An analytic reconstruction method for PET based on cubic splines

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Kastis, George A.^1 ; Kyriakopoulou, Dimitra^1 ; Fokas, Athanasios S.^1,2

Research Center of Mathematics, Academy of Athens, Soranou Efessiou 4, Athens 11527, Greece^1

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB30WA, United Kingdom^2

关键词: Hilbert transform;    Mathematical formulation;    Numerical implementation;    Reconstructed image;    Reconstruction method;    Reconstruction techniques;    Software libraries;    Visual comparison;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012128/pdf
DOI  :  10.1088/1742-6596/490/1/012128

来源: IOP

【 摘 要 】

PET imaging is an important nuclear medicine modality that measures in vivo distribution of imaging agents labeled with positron-emitting radionuclides. Image reconstruction is an essential component in tomographic medical imaging. In this study, we present the mathematical formulation and an improved numerical implementation of an analytic, 2D, reconstruction method called SRT, Spline Reconstruction Technique. This technique is based on the numerical evaluation of the Hilbert transform of the sinogram via an approximation in terms of 'custom made' cubic splines. It also imposes sinogram thresholding which restricts reconstruction only within object pixels. Furthermore, by utilizing certain symmetries it achieves a reconstruction time similar to that of FBP. We have implemented SRT in the software library called STIR and have evaluated this method using simulated PET data. We present reconstructed images from several phantoms. Sinograms have been generated at various Poison noise levels and 20 realizations of noise have been created at each level. In addition to visual comparisons of the reconstructed images, the contrast has been determined as a function of noise level. Further analysis includes the creation of line profiles when necessary, to determine resolution. Numerical simulations suggest that the SRT algorithm produces fast and accurate reconstructions at realistic noise levels. The contrast is over 95% in all phantoms examined and is independent of noise level.