Partial volume correction for positron emission images using the wavelet transform Antonello E Spinelli Carlo Bergamini Romano Zannoli Gianfranco Cicoria Mario Marengo Policlinico S. Orsola-Malpighi Department of Medical Physics Via Massarenti 9, 40138, Bologna, ITALY Luca Guerrieri Claudio Lamberti University of Bologna DEIS Viale Risorgimento 2, 40100, Bologna, ITALY Abstract: A method for partial volume correction of positron emission tomography (PET) images is proposed. The method is based on combining information from PET and high resolution anatomical images. Two different algorithms fast wavelet transform and ` a trous were implemented in order to decompose the PET and high resolution images. Results obtained using several simulated images show a significant partial volume reduction and image enhancement. The relative errors in the partial volume corrected image are always less than 3,6% with respect to 16% of the original image. Key–Words: Positron emission tomography, wavelet transform, partial volume correction 1 Introduction Positron emission tomography (PET) images provide important functional information however the poor spatial resolution with respect to other imaging tech- niques such as Computed Tomography (CT) and Mag- netic Resonance (MR) images lead to partial volume effect (PVE). The net results of PVE is an incorrect measurement of the true radiotracer concentration. As outlined by Aston et al. [1] PVE can be divided into two effects: tissue-fraction and point-spread effect. The tissue fraction effect arises from tissue hetero- geneity because the region of interest (ROI) used to determine radiotracer concentration contains signals from different tissues (for example gray and white matter). The point-spread effect arises from the fi- nite resolution of PET cameras. The spatial resolu- tion of a clinical PET tomograph is about 4-5 mm, while for example the resolution of CT, MR images is about 1-2 mm. Correction for PVE is of great importance for both semi-quantitative and quantita- tive measurements. Typically semi-quantitative mea- surements involve the estimation of the Standard Up- take Value (SUV) or the Tumor to background ratio (TBR). In both cases a ROI is drawn on the lesion and the mean value of the radiotracer concentration is measured. PVE typically reduces the value of the measured tracer concentration. Quantitative and more advanced approaches such as compartmental analysis are applied to measure the exchange of substances be- tween several compartments. PVE can lead to large errors in the estimated kinetic rate constants. In order to correct for PVE a wavelet-based approach was proposed in [2, 6]. It allows not only PVE cor- rection, but also images enhancement by adding high- resolution information obtained by a multi-resolution analysis of PET and high resolution (coregistered) im- ages. In the following a more general approach is proposed considering two types of wavelet decompo- sition algorithms such as the ` a trous [3] and the fast wavelet transform (FWT) introduced by Mallat [4]. The paper is organized as follow: in section 2 the nec- essary mathematical formalism is introduced, in sec- tion 3 the main results are presented, conclusions then follow. 2 Material and Methods 2.1 Image wavelet transform A wavelet base of L 2 (IR) can be constructed sim- ply by taking all the dilated and shifted versions of a mother wavelet: ψ j,n = 1 √ 2 j ψ  t - 2 j n 2 j  (1) Proceedings of the 6th WSEAS International Conference on Wavelet Analysis & Multirate Systems, Bucharest, Romania, October 16-18, 2006 45