The 13th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine
Abstract—Nowadays, x-ray computed tomography (CT) is
widely used to reveal patient’s anatomical information. However,
the side effect of radiation, relating to genetic or cancerous
diseases, has caused great public concern. The problem is how to
minimize radiation dose while maintaining image quality
significantly. As a practical application of compressed sensing
theory, one category of methods takes total variation (TV)
minimization as the sparse constraint, which makes it possible to
get a reconstruction image of high quality in the under-sampling
situation. On the other hand, a preliminary attempt of low-dose
CT reconstruction based on dictionary learning seems to be
another effective choice. But some critical parameters, such as the
regularization parameter, cannot be determined by detecting
datasets. In this paper, we propose a reweighted objective
function that contributes to a numerical calculation model of the
regularization parameter. A number of experiments demonstrate
that this strategy performs well with a better reconstruction
image and saving a large amount of time.
I. INTRODUCTION
OWADAYS, the fact that an overdose of radiation possibly
increases the risk of genetic and cancerous diseases makes
it urgent to develop creative and effective reconstruction
techniques to fit low-dose CT scanning protocol. One low-dose
approach is to decrease the number of projection angles, which
will lead to incomplete few-view data. In this case, analytic
algorithms, which are derived from a continuous imaging
model, are sensitive to insufficient projection data and arrive at
a terrible result [1]. However, algebraic algorithms like the
simultaneous algebraic reconstruction technique (SART) [2]
solved the reconstruction problem better by transforming it to a
series of linear equations.
Recently, Candes, Romberg and Tao [3][4] have made
compressed sensing theory popular in information theory field.
This theory indicates that a variety of signals can be represented
This work was partially supported by the National Natural Science
Foundation of China (NSFC) through Grant No.61201117 and No.61301042,
the Natural Science Foundation of Jiangsu province (NSFJ) through Grant
No.BK2012189, Science and Technology Program of Suzhou
(No.ZXY2013001). The CT images are provided by the PET Center, Huashan
Hospital, Fudan University, China.
Cheng Zhang, Jian Zheng, Ming Li, Yanfei Lu, and Jiali You are with
Medical Imaging Laboratory, Suzhou Institute of Biomedical Engineering and
Technology (SIBET) of Chinese Academy of Sciences, Suzhou, 215163, China.
Yihui Guan is with PET Center, Huashan Hospital, Fudan University, Shanghai,
200235, China
Corresponding author: ezhangf@mail.ustc.edu.cn
sparsely in a certain transform domain. Therefore, original
signal can be recovered accurately by far fewer samples
guaranteed by the principle called restricted isometry property
(RIP) [5]. To deal with few-view CT reconstruction problem,
many compressed sensing algorithms have been proposed. One
group is based on total variation (TV), which takes the total
variation of the image as the sparse constraint. The solution of
the projection linear equations is determined by minimizing the
TV term. Sidky and Pan presented an improved TV-based
algorithm named adaptive steepest descent projection onto
convex sets (ASD-POCS) in circular cone-beam framework [6].
Another similar method called gradient projection Barzilari
Borwein (GPBB) has a faster convergence speed [7]. Besides
the TV minimization algorithms, dictionary learning is also
helpful to sparse representation. During the reconstruction
process, the image is divided into many overlapped patches,
represented sparsely by over-complete elements of a particular
dictionary. Xu et al. proposed the adaptive dictionary based
statistical iterative reconstruction (ADSIR) algorithm and got a
better reconstruction result than TV-based methods in the
low-dose CT condition [8]. However, there is a special
parameter playing an important role in the reconstruction
program to balance the data fidelity term and the regularization
term while determining its value is time consuming with many
attempts. Hence, there is no doubt that providing a model to
select a proper value of this parameter according to the
scanning data is essential for the algorithm based on dictionary
learning, which leads to better result and time saving.
In this work, we firstly review the ADSIR algorithm [8] and
then make some modification on the objective function. Next,
the model of regularization parameter selection is proposed by
function fitting method. After that, a series of experiments are
performed and corresponding discussions are given. Finally,
there is a brief conclusion at the end of this paper.
II. NOTATION AND PROBLEM DESCRIPTION
A. Background and Notation Interpretation
According to previous work [8], the reconstruction problem
is equivalent to the following minimization.
2
2
20
1
ˆ
min
2
I
i
i s s s s
i
i s s
l
μ,α,D
Aμ E μ Dα α
(1)
Where
is the system matrix;
is a
linear attenuation coefficient distribution, which transforms the
A Model of Regularization Parameter Selection
in Low-dose X-ray CT Reconstruction Based on
Dictionary Learning
Cheng Zhang, Jian Zheng, Ming Li, Yanfei Lu, Jiali You, and Yihui Guan