PCA-based approach for inhomogeneous PSF estimation and partial volume correction in PET

The quality of the measurements obtained in Positron Emission Tomography (PET) is severely limited by partial volume effects (PVE). This study proposes a Partial Volume Correction (PVC) technique that considers the spatial variability of the system's Point Spread Function (PSF) across the Field Of View (FOV). The proposed PSF model uses Principal Component Analysis to express their variability according to a small number of components called eigen-PSF, forming an orthonormal basis. The interpolation of the coordinates of these PSFs in this created basis allows their precise estimation across the FOV of the system. The resulting image degradation model can be expressed as a weighted sum of convolutions that can be integrated efficiently into classical PVC algorithms. Initial results shows accurate PSF estimation as well as significant image restoration.