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Medical Physics / Volume 39 / Issue 2 / NUCLEAR MEDICINE PHYSICS

Med. Phys. 39, 589 (2012); http://dx.doi.org/10.1118/1.3673775 (14 pages)

Gap compensation during PET image reconstruction by constrained, total variation minimization

Seonmin Ahn

Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912

Soo Mee Kim and Jungah Son

Department of Nuclear Medicine, Seoul National University, Seoul 151-742, Korea and Institute of Radiation Medicine, Medical Research Center, and Interdisciplinary Programs in Radiation Applied Life Science Major, Seoul National University, Seoul 151-742, Korea

Dong Soo Lee

Department of Nuclear Medicine, Seoul National University, Seoul 151-742, Korea; Institute of Radiation Medicine, Medical Research Center, and Interdisciplinary Programs in Radiation Applied Life Science Major, Seoul National University, Seoul 151-742, Korea; and Department of WCU Molecular Medicine and Biopharmaceutical Sciences, Seoul National University, Seoul 151-742, Korea

Jae Sung Lee

Department of Nuclear Medicine, Seoul National University, Seoul 151-742, Korea; Institute of Radiation Medicine, Medical Research Center, and Interdisciplinary Programs in Radiation Applied Life Science Major, Seoul National University, Seoul 151-742, Korea; and Departments of Biomedical Sciences and WCU Brain and Cognitive Sciences, Seoul National University, Seoul 151-742, Korea

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(Received 25 August 2011; accepted 9 December 2011; revised 8 December 2011; published online 11 January 2012)

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Purpose: Positron emission tomography (PET) is a noninvasive molecular imaging tool with various clinical and preclinical applications. The polygonal structure of small-diameter PET scanners that are designed for specific purposes can lead to gaps between the detector modules and result in loss of PET data during measurement. In the current study, the authors applied the compressed sensing (CS)-based total variation (TV) minimization method to PET image reconstructions to reduce the artifacts caused by gaps in small-diameter PET systems.
Methods: The first step in each iteration estimates whether an image is consistent with the measured PET data using the existing common reconstruction algorithms (ART, OSEM, and RAMLA). The second step recovers sparsity in the gradient domain of the image by minimizing the TV of an estimated image. The authors evaluated the gap-compensable reconstruction algorithms with uniform disk and Shepp-Logan phantoms by simulating sinograms which contained Poisson random noise and a data loss due to detector gaps. In addition, these methods were applied to real high resolution research tomography (HRRT)-like sinograms of human brain and uniform phantom. A comparison with other methods for gap compensation prior to or during image reconstruction was also made. Quantitative evaluations were performed by computing the uniformity, root mean squared error, and difference between the reconstructed images of nongapped and gapped sinograms.
Results: The simulation results showed that the gap-compensable methods incorporating TV minimization could control gap artifacts, as well as Poisson random noise. In particular, OSEM-TV and RAMLA-TV showed distinct potential via the properties of convergence and robustness to different noise levels and gap angle.
Conclusions: A TV minimization strategy incorporated into commonly used PET reconstruction algorithms was useful for reducing the occurrence of artifacts due to gaps between detector modules in small-diameter PET scanners.

© 2012 American Association of Physicists in Medicine

ACKNOWLEDGMENTS

This work was supported by grants from the Atomic Energy R&D Program (2008-2003852, 2010-0026012) and the WCU Program (R32-10142) through the KOSEF, which is funded by the Korean Ministry of Education, Science and Technology.

Article Outline

  1. INTRODUCTION
  2. MATERIALS AND METHODS
    1. Gap-compensable reconstruction methods
      1. Reconstruction algorithms
      2. Total variation minimization
    2. Experimental datasets
    3. Evaluation methods
    4. Comparison to other methods
  3. RESULTS
    1. Numerical experiments
      1. Disk phantom
      2. Shepp-Logan phantom
    2. Evaluation using real measurement data
    3. Comparison to other methods
  4. DISCUSSIONS AND CONCLUSIONS
Digital Object Identifier
http://dx.doi.org/10.1118/1.3673775

KEYWORDS and PACS

Keywords

brain, gradient methods, image reconstruction, medical image processing, minimisation, neurophysiology, phantoms, positron emission tomography, random noise, stochastic processes, gap compensation, TV minimization, compressed sensing, positron emission tomography (PET), image reconstruction

PACS

PUBLICATION DATA

ISSN

0094-2405 (print)  

Publisher

$abstract.society.value is a Member of CrossRef American Association of Physicists in Medicine

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