1. The Use of Wavelet Filters to De-noise µPET Data
Joe Grudzinski

2. Motivation
Theoretically, FBP is best algorithm for determining distribution of radioactivity
Ramp filter amplify high frequency noise

3. Possible Solutions Fourier filters Wavelet filters
Only perfectly localized in frequency domain and not spatial domain
PET signals are non-stationary and do not exhibit global, periodic behavior
Wavelet filters
Perfectly localized in frequency and spatial domain
Possible to examine signals at differing resolutions

4. ‘A Trous’ Filter ‘With holes’ – add zeroes during up sample
Noise is distributed through all coefficients
Signal is concentrated in a few coefficients
With proper threshold, possible to remove noise
Noise is only in first 3 scales

5. Results
µPET/CT
124I-NM404
Removed Noise

6. Results
Ramp
Hamm
Shepp
Denoised Image
Original
Removed Noise

7. SNR Before Post Filtering
Results
SNR of The Mouse Tumor
SNR Before Filtering
2.89
SNR After Filtering
3.96
Percent Increase
37%
SNR Before Post Filtering
SNR After Filtering
Percent Change
Ramp
-25
Hamm
3.08
+6.68
Shepp
-9.8

8. Results Line Pairs/mm Before Wavelet Percent Change in Resolution Ramp
0.64
0.66 3
Shepp
0.465
0.62 25
Hamm
0.446
0.478
7.17

9. Conclusion Wavelets have provided benefits in post-processing
Higher resolution images provide better detectability of lesions in clinical applications when contrast is conserved