###### Abstract  
Quantitative analyses in nuclear medicine are increasingly used, both for diagnostic and therapeutic purposes. The Partial Volume Effect (PVE) is the most important factor of loss of quantification in Nuclear Medicine, especially for evaluation in Region of Interest (ROI) smaller than the Full Width at Half Maximum (FWHM) of the PSF. The aim of this work is to present a new approach for the correction of PVE, using a post-reconstruction process starting from a mathematical expression, which only requires the knowledge of the FWHM of the final PSF of the imaging system used. After the presentation of the theoretical derivation, the experimental evaluation of this method is performed using a PET/CT hybrid system and acquiring the IEC NEMA phantom with six spherical \"hot\" ROIs (with diameters of 10, 13, 17, 22, 28, and 37 mm) and a homogeneous \"colder\" background. In order to evaluate the recovery of quantitative data, the effect of statistical noise (different acquisition times), tomographic reconstruction algorithm with and without time-of-flight (TOF) and different signal-to-background activity concentration ratio (3:1 and 10:1) was studied. The application of the corrective method allows recovering the loss of quantification due to PVE for all sizes of spheres acquired, with a final accuracy less than 17%, for lesion dimensions larger than two FWHM and for acquisition times equal to or greater than two minutes. partial volume effect; quantitative analysis; point spread function; post-reconstruction-method +
Footnote †: journal: Medical Physics Unit, University Hospital of Santa Chiara, 56126 Pisa, Italy; [EMAIL_ADDRESS]  
Footnote †: journal: Medical Physics Unit, University Hospital of Santa Chiara, 56126 Pisa, Italy; [EMAIL_ADDRESS]  
Footnote †: journal: Medical Physics Unit, University Hospital of Santa Chiara, 56126 Pisa, Italy; [EMAIL_ADDRESS]  
Footnote †: journal: Medical Physics Unit, University Hospital of Santa Chiara, 56126 Pisa, Italy; d.  
structions including PSF compensation can increase SUV\({}_{\text{max}}\) more than 66% in small nodal metastases in breast cancer or for NSCLC [3; 4]. Moreover, an international survey reported that 52% of PET centers use alternative protocols with adapted reconstruction parameters. Additional complications arise considering the reconstruction variability between centers running similar systems. In fact, it has been reported that site-specific reconstruction parameters increased the quantitative variability among similar scanners [5; 6]. The use of post-processing corrective methods could be a way to reduce this variability in order to achieve a better harmonization of SUV measurements between different PET centers. In this context, quantitative parameters such as the SUV are strictly related to the system spatial resolution performances. Spatial resolution depends on the physics of PET imaging (positron range, collinearity, scatter), on the detector design, and on the reconstruction method. All these factors lead to some amount of blurring on the images, limiting the final spatial resolution of the system. The finite spatial resolution affects the quality of the image and the correct estimation of radioactivity concentration, which consequently causes difficulties in the application of a quantitative approach in the evaluation of PET studies [7]. From a theoretical point of view, spatial resolution is defined as the Full Width Half Maximum (FWHM) of the Point Spread Function (PSF) of the imaging system, which is the description of the image response to a point source [8]. Once the PSF is defined for the imaging system, the final image can be modelled as the real radioactivity distribution convolved by the PSF of the imaging system. The PSF of the PET system is responsible for the so-called partial volume effect (PVE), which affects images both qualitatively and quantitatively [9].