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

Authors:
Xiaoqun Zhang;Yujie Lu;Tony Chan
Affiliations:
Department of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China 200240;Center for Molecular Imaging, Institute of Molecular Medicine, University of Texas Health Science Center at Houston, Houston, USA 77030;HKUST, Kowloon, Hong Kong
Venue:
Journal of Scientific Computing
Year:
2012

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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 驴 1 and 驴 0 regularization. We show numerically that although several 驴 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 驴 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.