresholds Clearly possible to alter any wavelet coefficients Transform vector contains a range of values Removing the least significant components the least significant influences on the signal are removed Coherent structures within the signal are identified Known as magnitude thresholding; many types Also scale dependent thresholds; frequency
Reconstruction Universal Magnitude threshold Inverse Wavelet Transform
Induced Charge Co-57
Induced Charge Am-241
Wavelet Analysis of Noise
Future Work Investigate position resolution with induced charge magnitudes Investigate different wavelet techniques Investigate new threshold techniques in wavelet analysis Apply wavelet analysis online