Fast reconstruction in fluorescence molecular
tomography using data compression of
intra- and inter-projections
Jiulou Zhang (张久楼)
1
, Junwei Shi (时军威)
1
, Simin Zuo (左思敏)
1
,FeiLiu(刘 飞)
1,2
,
Jing Bai (白 净)
1
, and Jianwen Luo (罗建文)
1,3,
*
1
Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing 100084, China
2
Tsinghua-Peking Center for Life Sciences, Beijing 100084, China
3
Center for Biomedical Imaging Research, Tsinghua University, Beijing 100084, China
*Corresponding author: luo_jianwen@tsinghua.edu.cn
Received November 20, 2014; accepted April 29, 2015; posted online June 4, 2015
In order to improve the reconstruction accuracy in fluorescence molecular tomography (FMT), a common ap-
proach is to increase the number of fluorescence data or projections. However, this approach consumes too much
memory space and computational time. In this Letter, a data compression strategy that involves the removal of
the redundant information from both intra- and inter-projections is proposed to reduce the dimension of the
FMT inverse problem. The performance of this strategy is tested with phantom and in vivo mouse experiments.
The results demonstrate that the proposed data compression strategy can accelerate the FMT reconstruction
nearly tenfold and almost without any quality degradation.
OCIS codes: 100.3010, 100.3190, 260.2510.
doi: 10.3788/COL201513.071002.
Compared with other imaging methods like optical coher-
ent tomography
[1]
and Laminar optical tomography
[2]
,
fluorescence molecular tomography (FMT) has been de-
veloped as a tool with special advantages to quantitatively
determine the distribution of fluorophores in small ani-
mals
[3]
. To improve the reconstruction accuracy in FMT,
tens of thousands or even more fluorescence measurements
are generally obtained to solve the inverse problem. How-
ever, this approach consumes too much memory space
and computational time in the FMT reconstruction.
Several methods have been proposed to accelerate the
reconstruction process in the past few years. By solving
a simplified system matrix equation in the wavelet do-
main
[4]
, data and solution compression based on wavelet
transformation are adopted for efficient reconstruction
[5]
.
However, these two methods are both implemented in
the transformation domain; thus, the computational
procedures are complex. The dimension of the FMT in-
verse problem can be reduced by a principal component
analysis (PCA)
[6]
, but this approach only considers
the intra-projection redundant information. The compres-
sion method presented in Ref. [
7] takes advantage of the
inter-projection redundant information, but an additional
cluster analysis is necessary before the process of compres-
sion. In this Letter, a fluorescence data compression
(FDC) strategy, which considers the redundant informa-
tion from both the intra- and inter-projections, is proposed
to accelerate the FMT reconstruction. The compression of
the fluorescence data is achieved by a PCA.
The Monte Carlo method is considered to be the golden
standard to describe the propagation of photons in biologi-
cal tissues, but it is very time consuming
[8]
. Therefore, the
diffusion equation (DE) known as the lower-order
approximation of radiative transfer equation is applied
in this Letter as follows
[9]
:
½−∇D∇ þ μ
a
Gðr; r
s
Þ¼−δðr − r
s
Þ; (1)
where r and r
s
are the arbitrary location and source posi-
tion, respectively, Gðr; r
s
Þ denotes the Green’s function of
the photons’ propagation from location r
s
to r, and
δðr − r
s
Þ is the excitation source. D ¼ 1∕3ðμ
a
þ μ
0
s
Þ is con-
sidered as the diffusion coefficient of the biological tissues,
and μ
a
and μ
0
s
are the absorption coefficient and reduced
scattering coefficient, respectively. In order to solve this
DE, Eq. (
1) is restrained by the Robin-type boundary
condition
[10]
, as follows:
2ρD
∂Gðr; r
s
Þ
∂n
þ Gðr; r
s
Þ¼0; (2)
where ρ is a mismatch constant of relative optical indices
within and outside of the boundary, and the vector n de-
notes the outward normal vector of the tissue surface. The
cubic mesh is used to calculate the solution of DE in this
Letter. Then, after the image domain is discretized into
tens of thousands or even more small cubes, each projec-
tion of the FMT problem can be linearized on the basis of
the Kirchhoff approximation
[11]
to obtain the following
form:
W
s
X ¼ b
s
; (3)
where W
s
is the weight matrix from one projection, b
s
is a
column vector of the corresponding fluorescence data, and
COL 13(7), 071002(2015) CHINESE OPTICS LETTERS July 10, 2015
1671-7694/2015/071002(5) 071002-1 © 2015 Chinese Optics Letters