Iterative reconstruction of Fourier‐rebinned PET data using sinogram blurring function estimated from point source scans

Abstract

The accuracy of the system model that governs the transformation from the image space to the projection space in positron emission tomography (PET) greatly affects the quality of reconstructed images. For efficient computation in iterative reconstructions, the system model in PET can be factored into a product of geometric projection and sinogram blurring function. To further speed up reconstruction, fully 3D PET data can be rebinned into a stack of 2D sinograms and then be reconstructed using 2D iterative algorithms. The purpose of this work is to develop a method to estimate the sinogram blurring function to be used in reconstruction of Fourier-rebinned data. In a previous work, the authors developed an approach to estimating the sinogram blurring function of nonrebinned PET data from experimental scans of point sources. In this study, the authors extend this method to the estimation of sinogram blurring function for Fourier-rebinned PET data. A point source was scanned at a set of sampled positions in the microPET II scanner. The sinogram blurring function is considered to be separable between the transaxial and axial directions. A radially and angularly variant 2D blurring function is estimated from Fourier-rebinned point source scans to model the transaxial blurring with consideration of the detector block structure of the scanner; a space-variant 1D blurring kernel along the axial direction is estimated separately to model the correlation between neighboring planes due to detector intrinsic blurring and Fourier rebinning. The estimated sinogram blurring function is incorporated in a 2D maximum a posteriori (MAP) reconstruction algorithm for image reconstruction. Physical phantom experiments were performed on the microPET II scanner to validate the proposed method. The authors compared the proposed method to 2D MAP reconstruction without sinogram blurring model and 2D MAP reconstruction with a Monte Carlo based blurring model. The results show that the proposed method produces images with improved contrast and spatial resolution. The reconstruction time is unaffected by the new method since the blurring component takes a relatively negligible part of the overall reconstruction time. The proposed method can estimate sinogram blurring matrix for Fourier-rebinned PET data and can be used to improve contrast and spatial resolution of reconstructed images. The method can be applied to other human and animal scanners.