Article Contents
Article Contents

# Fast non-uniform Fourier transform based regularization for sparse-view large-size CT reconstruction

• Spare-view CT imaging is advantageous to decrease the radiation exposure, acquisition time and computational cost, but suffers from severe streak noise in reconstruction if the classical filter back projection method is employed. Although a few compressed sensing based algorithms have recently been proposed to remedy the insufficiency of projections and have achieved remarkable improvement in reconstruction quality, they face computational challenges for large-scale CT images (e.g., larger than 2000℅2000 pixels). In this paper, we present a fast non-uniform Fourier transform based reconstruction method, targeting at under-sampling high resolution Synchrotron-based micro-CT imaging. The proposed method manipulates the Fourier slice theorem to avoid the involvement of large-scale system matrices, and the reconstruction process is performed in the Fourier domain. With a total variation penalty term, the proposed method can be formulated into an unconstrained minimization problem, which is able to be efficiently solved by the limited-memory BFGS algorithm. Moreover, direct non-uniform Fourier transform is computationally costly, so the developed NUFFT algorithm is adopted to approximate it with little loss of quality. Numerical simulation is implemented to compare the proposed method with some other competing approaches, and then real data obtained from the Australia Synchrotron facility are tested to demonstrate the practical applications of the proposed approach. In short, the significance of the proposed approach includes (1) that it can handle high-resolution CT images with millions of pixels while several other contemporary methods fail; (2) that it can achieve much better reconstruction quality than other methods when the projections are insufficient.

 Citation:

• Figure 1.  Parallel beam geometry: a detector measures an integral of attenuation along the line at angle θ and distance r to the iso-center

Figure 2.  Sampling distribution in Fourier space based on the Fourier slice theorem

Figure 3.  An example of the Fourier slice theorem for CT imaging

Figure 4.  Pseudo code implementation for proposed algorithm

Figure 5.  Performance comparison with different number of views

Figure 6.  Visual comparison for different algorithms with 60 views, 90 views, 180 views

Figure 7.  Reconstruction with 180 projections: FBP (left) vs Proposed method (right)

Figure 8.  Reconstruction with 1800 projections: FBP (left) vs Proposed method (right)

Table 1.  Reconstruction with 60 projections

 Methods SNR RMSE SSIM Time (s) FBP 9.76 0.080 0.851 0.25 Zhu et al. 9.83 0.079 0.922 7.62 Hashemi et al. 2.31 0.188 0.686 10.33 Proposed 10.95 0.069 0.911 5.07

Table 2.  Reconstruction with 90 projections

 Methods SNR RMSE SSIM Time (s) FBP 10.80 0.071 0.916 0.38 Zhu et al. 10.41 0.074 0.946 9.16 Hashemi et al. 3.60 0.162 0.760 9.70 Proposed 12.23 0.060 0.936 5.74

Table 3.  Reconstruction with 180 projections

 Methods SNR RMSE SSIM Time (s) FBP 11.22 0.067 0.946 0.74 Zhu et al. 10.47 0.073 0.949 15.71 Hashemi et al. 10.23 0.075 0.934 9.67 Proposed 13.43 0.052 0.950 7.79
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