Applications of wavelets in PET modelling - a literature survey

Hammersmith, London Turkheimer et al 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

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

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

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

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

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

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 WT vs. statistical parametric mapping

Karolinska hospital, Stockholm Cselenyi et al Binding potential (BP) study with [ 11 C]FLB 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

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

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

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

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

References F. Turkheimer et al.:Multiresolution Analysis of Emission Tomography Images in the Wavelet Domain, J Cereb. Blood Flow Metab. 19: (1999) F. Turkheimer et al.:Modeling Dynamic PET-SPECT Studies in the Wavelet Domain, J Cereb. Blood Flow Metab. 20: (2000) F. Turkheimer et al.:Statistical Modeling of Positron Emission Tomography Images in Wavelet Space, J Cereb. Blood Flow Metab. 20: (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)

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: (2000)