PET Image Reconstruction Based on a Constrained Filter

Abstract The paper aims to propose an algorithm for PET(positron emission tomography) image reconstruction. Different from the algorithms designed to satisfy a single performance index in most cases, our algorithm inherently involves for two objects. Due to that the information upon noises is utilized fully, our algorithm provides a better reconstructed results than the one for the a single index when one obtains only some information on noises but does not know whether the statistics matches the noise level well in advance. The conclusion is also supported by the numerical experiments.

[1]  J. Mazziotta,et al.  Brain Mapping: The Methods , 2002 .

[2]  Richard M. Leahy,et al.  Statistical approaches in quantitative positron emission tomography , 2000, Stat. Comput..

[3]  T. Kailath,et al.  Indefinite-quadratic estimation and control: a unified approach to H 2 and H ∞ theories , 1999 .

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

[5]  Huafeng Liu,et al.  PET Image Reconstruction: A Robust State Space Approach , 2005, IPMI.

[6]  F. J. Anscombe,et al.  THE TRANSFORMATION OF POISSON, BINOMIAL AND NEGATIVE-BINOMIAL DATA , 1948 .

[7]  Huafeng Liu,et al.  State Space Strategies for Estimation of Activity Map in PET Imaging , 2004, MIAR.

[8]  Song Wang,et al.  Robust Framework for PET Image Reconstruction Incorporating System and Measurement Uncertainties , 2012, PloS one.

[9]  Huafeng Liu,et al.  PET image reconstruction based on particle filter framework , 2012, Proceedings of 2012 IEEE-EMBS International Conference on Biomedical and Health Informatics.

[10]  Steve R. Gunn,et al.  Tracer kinetic modeling via basis pursuit , 2002 .

[11]  M. Casey,et al.  PET reconstruction with system matrix derived from point source measurements , 2004, IEEE Transactions on Nuclear Science.

[12]  J. M. Ollinger,et al.  Positron Emission Tomography , 2018, Handbook of Small Animal Imaging.

[13]  J. Fessler.  Statistical Image Reconstruction Methods for Transmission Tomography , 2000 .

[14]  Bernd Weissmuller,et al.  Radiological Imaging The Theory Of Image Formation Detection And Processing , 2016 .

[15]  Jeffrey A. Fessler.  Penalized weighted least-squares image reconstruction for positron emission tomography , 1994, IEEE Trans. Medical Imaging.