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

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

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

‘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

Results µPET/CT 124I-NM404 Removed Noise

Results Ramp Hamm Shepp Denoised Image Original Removed Noise

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 3.581792 2.671076 -25 Hamm 3.08 3.290405 +6.68 Shepp 3.016362 2.719702 -9.8

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

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