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PET Image Reconstruction: A Robust State Space Approach

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Part of the book series:Lecture Notes in Computer Science ((LNIP,volume 3565))

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Abstract

Statistical iterative reconstruction algorithms have shown improved image quality over conventional nonstatistical methods in PET by using accurate system response models and measurement noise models. Strictly speaking, however, PET measurements, pre-corrected for accidental coincidences, are neither Poisson nor Gaussian distributed and thus do not meet basic assumptions of these algorithms. In addition, the difficulty in determining the proper system response model also greatly affects the quality of the reconstructed images. In this paper, we explore the usage of state space principles for the estimation of activity map in tomographic PET imaging. The proposed strategy formulates the organ activity distribution through tracer kinetics models, and the photon-counting measurements through observation equations, thus makes it possible to unify the dynamic reconstruction problem and static reconstruction problem into a general framework. Further, it coherently treats the uncertainties of the statistical model of the imaging system and the noisy nature of measurement data. SinceH ∞  filter seeks minimum-maximum-error estimates without any assumptions on the system and data noise statistics, it is particular suited for PET image reconstruction where the statistical properties of measurement data and the system model are very complicated. The performance of the proposed framework is evaluated using Shepp-Logan simulated phantom data and real phantom data with favorable results.

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Author information

Authors and Affiliations

  1. State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, China

    Huafeng Liu & Yi Tian

  2. Medical Image Computing Group, Department of Electrical and Electronic Engineering, Hong Kong University of Science and Technology, Hong Kong

    Pengcheng Shi

Authors
  1. Huafeng Liu

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  2. Yi Tian

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  3. Pengcheng Shi

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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, The University of Iowa, IA 52242, Iowa City

    Gary E. Christensen

  2. Department of Electrical and Computer Engineering, University of Iowa, IA 52242, Iowa City, USA

    Milan Sonka

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© 2005 Springer-Verlag Berlin Heidelberg

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Liu, H., Tian, Y., Shi, P. (2005). PET Image Reconstruction: A Robust State Space Approach. In: Christensen, G.E., Sonka, M. (eds) Information Processing in Medical Imaging. IPMI 2005. Lecture Notes in Computer Science, vol 3565. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11505730_17

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