多光谱生物发光成像的稀疏贝叶斯重建方法

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本文探讨了一种基于多类型先验信息的稀疏贝叶斯重构方法，应用于多光谱生物发光成像（BLT）。在贝叶斯框架下，作者们针对BLT问题中的不适定性提出了创新性的解决方案。首先，他们考虑了源的稀疏特性，这是一种关键的先验假设，有助于减少图像重建中的噪声和伪影，提高重建结果的准确性。由于多光谱情况下计算负担增加，作者们采取了一系列策略来优化计算效率，例如并行计算、低秩矩阵分解和迭代算法的加速。五种类型的先验信息被整合进模型，包括： 1. 源的稀疏性：通过引入稀疏编码，该方法假设生物发光源信号在实际空间中是局部稀疏分布的，这样有助于找到少数活跃的发光区域，从而减少未知参数的数量。 2. 多光谱信息：利用不同波段的生物发光数据，这些数据反映了生物分子对特定光谱的响应，通过联合分析，可以提供额外的结构信息。 3. 物理约束：利用生物学和光学原理，如光传输模型和生物发光效率函数，为重建过程设定合理的物理约束。 4. 统计建模：通过概率模型，如高斯分布或复杂先验，赋予数据和参数以统计解释，这有助于处理不确定性并提高估计的稳定性。 5. 迭代优化：通过迭代求解过程，结合贝叶斯更新规则和正则化技术，逐步逼近最优解，同时保持计算资源的有效利用。这种方法的优势在于它能够有效地平衡重建精度和计算效率，尤其适用于在实际应用中，如生物医学成像，需要快速处理大量数据和复杂场景的情况下。通过实验验证，这种稀疏贝叶斯重构方法能够显著改善多光谱BLT的性能，提升图像质量和重建速度，为相关领域的研究和临床应用提供了强有力的工具。

1010 CHINESE OPTICS LETTERS / Vol. 8, No. 10 / Octob er 10, 2010

Sparse Bayesian reconstruction method for multispectral

bioluminescence tomography

Jinchao Feng (冯冯冯金金金超超超)

, Kebin Jia (贾贾贾克克克斌斌斌)

, Chenghu Qin (秦秦秦承承承虎虎虎)

, Shouping Zhu (朱朱朱守守守平平平)

Xin Yang (杨杨杨鑫鑫鑫)

, and Jie Tian (田田田捷捷捷)

2,3∗

College of Electronic Information and Control Engineering, Beijing University of Technology, Beijing 100124, China

Medical Image Pro cessing Group, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China

Life Science Research Center, Xidian University, Xi’an 710071, China

∗

E-mail: tian@ieee.org

Received March 1, 2010

We present a sparse Bayesian reconstruction method based on multiple types of a priori information

for multispectral bioluminescence tomography (BLT). In the Bayesian approach, five kinds of a priori

information are incorp orated, reducing the ill-posedness of BLT. Specifically, source sparsity characteristic

is considered to promote reconstruction results. Considering the computational burden in the multispectral

case, a series of strategies is adopted to improve computational efficiency, such as optimal p ermissible

source region strategy and node model of the finite element method. The performance of the proposed

algorithm is validated by a heterogeneous three-dimensional (3D) micron scale computed tomography atlas

and a mouse-shaped phantom. Reconstructed results demonstrate the feasibility and effectiveness of the

prop osed algorithm.

OCIS co des: 100.3010, 100.3190, 170.3010, 170.6960.

doi: 10.3788/COL20100810.1010.

The emergence of new imaging modalities and ap-

proaches that provide cellular and molecular informa-

tion has led to the nascent field of molecular imag-

ing. Methods based on detecting optical signals in a

small animal have been leading this field

[1,2]

. The light-

emitting enzymes, and the technologies for detecting

their weak bioluminescent signals with a highly sensi-

tive charge-coupled device (CCD) camera in living sub-

jects, comprise the method called in vivo bioluminescence

imaging

[3]

Much effort has been devoted to transforming biolumi-

nescence imaging from a planar imaging technique into a

truly three-dimensional (3D) tomographic modality ap-

plication to small animals, because planar bioluminescent

imaging cannot provide depth information

[3]

. The reso-

lution of planar bioluminescent imaging is also limited

due to the nature of surface imaging. Therefore, biolu-

minescence tomography (BLT) is developed to explore

depth information and enhance bioluminescence imaging

resolution. As a result, BLT is particularly attractive for

in vivo applications.

Generally, BLT is an ill-posed problem and the unique-

ness of the BLT solution has been proven theoretically

[4]

The uniqueness theory is not only instructional in recon-

structing a bioluminescent source distribution, but also

presents that the ill-posedness of BLT could be overcome

with sufficient a priori information.

Since the concept of BLT was introduced, it has

made great progress in modeling and reconstruction

algorithms

[5−11]

. Currently, BLT reconstruction-based

spectrum information has gained much attention as

BLT reconstruction results have improved, with hyper-

spectral and multisp ectral methods

[5−8]

. In addition, the

importance of multiple types of a priori information has

been recognized. The more the a priori information one

applies, the better the results obtained.

The Bayesian approach provides a framework to in-

corporate multiple types of a priori information. We

have proposed a BLT reconstruction algorithm based on

the Bayesian approach to reconstruct a bioluminescent

source, in which a generalized adaptive Gaussian Markov

random field (GGMRF) prior model for unknown source

density estimation is presented

[9]

. However, the sparse

nature of the internal source to promote reconstructed

quality is not considered in the prior model

[10]

. Further-

more, the permissible source region used in the previous

algorithm is inferred through the light p ower distribu-

tion on the surface, which is hardly determined when

the underlying source is located in a deep position. The

large-scale reconstruction data also significantly affect

reconstructed efficiency in the multispectral case.

In this letter, we describe a sparse Bayesian approach

for multispectral BLT. Furthermore, multiple types of

a priori information are incorp orated into the Bayesian

framework to reduce the ill-posedness of the BLT prob-

lem, specifically the sparsity of source and the optimal

permissible source region.

In bioluminescence imaging, photon propagation can

be described by the steady-state diffusion equation and

Robin boundary condition. Taking into account the in-

ﬂuence of light wavelength λ on tissue optical property,

the following model is thus given:

−∇ · [D(r, λ)∇Φ(r, λ)] + µ

(r, λ)Φ(r, λ)

= x(r, λ) (r ∈ Ω), (1)

Φ(r, λ) + 2 A(r; n, n

)D(r, λ)[ν(r)

·∇Φ(r, λ)] = 0 (r ∈ ∂Ω), (2)

where Ω is a bounded smooth domain; ∂Ω is the cor-

responding boundary; Φ(r,λ) denotes the photon ﬂux

1671-7694/2010/101010-05

° 2010 Chinese Optics Letters

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