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

Xiaoqun Zhang; Yujie Lu; Tony Chan

doi:10.1007/s10915-011-9533-z

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 journal › Article › peer-review

36 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 language	English (US)
Pages (from-to)	519-535
Number of pages	17
Journal	Journal of Scientific Computing
Volume	50
Issue number	3
DOIs	https://doi.org/10.1007/s10915-011-9533-z
State	Published - Mar 1 2012
Externally published	Yes

Bibliographical note

Publisher Copyright:
© Springer Science+Business Media, LLC 2011.

Keywords

Bioluminescence tomography
Orthogonal matching pursuit
Poisson noise
Source reconstruction
ℓ regularization

ASJC Scopus subject areas

Software
General Engineering
Computational Mathematics
Theoretical Computer Science
Applied Mathematics
Numerical Analysis
Computational Theory and Mathematics

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10.1007/s10915-011-9533-z

Cite this

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title = "A novel sparsity reconstruction method from poisson data for 3D bioluminescence tomography",

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.",

keywords = "Bioluminescence tomography, Orthogonal matching pursuit, Poisson noise, Source reconstruction, ℓ regularization",

author = "Xiaoqun Zhang and Yujie Lu and Tony Chan",

note = "Publisher Copyright: {\textcopyright} Springer Science+Business Media, LLC 2011.",

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doi = "10.1007/s10915-011-9533-z",

language = "English (US)",

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TY - JOUR

T1 - A novel sparsity reconstruction method from poisson data for 3D bioluminescence tomography

AU - Zhang, Xiaoqun

AU - Lu, Yujie

AU - Chan, Tony

N1 - Publisher Copyright: © Springer Science+Business Media, LLC 2011.

PY - 2012/3/1

Y1 - 2012/3/1

N2 - 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.

AB - 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.

KW - Bioluminescence tomography

KW - Orthogonal matching pursuit

KW - Poisson noise

KW - Source reconstruction

KW - ℓ regularization

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U2 - 10.1007/s10915-011-9533-z

DO - 10.1007/s10915-011-9533-z

M3 - Article

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SN - 0885-7474

VL - 50

SP - 519

EP - 535

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 3

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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