A Novel Sparsity Reconstruction Method from Poisson Data for 3D Bioluminescence Tomography |
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Authors: | Xiaoqun Zhang Yujie Lu Tony Chan |
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Affiliation: | (1) VT-WFU School of Biomedical Engineering and Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060, USA;(2) Chemical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060, USA |
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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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Keywords: | |
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