1. Applications of wavelets in PET modelling - a literature survey

2. Hammersmith, London Turkheimer et al. 1999-2000 3 articles of the subject theoretical framework of wavelets image reconstruction and image processing Dyadic wavelet transform (DWT) and translation invariant DWT (DWT-TI) techniques applications to dynamic PET-SPECT studies Parametric images: kinetic and statistical modelling in wavelet space

3. Denoising images with wavelets Wavelet transform of dynamic image Thresholding (e.g. SURE, universal, Bonferroni) Inverse transform

4. Studies Low-resolution SPECT study Hoffman brain phantom DWT vs. DWT-TI in 2D High-resolution PET images FDG brain study universal thresholding vs. SURE thresholding Very high-resolution PET images [ 11 C]PK11195 study of peripheral benzodiazepine receptors in the brain high signal-to-noise ratio

5. Image domain Wavelet domain Wavelet transform Inverse wavelet transform t Dynamic image WT(Dynamic image) Kinetic modelling Statistical thresholding Parametric WT thresholded Parametric image

6. Studies Synthetic dynamic study artificial data set with nonstationary noise field FDG dynamic PET study Patlak plot [ 11 C]raclopride PET dynamic study D2-receptor distribution in normal brain Logan plot vs. WT

7. Image domain Wavelet domain Wavelet transform Inverse wavelet transform i Multiple images WT multiple images Statistical modelling Wavelet filter Parametric WT Filtered Parametric WT Filtered parametric map

8. Studies Randomization study null dataset with PET H 2 15 O activation/rest -> two groups of simulated datasets Parametric study of cerebral blood flow response to word recognition 5 right-handed normal subjects Measuring the effect of depression on brain serotonin receptors with [ 11 C]WAY-100635 WT vs. statistical parametric mapping

9. Karolinska hospital, Stockholm Cselenyi et al. 2002 Binding potential (BP) study with [ 11 C]FLB 457 4 methods traditional ROI analysis (reference data) pixel-based analysis 2 variants of wavelet-aided analyses Aim is to decrease the noise-sensitivity of a parameter estimation procedure with wavelet approach 10 healthy male subjects

10. ROI analysis BP was estimated using the reference region version of Logan’s graphical analysis (reference region=cerebellar cortex)

11. Pixel-by-Pixel analysis radioactivity of a pixel= area under the curve (AUC) of the corresponding TAC Fitting is done with the same Logan analysis as in ROI-based version Final product: parametric image of the density of dopamine D 2 receptors in brain Anatomical standardisation Average BPs were determined in the same ROIs used with ROI-based analysis

12. Wavelet-based estimation two-dimensional translation-invariant (2DTI) and three-dimensional (3-DWT) wavelet transform coefficients of the dynamic WT analysed in the same manner as in pixel-based approach except for the thresholding Final product: parametric map of BP values Anatomical standardisation and averaging within ROIs done as in pixel-based analysis

13. Results Compared to the ROI-based analyses, the BP values were ~50% with pixel-based analysis (heterogeneous image) ~78% with 2DTI ~100% with 3-DWT

14. References F. Turkheimer et al.:Multiresolution Analysis of Emission Tomography Images in the Wavelet Domain, J Cereb. Blood Flow Metab. 19:1189-1208 (1999) F. Turkheimer et al.:Modeling Dynamic PET-SPECT Studies in the Wavelet Domain, J Cereb. Blood Flow Metab. 20:879-893 (2000) F. Turkheimer et al.:Statistical Modeling of Positron Emission Tomography Images in Wavelet Space, J Cereb. Blood Flow Metab. 20:1610-1618 (2000) Z. Cselenyi et al.:Wavelet-Aided Parametric Mapping of Cerebral Dopamine D 2 Receptors Using the High Affinity PET Radioligand [ 11 C]FLB 457, NeuroImage 17:47-60 (2002)

15. Other articles J.-W. Lin et al.:Improving PET-Based Physiological Quantification Through Methods of Wavelet Denoising, IEEE trans. bio. eng. Vol48, No.2 (2001) P. Millet et al.: Wavelet Analysis of Dynamic PET Data: Applications to the Parametric Imaging of Benzodiazepine Receptor Concentration, NeuroImage 11:458-472 (2000)