Computed tomography (CT) is an imaging technique that employs X-ray transmission and multi-angle projection to reconstruct the internal structure of an object. Meanwhile, it is commonly adopted in medical diagnosis and industrial non-destructive testing due to its non-invasive and intuitive characteristics. Parallel translational computed tomography (PTCT) acquires projection data by moving a flat panel detector (FPD) and a radiation source in parallel linear motion relative to the detection object. This method has promising applications in industrial inspection. Due to the limitations of the inspection environment and the structure of the inspection system, there are scenarios where it is difficult to realize multi-segment PTCT scanning and imaging, and only single-segment PTCT scanning and imaging can be performed. Since the single-segment PTCT can only obtain the equivalent projection data at a limited angle, its reconstruction problem belongs to limited-angle CT reconstruction. Images reconstructed by traditional algorithms will suffer from serious artifacts. Deep learning-based limited-angle CT image reconstruction has yielded remarkable results, among which model-based data-driven methods have caught much attention. However, such deep networks with CNNs as the main structure tend to focus on the local neighborhood information of the image and ignore the non-local features. Additionally, research on iterative algorithms shows that non-local features can improve detail preservation, which is important for limited-angle CT reconstruction.

To address the limited-angle artifact in PTCT image reconstruction, we propose a deep iterative unfolding method (STICA-Net, Fig. 3) that learns local and non-local regular terms. The method unfolds a gradient descent algorithm with a fixed number of iterations to a neural network and utilizes convolutional modules with the coordinate attention (CA) mechanism and Swin-Transformer modules deployed as iterative modules in alternating cascades to form an end-to-end deep reconstruction network. The convolution module learns local regularization, in which CA is leveraged to reduce image smoothing. The Swin-Transformer module learns non-local regularization to improve the network's ability to restore image details. Among neighboring modules, iterative connection (IC) is adopted to enhance the model's ability to extract deeper features and improve the efficiency of each iteration. The employed experimental comparison methods are FBP, SIRT, SwinIR, FISTA-Net, and LEARN. The quality of the reconstructed image is comprehensively evaluated by utilizing three sets of quantitative indicators of root mean square error (RMSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM). Meanwhile, comparison experiments are conducted on both simulated and real datasets to verify the feasibility of the proposed method. Additionally, we perform ablation experiments to confirm the effectiveness of each component of the network.

We present the results of a contrast experiment of 90° limited-angle rotational scanning CT using the simulation data 2DeteCT dataset. The results demonstrate the effectiveness of the STICA-Net method for limited-angle reconstruction (Fig. 7). It is noted that PTCT image reconstruction is a limited-angle problem. To verify STICA-Net's effectiveness in PTCT limited-angle reconstruction, we employ the same dataset to generate projection data with an equivalent scanning angle of 90° via PTCT scanning, and then compare different methods. The results of both subjective image evaluation (Fig. 8) and quantitative evaluation index (Table 2) show that STICA-Net can solve the limited-angle problem of PTCT and achieve high-quality image reconstruction. By building the PTCT experimental platform (Fig. 6), the actual dataset of carbon fiber composite core wire (ACCC) is obtained. The two example results (Fig. 11) of the ACCC dataset indicate that the reconstructed images of the traditional method still contain a significant number of artifacts in the absence of large-angle data. However, the artifacts in the reconstructed images of FISTA-Net and LEARN have been significantly reduced. Although FISTA-Net produces better reconstruction results than LEARN, the details are still somewhat blurred. Compared with the suboptimal SwinIR, the PSNR of STICA-Net increases by 4.72% and 5.53%, the SSIM rises by 2.88% and 1.59%, and the RMSE decreases by 15.94% and 19.32% respectively. Meanwhile, ablation experiments verify the effectiveness of different network structures in PTCT limited-angle reconstruction. Figure 10 demonstrates clear improvement in the numerical values of each index as network structures are added incrementally.

To deal with the difficulty of PTCT image reconstruction, we theoretically conclude that PTCT image reconstruction is a limited-angle problem by building a PTCT geometric model, and then propose the STICA-Net model. Ablation experiments confirm the effectiveness of each model component in improving the reconstructed image. Compared to the contrast algorithm, the proposed method significantly improves image quality and yields the best quantitative evaluation indicators across different data types. Additionally, comprehensive results demonstrate that the proposed method outperforms the contrast algorithm in terms of PTCT limited-angle artifact suppression and detail recovery, and high-quality image reconstruction can be achieved. This is beneficial for promoting the in-service detection application of PTCT. However, the method's limitation is that although the ablation experiments demonstrate that the inclusion of the Swin-Transformer structure enhances image results, more memory is needed to store weights and intermediate features, which restricts the utilization of higher-resolution images in our study. In the future, the network module will be further improved to make the network more lightweight.