Speaker
Dr
Zhi-Feng Huang
(Dept. of Engineering Physics, Tsinghua Univ., China)
Description
X-ray diffraction enhanced imaging (DEI) has extremely high sensitivity and
resolution of weakly absorbing low-Z samples, so it becomes an effective method for
molecular imaging recently, especially in the medical and biological fields. Many
experiments have been performed and high-resolution phase-contrast images of many
elaborate details of the samples, such as human breast cancers and joint cartilages
et al, have been obtained using the DEI method. The computed tomography of the DEI
(DEI-CT) can reconstructed the distribution of the refractive index decrement (n')
or the refractive index (n) of the sample, where n'=1-n. But the basic theories and
reconstruction algorithms are different from traditional absorption-contrast CT if
the rotated axis of the sample is parallel to the diffractive plane of the
analyzer. Here, the projections of this CT mode are called ‘directional-derivative
projections’. This reconstruction problem of directional-derivative projections
have been investigated by K.M.Pavlov, I.Koyama, A.Maksimenko and Pei-Ping Zhu et
al, who proposed different ‘two-step’ algorithms, including ‘restoration then
reconstruction’ and ‘reconstruction then restoration’ methods. However, the
restoration process may result in artifacts and inaccurate values in CT images.
This paper is dedicated to a direct reconstruction algorithm for directional-
derivative projections. The new algorithm can directly reconstruct the distribution
of the refractive index decrement of the sample without restoration process like
the filtered backprojection algorithm (FBP) of the traditional CT. A mathematical
deduction is described in detail, based on the differential theory of two-
dimensional Fourier transform and the theory of polar coordinate in the frequency
domain. A reconstruction formula of directional-derivative projections similar to
the basic formula of the FBP algorithm is obtained. The difference of the new
algorithm from the FBP algorithm is that it uses the Hilbert filter instead of the
RL or SL filter in the frequency domain. It can obtain accurate values of the
refractive index decrement of the sample without any calibration. Finally, a
computer simulation of the DEI-CT is presented to produce directional-derivative
projections. The simulated cylinder is rotated in a step of 1.0 degree within 180
degrees, so 180 directional-derivative projections in total are obtained during the
simulated experiment. The projections are with or without noise. For projection in
each direction, 41 DEI images are measured in different positions of the simulated
rocking curve. Afterwards, refraction-angle images are calculated by the multiple-
image statistical method. The results from the new algorithm are compared with the
results from ‘two-step’ algorithms using with-noise and without-noise projections.
The new algorithm is well validated in the experiment. Since it is a ‘one-step’
process and does not require any restoration process, it avoids artifacts brought
by restoration, especially for noisy projections. In conclusion, the new algorithm
makes an advance in this field. We believe that it is a perfect form of the direct
computed tomographic reconstruction algorithm for directional-derivative
projections of the DEI-CT.
Author
Dr
Zhi-Feng Huang
(Dept. of Engineering Physics, Tsinghua Univ., China)
Co-authors
Prof.
Ke-Jun Kang
(Dept. of Engineering Physics, Tsinghua Univ., China)
Dr
Zheng Li
(Dept. of Engineering Physics, Tsinghua Univ., China)
