A volume of intersection approach for on-the-fly system matrix calculation in 3D PET image reconstruction.

The aim of this study is the evaluation of on-the-fly volume of intersection computation for system's geometry modelling in 3D PET image reconstruction. For this purpose we propose a simple geometrical model in which the cubic image voxels on the given Cartesian grid are approximated with spheres and the rectangular tubes of response (ToRs) are approximated with cylinders. The model was integrated into a fully 3D list-mode PET reconstruction for performance evaluation. In our model the volume of intersection between a voxel and the ToR is only a function of the impact parameter (the distance between voxel centre to ToR axis) but is independent of the relative orientation of voxel and ToR. This substantially reduces the computational complexity of the system matrix calculation. Based on phantom measurements it was determined that adjusting the diameters of the spherical voxel size and the ToR in such a way that the actual voxel and ToR volumes are conserved leads to the best compromise between high spatial resolution, low noise, and suppression of Gibbs artefacts in the reconstructed images. Phantom as well as clinical datasets from two different PET systems (Siemens ECAT HR(+) and Philips Ingenuity-TF PET/MR) were processed using the developed and the respective vendor-provided (line of intersection related) reconstruction algorithms. A comparison of the reconstructed images demonstrated very good performance of the new approach. The evaluation showed the respective vendor-provided reconstruction algorithms to possess 34-41% lower resolution compared to the developed one while exhibiting comparable noise levels. Contrary to explicit point spread function modelling our model has a simple straight-forward implementation and it should be easy to integrate into existing reconstruction software, making it competitive to other existing resolution recovery techniques.

[1]  C. Watson,et al.  Extension of Single Scatter Simulation to Scatter Correction of Time-of-Flight PET , 2007, IEEE Transactions on Nuclear Science.

[2]  M Defrise,et al.  Non-Gaussian space-variant resolution modelling for list-mode reconstruction , 2010, Physics in medicine and biology.

[3]  Arman Rahmim,et al.  Resolution modeling in PET imaging: Theory, practice, benefits, and pitfalls. , 2013, Medical physics.

[4]  Vladimir Y. Panin,et al.  Fully 3-D PET reconstruction with system matrix derived from point source measurements , 2006, IEEE Transactions on Medical Imaging.

[5]  C. C. Watson.  New, faster, image-based scatter correction for 3D PET , 1999 .

[6]  H. Malcolm Hudson,et al.  Accelerated image reconstruction using ordered subsets of projection data , 1994, IEEE Trans. Medical Imaging.

[7]  L. Shepp,et al.  A Statistical Model for Positron Emission Tomography , 1985 .

[8]  Joel S Karp,et al.  Optimization of a fully 3D single scatter simulation algorithm for 3D PET. , 2004, Physics in medicine and biology.

[9]  Roger Lecomte,et al.  Detector response models for statistical iterative image reconstruction in high resolution PET , 1998 .

[10]  Andrew J. Reader,et al.  EM algorithm system modeling by image-space techniques for PET reconstruction , 2003 .

[11]  Keishi Kitamura,et al.  Transaxial system models for jPET-D4 image reconstruction , 2005, Physics in medicine and biology.

[12]  Performance analysis of different PSF shapes for the quad-HIDAC PET submillimetre resolution recovery☆ , 2011 .

[13]  Arman Rahmim,et al.  A scatter-corrected list-mode reconstruction and a practical scatter/random approximation technique for dynamic PET imaging. , 2007, Physics in medicine and biology.

[14]  R. Tibshirani,et al.  Generalized Additive Models , 1986 .

[15]  H. Zaidi,et al.  Design and performance evaluation of a whole-body Ingenuity TF PET–MRI system , 2011, Physics in medicine and biology.

[16]  I. Buvat,et al.  A review of partial volume correction techniques for emission tomography and their applications in neurology, cardiology and oncology , 2012, Physics in medicine and biology.

[17]  J. Ollinger,et al.  Maximum likelihood reconstruction in fully 3D PET via the SAGE algorithm , 1996, 1996 IEEE Nuclear Science Symposium. Conference Record.

[18]  S. Ross,et al.  Properties and Mitigation of Edge Artifacts in PSF-Based PET Reconstruction , 2011, IEEE Transactions on Nuclear Science.

[19]  K Thielemans,et al.  Image-based point spread function implementation in a fully 3D OSEM reconstruction algorithm for PET , 2010, Physics in medicine and biology.

[20]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.

[21]  Nadim Joni Shah,et al.  Fully-3D PET Image Reconstruction Using Scanner-Independent, Adaptive Projection Data and Highly Rotation-Symmetric Voxel Assemblies , 2011, IEEE Transactions on Medical Imaging.

[22]  Ragni Piene,et al.  The Legacy of Niels Henrik Abel , 2004 .

[23]  C. Leroy,et al.  Evaluation of the volume of intersection of a sphere with a cylinder by elliptic integrals , 1990 .

[24]  Robert M. Lewitt,et al.  Practical considerations for 3-D image reconstruction using spherically symmetric volume elements , 1996, IEEE Trans. Medical Imaging.

[25]  D. Townsend,et al.  Physical and clinical performance of the mCT time-of-flight PET/CT scanner , 2011, Physics in medicine and biology.

[26]  Uwe Just,et al.  Optimized list-mode acquisition and data processing procedures for ACS2 based PET systems. , 2006, Zeitschrift fur medizinische Physik.

[27]  R M Lewitt,et al.  Multidimensional digital image representations using generalized Kaiser-Bessel window functions. , 1990, Journal of the Optical Society of America. A, Optics and image science.

[28]  Michael Zibulevsky,et al.  The Design and Implementation of COSEM, an Iterative Algorithm for Fully 3D Listmode Data , 2001, IEEE Trans. Medical Imaging.

[29]  Jürgen Scheins,et al.  Analytical calculation of volumes-of-intersection for iterative, fully 3-D PET reconstruction , 2006, IEEE Transactions on Medical Imaging.

[30]  Steven G. Ross,et al.  Application and Evaluation of a Measured Spatially Variant System Model for PET Image Reconstruction , 2010, IEEE Transactions on Medical Imaging.

[31]  Pablo Aguiar,et al.  Geometrical and Monte Carlo projectors in 3D PET reconstruction. , 2010, Medical physics.

[32]  H Bergmann,et al.  Influence of PET reconstruction parameters on the TrueX algorithm. A combined phantom and patient study. , 2013, Nuklearmedizin. Nuclear medicine.

[33]  K Thielemans,et al.  Impact of PSF modelling on the convergence rate and edge behaviour of EM images in PET , 2010, IEEE Nuclear Science Symposuim & Medical Imaging Conference.

[34]  Gunnar Brix,et al.  Fast implementation of the single scatter simulation algorithm and its use in iterative image reconstruction of PET data , 1999, 1999 IEEE Nuclear Science Symposium. Conference Record. 1999 Nuclear Science Symposium and Medical Imaging Conference (Cat. No.99CH37019).

[35]  V. Bettinardi,et al.  Physical performance of the new hybrid PET∕CT Discovery-690. , 2011, Medical physics.

[36]  Paul E. Kinahan,et al.  Application of a spatially variant system model for 3-D whole-body pet image reconstruction , 2008, 2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[37]  F Hofheinz,et al.  Effects of cold sphere walls in PET phantom measurements on the volume reproducing threshold , 2010, Physics in medicine and biology.