PSF-Informed Reconstruction: An Enhanced 2D Directional Filtered Backprojection Method for Cone-Beam Rotary Computed Laminography
Authors: Chengxiang Wang, Wei Yu, Baodong Liu
Organizations: School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China · School of Biomedical Engineering and Imaging, Xianning Medical College, Hubei University of Science and Technology, Xianning, 437100, China · Beijing Engineering Research Center of Radiographic Techniques and Equipment, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China · School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing, China · Jinan Laboratory of Applied Nuclear Science, Jinan, China
Cone-beam rotary computed laminography (CL) presents a viable alternative to cone-beam CT for imaging objects with high aspect ratios. Conventional reconstruction techniques, such as CL-FBP and CL-FDK, often yield suboptimal results charac?terized by pronounced superimposition artifacts, reduced contrast,and blurred edges, primarily due to their reliance on 1D row-wise filtering along detector rows. To address these limitations and improve reconstruction quality, we proposed a novel 2D directional filtered backprojection (DFBP) method based on the point spread function (PSF). First, an exact expression for the projection process is derived by establishing the relationship between a reconstructed pixel and its corresponding projection point on the detector. Second, a revised backprojection process incorporating two weighting factors is introduced to counteract the nonlinearity inherent in conventional backprojection, leading to a simplified PSF formulation. Third, to circumvent the computational burden of 3D image space filtering,an approximate method by linearizing the coordinate relationship in Fourier space under some assumptions is developed that transfers the 3D filtering operation to the 2D projection space. This approach facilitates the derivation of a formally simple yet effective 2D direc?tional filter, which integrates a 2D von Hann window and a 2D sinc window. Experimental results demonstrate that the proposed method produces reconstructions with superior contrast, sharper boundaries,and fewer superimposition artifacts compared to CL-FBP and CL?FDK. Moreover, it enables more accurate recovery of internal structures, such as bubble defects and electronic components.
Figures & tables
Fig. 1: The cone-beam rotary CL illumination of a flat-panel detector. The X-ray source and detector rotate on a circle with radius SOsinτ and ODsinτ , respectively. The variable τ∈(0,90∘) is the tilted angle. y′ is the projection of y -axis on the X-source rotation plane. θ is the projection angle. E is a voxels. The measured projection value at location C along line L is denoted by ϕθ(a,b) .
Fig. 2: Cone-beam rotary CL projection data of two PCBs. The first row displays the projection data of PCB 1, while the second row corresponds to PCB 2. The first column shows the projections at an projection angle of 14∘ and the second column presents the projections at 324∘ .
Fig. 3: Comparison of image reconstruction results for PCB 1 using different algorithms. Reconstructed slices from two distinct layers (88 and 141) are displayed for the CL-FBP, CL-FDK, and the proposed DFBP.
Fig. 4: Cross-sectional views of different planes for PCB 1.
Fig. 5: The volume rendering based on maximum density projection of the reconstructed results of PCB 1 using three distinct algorithms.
Fig. 6: Comparison of image reconstruction results for PCB 2 using different algorithms. Reconstructed slices from two distinct layers (10 and 50) are displayed for the CL-FBP, CL-FDK, and the proposed DFBP.
Fig. 7: Magnified view of the region of interest (ROI) indicated by the yellow rectangles in Figure 6 .
Fig. 8: Cross-sectional views of different planes for PCB 2.
Fig. 9: The volume rendering based on maximum density projection of the reconstructed results of PCB 2 using three distinct algorithms.
Image reconstruction recovers images, volumes, or scenes from incomplete, noisy, indirect, or compressed measurements using physical models and learned priors.
Computed Laminography (CL) is a key technology for the nondestructive testing of large plate-shaped objects. However, field-of-view (FOV) limitations inevitably lead to truncation of projected data, an ill-posed inverse problem that causes severe reconstruction artifacts. Existing deep learning methods typically rely on 2D architectures that lack rigorous data consistency constraints. Furthermore, they conventionally confine artifact removal strictly to the FOV, discarding potentially recoverable information outside it. To overcome these limitations, we first introduce a comprehensive CL FOV analysis, categorizing the space into data-complete, data-incomplete, and data-free regions. By extending our reconstruction target to encompass the data-incomplete region, we significantly expand the effective imaging range and enhance scanning efficiency. To achieve this, we propose a novel wavelet-optimized pseudo-3D accelerated diffusion model for CL truncation reconstruction (CL-DM). Our method utilizes a standard 2D diffusion model for slice aggregation, combined with a 3D model-based iterative reconstruction (MBIR) method to ensure strict data consistency. To mitigate inter-slice discontinuities, we introduce wavelet regularization along the z-direction, paired with a translation-invariant (TI) mechanism and a low-frequency preservation strategy. Finally, we introduce a 3D fast sampling architecture, significantly accelerating inference speed. Extensive simulations and real-world experiments demonstrate that CL-DM is superior in effectively eliminating truncation artifacts and restoring high-fidelity, continuous 3D structures.
Rotational Scanning Computed Laminography (RCL) is widely utilized for the Non-Destructive Testing (NDT) of large planar components. However, to facilitate rapid inspection, continuous sparse-view scanning is often employed, where the angular integration effect during exposure induces rotational blur in the projection domain. Furthermore, the data incompleteness inherent in sparse sampling manifests as sparse artifacts in the reconstructed image domain. To address these cross-domain degradations, this paper proposes RCL-Mamba, a measurement-oriented dual-domain State Space Model (SSM)-based image restoration network. The framework adopts a cascaded joint processing strategy: it first corrects the rotational blur in the projection domain and subsequently suppresses the sparse artifacts in the image domain. Additionally, we design a Mamba-CNN dual-branch module to adaptively balance large-scale blur correction with local detail recovery. Evaluations on both simulated datasets and real-world Printed Circuit Board (PCB) scans demonstrate that RCL-Mamba outperforms existing baselines in blur removal, artifact suppression, and structural preservation. Line-profile-based structural measurement further verifies that the proposed method better preserves via/pad boundaries and slender trace profiles. Crucially, by reducing the required scanning views from 512 to 64, our method enhances inspection efficiency by approximately 8-fold without compromising reconstruction quality, offering a robust measurement-oriented restoration solution for high-throughput RCL inspection with improved structural measurement fidelity.
Xuyang Duan, Genyuan Zhang, Zhenjiang Dong +4
Key Laboratory of Optoelectronic Technology and Systems, Ministry of Education, Chongqing University, Chongqing, 400044, China · Engineering Research Center of Industrial CT Nondestructive Testing, Ministry of Education, Chongqing University, Chongqing, 400044, China
This paper presents a novel Direct Integration Theorem (DIT), derived as a non-trivial corollary of the classical Central Slice Theorem (CST). The DIT provides a mathematically consistent transition from the continuous to the discrete domain - a fundamental challenge in computed tomography - thereby eliminating the need for frequency-domain interpolation without resorting to conventional ramp-filtering. The proposed approach circumvents two principal limitations inherent in traditional methods: (i) the zero-frequency singularity and spectral distortions introduced by the mandatory ramp-filtering step, and (ii) discretization inaccuracies associated with frequency-domain interpolation. Based on the DIT, we develop a rigorous framework for consistent discrete solutions of the inverse Radon problem. Mathematical modeling demonstrates that this approach achieves quasi-exact reconstruction, with errors constrained solely by sampling parameters and grid geometry. Furthermore, while Filtered Back Projection (FBP) inherently distorts the variance of the reconstructed image, the DIT-based algorithm preserves it. Comparative simulations confirm that the proposed method eliminates common artifacts, such as intensity cupping, and consistently outperforms FBP in terms of PSNR, SSIM, and reprojection fidelity, faithfully restoring the original image's statistical characteristics.
Mikhail G. Mozerov
Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, 127051 Russia