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. 2021:9:58537-58548.
doi: 10.1109/access.2021.3071492. Epub 2021 Apr 7.

Refined Locally Linear Transform-Based Spectral-Domain Gradient Sparsity and Its Applications in Spectral CT Reconstruction

Qian Wang  1 , Morteza Salehjahromi  1 , Hengyong Yu  1
Affiliations

Refined Locally Linear Transform-Based Spectral-Domain Gradient Sparsity and Its Applications in Spectral CT Reconstruction

Qian Wang et al. IEEE Access. 2021.

Abstract

Spectral computed tomography (CT) is extension of the conventional single spectral CT (SSCT) along the energy dimension, which achieves superior energy resolution and material distinguishability. However, for the state-of-the-art photon counting detector (PCD) based spectral CT, because the emitted photons with a fixed total number for each X-ray beam are divided into several energy bins, the noise level is increased in each reconstructed channel image, and it further leads to an inaccurate material decomposition. To improve the reconstructed image quality and decomposition accuracy, in this work, we first employ a refined locally linear transform to convert the structural similarity among two-dimensional (2D) spectral CT images to a spectral-dimension gradient sparsity. By combining the gradient sparsity in the spatial domain, a global three-dimensional (3D) gradient sparsity is constructed, then measured with L 1-, L 0- and trace-norm, respectively. For each sparsity measurement, we propose the corresponding optimization model, develop the iterative algorithm, and verify the effectiveness and superiority with real datasets.

Keywords: Refined locally linear transform; constrained optimization; iterative reconstruction; material decomposition; sparsity construction; spectral CT; spectral-dimension gradient sparsity; structural similarity.

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Figures

FIGURE 1.
FIGURE 1.
Scan settings for real experiments.
FIGURE 2.
FIGURE 2.
Reconstructed channel images of real experiment 1. The display window is [0,0.3] for channel 1, [0,0.26] for channel 2, and [0,0.22] for channel 3.
FIGURE 3.
FIGURE 3.
Zoomed-in patches of Fig. 2, which are marked by red boxes.
FIGURE 4.
FIGURE 4.
Decomposed material images of real experiment 1. The display window is [0,1] for all the results.
FIGURE 5.
FIGURE 5.
Zoomed-in patches of Fig. 4, which are marked by red boxes.
FIGURE 6.
FIGURE 6.
Reconstructed channel images (channel 1–3) of real experiment 2. The display window is [0,0.6] for channel 1, [0,0.6] for channel 2, and [0,0.5] for channel 3.
FIGURE 7.
FIGURE 7.
Reconstructed channel images (channel 4–6) of real experiment 2. The display window is [0,0.5] for channel 4, [0,0.4] for channel 5, and [0,0.3] for channel 6.
FIGURE 8.
FIGURE 8.
Zoomed-in patches of Fig. 6, which are marked by left red boxes.
FIGURE 9.
FIGURE 9.
Zoomed-in patches of Fig. 7, which are marked by left red boxes.
FIGURE 10.
FIGURE 10.
Zoomed-in patches of Fig. 6, which are marked by right red boxes.
FIGURE 11.
FIGURE 11.
Zoomed-in patches of Fig. 7, which are marked by right red boxes.
FIGURE 12.
FIGURE 12.
Decomposed material images of real experiment 2. The display window is [0,1] for all the results.
FIGURE 13.
FIGURE 13.
Zoomed-in patches of Fig. 12, which are marked by left red boxes.
FIGURE 14.
FIGURE 14.
Zoomed-in patches of Fig. 12, which are marked by right red boxes.
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