Material Decomposition in Photon Counting Detector
Using Iterative Algorithm
Jieun Chang, Sunhee Wi, Jiseoc Lee and Seungryong Cho
Department of Nuclear and Quantum Engineering, KAIST
Introduction
Geometry and Phantom
● Using photon counting detector, image reconstruction in multiple energy is
available. One of applications of photon counting detector is material
decomposition.
● Noise propagation is challenging issue in material decomposition method.
● Using iterative material decomposition method rather than analytic algorithm,
noise propagation was highly reduced, resulting in material decomposed image.
● As conceptual diagram shows in Fig. 1, image from conventional detector was
reconstructed first. Then, image from photon counting detector at each energy
was reconstructed using GMI information from conventional detector.
● To get the information from conventional detector, both of conventional
detector and photon counting detector are aligned together as shown in Fig. 2.
● Filter is to be set in front of the source so that the number of incident photon
can be reduced as a factor of 100.
● Phantom is composed of water cylinder which has another two cylinders of
similar linear attenuation coefficient. One is carbonated calcium and the other
is contrast medium called iohexol.
Methods
Kaczmarz’s Projection
● Linear attenuation coefficient, 𝜇 𝑥, 𝐸𝑛
can be rewritten as linear
combinations of linear attenuation coefficient of basis materials, 𝜇𝑚 (𝐸𝑛 ).
● Using 3 energy bins, 4 equations can be constructed including one more
𝑀
equation, which is the summation of all coefficients, 𝑚=1 𝑏𝑚 (𝑥) should be 1.
● Kaczmarz’s projection method gives projection to each hyperplane. Projecting
to each hyper-plane iteratively yields convergent point. 𝑏𝑚 (𝑥), cross point of
all hyperplanes should be the spatial distribution of density fraction of m-th
basis material.
Fig. 2 Geometry of proposed system
𝑏𝑚 (𝑥)(𝑖)
(𝑖−1) ∙ 𝜇 (𝐸 )−𝜇 𝑥, 𝐸
𝑏
(𝑥)
𝑚
𝑚 𝑛
𝑛
(𝑖−1)
= 𝑏𝑚 (𝑥)
−
∙ 𝜇𝑚 (𝐸𝑛 )
𝜇𝑚 (𝐸𝑛 ) ∙ 𝜇𝑚 (𝐸𝑛 )
Fig. 3 Phantom with similar attenuation coefficient
Results
𝑏𝑚 (𝑥) is a density fraction of m-th basis material
GMI(Gradient Magnitude Image) Guided Image Reconstruction
● Current limitation of photon counting detector is the number of incident
photons on the detector. Since poisson noise is a square root of the number of
incident photons, signal to noise of photon counting detector is much lower
than that of conventional detector.
● Making use of information from conventional detector plays an important role
in reconstructing the image from photon counting detector.
● GMI is the boundary information of image.
𝑓 = 𝑎𝑟𝑔𝑚𝑖𝑛 (𝛼 𝑓
𝑇𝑉
+𝛽
2
𝑓𝑝 𝐺𝑀𝐼 − 𝑓𝐺𝑀𝐼
2
1st bin
Fig. 4 Reconstructed image
from conventional detector
(a)
2nd bin
3rd bin
Graph. 1 Energy spectrum for photon counting detector
(b)
(c)
)
𝑓𝑝 is a prior image
𝛼, 𝛽 is a weighting parameter
Fig. 5 Reconstructed image from photon counting detector. (a) : 1st bin, (b) : 2nd bin, (c) : 3rd bin
Conventional detector module
Photon counting detector module
Reconstruction algorithm
GMI recon algorithm
CBCT recon image
GMI guided recon image
Fig. 6 Material decomposed image
White=contrast medium, Gray=Calcium
carbonate, Black=Water
● In Fig.4, contrast medium and calcium
carbonate can not be distinguished each
other.
● Using 0.01% of photons comparing with
conventional detector, images from each
energy bins were reconstructed as shown
in Fig.5.
● Fig. 6 shows a material decomposed
image using iterative algorithm.
Conclusions
Material decomposition
Fig. 1 Conceptual diagram of proposed system
● Performing material decomposition, feasibility of iterative algorithm was studied.
● Two materials are visibly distinguished in recon images from photon counting
detector whereas not in recon image from conventional detector.
References
1. Katsuyuki Taguchi et al., “Image-domain material decomposition using photon counting CT”