A novel sparsity reconstruction method from poisson data for 3D bioluminescence tomography

Xiaoqun Zhang*, Yujie Lu, Tony Chan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

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 ℓ1 and ℓ0 regularization. We show numerically that although several ℓ1 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 ℓ0 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.

Original languageEnglish (US)
Pages (from-to)519-535
Number of pages17
JournalJournal of Scientific Computing
Volume50
Issue number3
DOIs
StatePublished - Mar 1 2012

Keywords

  • Bioluminescence tomography
  • Orthogonal matching pursuit
  • Poisson noise
  • Source reconstruction
  • ℓ regularization

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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