IEEE TRANSACTIONS ON NANOBIOSCIENCE, VOL. 14, NO. 2, MARCH 2015 229
BSIRT: A Block-Iterative SIRT Parallel Algorithm
Using Curvilinear Projection Model
Fa Zhang, Jingrong Zhang, Albert Lawrence, Fei Ren, Xuan Wang, Zhiyong Liu, and Xiaohua Wan*
Abstract—Large-field high-resolution electron tomography
enables visualizing detailed mechanisms under global structure.
As field enlarges, the distortions of reconstruction and proce
ssing
time become more critical. Using the curvilinear projection model
can improve the quality of large-field ET reconstruction, but its
computational complexity further exacerbates the p
rocessing
time. Moreover, there is no parallel strategy on GPU for itera-
tive reconstruction method with curvilinear projection. Here we
propose a new Block-iterative SIRT parallel algor
ithm with the
curvilinear projection model (BSIRT) for large-field ET recon-
struction, to improve the quality of reconstruction and accelerate
the reconstruction process. We also develop so
me key techniques,
including block-iterative method with the curvilinear projection,
a scope-based data decomposition method and a page-based
data transfer scheme to implement the par
allelization of BSIRT
on GPU platform. Experimental results show that BSIRT can
improve the reconstruction quality as well as the speed of the
reconstruction process.
Index Terms—Curvilinear projection model, electron tomog-
raphy, iterative methods, parallel, reconstruction.
I. INTRODUCTION
E
LECTRON tomography (ET) has emerged as a powerful
technique in analyzing three-dimensional (3D) structures
of complex viruses, organelles, cells, and tissues at nanometer
scale [1]. In ET, a series of projection images are obtained by
tilting the specimen around tilting axis. The 3D structure of the
specimen can then be derived from those projection images, by
reconstruction algorithms. Due to physical limitations of mi-
croscopes, the angular tilting range is limited (usually within
60 60 or 70 70 ). Moreover, specimens must be im-
aged at low electron doses, which make projection images ex-
Manuscript received September 30, 2014; revised December 02, 2014; ac-
cepted January 03, 2015. Date of publication February 11, 2015; date of current
version April 07, 2015. This work is supported by grants National Natural Sci-
ence Foundation of China (61232001, 61202210, 61472397 and 61103139) and
the Strategic Priority Research Program of the Chinese Academy of Sciences
(Grant No. XDB08030202). Asterisk indicates corresponding author.
Corresponding author: X. Wan (e-mail: wanxiaohua@ict.ac.cn).
F. Zhang, J. Zhang, F. Ren, and Z. Liu are with Key Lab of Intelligent
Information Processing, Institute of Computing Technology, Chinese Academy
of Sciences, Beijing 100190, China (e-mail: zhangfa@ict.ac.cn; zhangjin-
grong@ict.ac.cn; renfei@ict.ac.cn; zyliu@ict.ac.cn)
J. Zhang is also with University of Chinese Academy of Sciences and is
co-first author in this work.
A. Lawrence is with National Center for Microscopy and Imaging Research,
University of California, San Diego, La Jolla, CA 92093 USA (e-mail: albert.
rick.lawrence@gmail.com).
X. Wang is with Yanshan University, Qinhuangdao 066004, China (e-mail:
wangxuan@ysu.edu.cn)
*X. Wan are with Key Lab of Intelligent Information Processing, Institute of
Computing Technology, Chinese Academy of Sciences, Beijing, China. 100190
(e-mail: wanxiaohua@ict.ac.cn).
Digital Object Identifier 10.1109/TNB.2015.2393377
tremely noisy. In order to obtain high-resolution reconstructed
results, several iterative methods, such as SIRT [2], BICAV [3],
and ASART [4], have been developed to handle the incomplete
and noisy projection images in ET reconstruction.
As the size of projection images increased, large-field
high-resolution studies are very interesting because the detailed
mechanisms can be visualized and understood globally in
the context of surrounding structures [5]. However, most of
existing reconstruction methods for large-field ET are based on
the straight-line projection model, which is not accurate since
electron trajectories are helical under the influence of magnetic
field, in electron microscopes. The distortions become more
pronounced in large-filed ET reconstruction [6]. To decrease
these distortions, a global nonlinear (curvilinear) projection
model is proposed and has been already used in software
package TxBR [6] and iterative reconstruction methods [7].
While the computation of curvilinear projection model is more
complex and could not be used widely in practice.
High performance computing has been traditionally ap-
plied to address the computationally demanding problems in
large-field ET reconstruction. Parallel strategies on clusters
have been widely used [6]–[8]. Graphics processing units
(GPUs) offer an attractive alternative platform in terms of the
high peak performance and cost effectiveness. TxBR adopts a
GPU parallel scheme to calculate 3D reconstruction using the
curvilinear model and backprojection algorithm [8]. However,
this scheme is not suitable for iterative reconstruction methods,
since it costs time to repeatedly transfer all the sections into
GPU's memory in each iteration. Moreover, the size of pro-
jection images has reached to
or larger, the
size of final reconstruction volume will be several GBytes [9],
which further limits parallelization of large-field reconstruction
on GPUs owing to the limited memory in GPUs.
Facing problems above, we propose a new block-iterative
SIRT parallel algorithm with the curvilinear projection model
(BSIRT) for large-field ET reconstruction. Compared to other
previous methods, our algorithm owns several advantages.
First, we combine the SIRT method with the curvilinear projec-
tion model to improve the resolution of reconstruction results.
Second, in BSIRT, we employ a data normalization method and
a revised relaxation parameter to improve the quality of recon-
struction, apply a block-iterative reconstruction to accelerate
the convergence process. Third, we develop a scope-based data
decomposition method to partition the projection series. Last,
for the limitation of GPU memory, we devise a page-based data
transfer scheme, which reduces significantly the redundant data
transferring. Then we implement the parallelization of BSIRT
on GPU platform. Experimental results show that BSIRT makes
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