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A Novel Sparsity Reconstruction Method from Poisson Data for 3D Bioluminescence Tomography

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An Erratum to this article was published on 28 September 2011

Abstract

In this paper, we consider 3D Bioluminescence tomography (BLT) source reconstruction from Poisson data in three dimensional space. With a priori information of sources sparsity and MAP estimation of Poisson distribution, we study the minimization of Kullback-Leihbler divergence with ℓ 1 and ℓ 0 regularization. We show numerically that although several ℓ 1 minimization algorithms are efficient for compressive sensing, they fail for BLT reconstruction due to the high coherence of the measurement matrix columns and high nonlinearity of Poisson fitting term. Instead, we propose a novel greedy algorithm for ℓ 0 regularization to reconstruct sparse solutions for BLT problem. Numerical experiments on synthetic data obtained by the finite element methods and Monte-Carlo methods show the accuracy and efficiency of the proposed method.

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Authors and Affiliations

  1. Department of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China

    Xiaoqun Zhang

  2. Center for Molecular Imaging, Institute of Molecular Medicine, University of Texas Health Science Center at Houston, 1825 Pressler Street SRB 330, Houston, TX, 77030, USA

    Yujie Lu

  3. HKUST, Clear Water Bay, Kowloon, Hong Kong

    Tony Chan

Authors
  1. Xiaoqun Zhang
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  2. Yujie Lu
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  3. Tony Chan
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Corresponding author

Correspondence to Xiaoqun Zhang.

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An erratum to this article can be found at http://dx.doi.org/10.1007/s10915-011-9544-9.

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Zhang, X., Lu, Y. & Chan, T. A Novel Sparsity Reconstruction Method from Poisson Data for 3D Bioluminescence Tomography. J Sci Comput 50, 519–535 (2012). https://doi.org/10.1007/s10915-011-9533-z

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  • DOI: https://doi.org/10.1007/s10915-011-9533-z

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