Neural network Hilbert transform based filtered backprojection for fast inline x-ray inspection

X-ray imaging is an important tool for quality control since it allows to inspect the interior of products in a non-destructive way. Conventional x-ray imaging, however, is slow and expensive. Inline x-ray inspection, on the other hand, can pave the way towards fast and individual quality control, provided that a sufficiently high throughput can be achieved at a minimal cost. To meet these criteria, an inline inspection acquisition geometry is proposed where the object moves and rotates on a conveyor belt while it passes a fixed source and detector. Moreover, for this acquisition geometry, a new neural-network-based reconstruction algorithm is introduced: the neural network Hilbert transform based filtered backprojection. The proposed algorithm is evaluated both on simulated and real inline x-ray data and has shown to generate high quality reconstructions of 400 x 400 reconstruction pixels within 200 ms, thereby meeting the high throughput criteria

An Efficient Estimation Method for Reducing the Axial Intensity Drop in Circular Cone-Beam CT

Reconstruction algorithms for circular cone-beam (CB) scans have been extensively studied in the literature. Since insufficient data are measured, an exact reconstruction is impossible for such a geometry. If the reconstruction algorithm assumes zeros for the missing data, such as the standard FDK algorithm, a major type of resulting CB artifacts is the intensity drop along the axial direction. Many algorithms have been proposed to improve image quality when faced with this problem of data missing; however, development of an effective and computationally efficient algorithm remains a major challenge. In this work, we propose a novel method for estimating the unmeasured data and reducing the intensity drop artifacts. Each CB projection is analyzed in the Radon space via Grangeat's first derivative. Assuming the CB projection is taken from a parallel beam geometry, we extract those data that reside in the unmeasured region of the Radon space. These data are then used as in a parallel beam geometry to calculate a correction term, which is added together with Hu's correction term to the FDK result to form a final reconstruction. More approximations are then made on the calculation of the additional term, and the final formula is implemented very efficiently. The algorithm performance is evaluated using computer simulations on analytical phantoms. The reconstruction comparison with results using other existing algorithms shows that the proposed algorithm achieves a superior performance on the reduction of axial intensity drop artifacts with a high computation efficiency

3D Analytic Cone-Beam Reconstruction for Multiaxial CT Acquisitions

A conventional 3rd generation Computed Tomography (CT) system with a single circular source trajectory is limited in terms of longitudinal scan coverage since extending the scan coverage beyond 40 mm results in significant cone-beam artifacts. A multiaxial CT acquisition is achieved by combining multiple sequential 3rd generation axial scans or by performing a single axial multisource CT scan with multiple longitudinally offset sources. Data from multiple axial scans or multiple sources provide complementary information. For full-scan acquisitions, we present a window-based 3D analytic cone-beam reconstruction algorithm by tessellating data from neighboring axial datasets. We also show that multi-axial CT acquisition can extend the axial scan coverage while minimizing cone-beam artifacts. For half-scan acquisitions, one cannot take advantage of conjugate rays. We propose a cone-angle dependent weighting approach to combine multi-axial half-scan data. We compute the relative contribution from each axial dataset to each voxel based on the X-ray beam collimation, the respective cone-angles, and the spacing between the axial scans. We present numerical experiments to demonstrate that the proposed techniques successfully reduce cone-beam artifacts at very large volumetric coverage

BPF Algorithms for Multiple Source-Translation Computed Tomography Reconstruction

Micro-computed tomography (micro-CT) is a widely used state-of-the-art instrument employed to study the morphological structures of objects in various fields. Object-rotation is a classical scanning mode in micro-CT allowing data acquisition from different angles; however, its field-of-view (FOV) is primarily constrained by the size of the detector when aiming for high spatial resolution imaging. Recently, we introduced a novel scanning mode called multiple source translation CT (mSTCT), which effectively enlarges the FOV of the micro-CT system. Furthermore, we developed a virtual projection-based filtered backprojection (V-FBP) algorithm to address truncated projection, albeit with a trade-off in acquisition efficiency (high resolution reconstruction typically requires thousands of source samplings). In this paper, we present a new algorithm for mSTCT reconstruction, backprojection-filtration (BPF), which enables reconstructions of high-resolution images with a low source sampling ratio. Additionally, we found that implementing derivatives in BPF along different directions (source and detector) yields two distinct BPF algorithms (S-BPF and D-BPF), each with its own reconstruction performance characteristics. Through simulated and real experiments conducted in this paper, we demonstrate that achieving same high-resolution reconstructions, D-BPF can reduce source sampling by 75% compared with V-FBP. S-BPF shares similar characteristics with V-FBP, where the spatial resolution is primarily influenced by the source sampling.Comment: 22 pages, 12 figure

FDK-Type Algorithms with No Backprojection Weight for Circular and Helical Scan CT

We develop two Feldkamp-type reconstruction algorithms with no backprojection weight for circular and helical trajectory with planar detector geometry. Advances in solid-state electronic detector technologies lend importance to CT systems with the equispaced linear array, the planar (flat panel) detectors, and the corresponding algorithms. We derive two exact Hilbert filtered backprojection (FBP) reconstruction algorithms with no backprojection weight for 2D fan-beam equispace linear array detector geometry (complement of the equi-angular curved array detector). Based on these algorithms, the Feldkamp-type algorithms with no backprojection weight for 3D reconstruction are developed using the standard heuristic extension of the divergent beam FBP algorithm. The simulation results show that the axial intensity drop in the reconstructed image using the FDK algorithms with no backprojection weight with circular trajectory is similar to that obtained by using Hu's and T-FDK, algorithms. Further, we present efficient algorithms to reduce the axial intensity drop encountered in the standard FDK reconstructions in circular cone-beam CT. The proposed algorithms consist of mainly two steps: reconstruction of the object using FDK algorithm with no backprojection weight and estimation of the missing term. The efficient algorithms are compared with the FDK algorithm, Hu's algorithm, T-FDK, and Zhu et al.'s algorithm in terms of axial intensity drop and noise. Simulation shows that the efficient algorithms give similar performance in axial intensity drop as that of Zhu et al.'s algorithm while one of the efficient algorithms outperforms Zhu et al.'s algorithm in terms of computational complexity

Imaging system performing substantially exact reconstruction and using non-traditional trajectories

A method and apparatus for reconstruction of a region of interest (ROI) for an object using an imaging system is provided. The imaging system may substantially exactly reconstruct the ROI with a straight line trajectory. In the straight line trajectory, the ROI is not bounded or encircled by the actual trajectory of the source (e.g., no chords that are composed from two points on the source trajectory intersect or fill the ROI to be imaged). However, the ROI may be substantially reconstructed by using "virtual" chords to reconstruct the ROI. The virtual chords are such that no point on the trajectory is included in the virtual chord (such as one that is parallel to the straight line trajectory). These virtual chords may intersect and fill the ROI, thus enabling substantially exact reconstruction. Further, in reconstructing the image, the straight line trajectory may be assumed to be infinite in length

OSNet & MNetO: Two Types of General Reconstruction Architectures for Linear Computed Tomography in Multi-Scenarios

Recently, linear computed tomography (LCT) systems have actively attracted attention. To weaken projection truncation and image the region of interest (ROI) for LCT, the backprojection filtration (BPF) algorithm is an effective solution. However, in BPF for LCT, it is difficult to achieve stable interior reconstruction, and for differentiated backprojection (DBP) images of LCT, multiple rotation-finite inversion of Hilbert transform (Hilbert filtering)-inverse rotation operations will blur the image. To satisfy multiple reconstruction scenarios for LCT, including interior ROI, complete object, and exterior region beyond field-of-view (FOV), and avoid the rotation operations of Hilbert filtering, we propose two types of reconstruction architectures. The first overlays multiple DBP images to obtain a complete DBP image, then uses a network to learn the overlying Hilbert filtering function, referred to as the Overlay-Single Network (OSNet). The second uses multiple networks to train different directional Hilbert filtering models for DBP images of multiple linear scannings, respectively, and then overlays the reconstructed results, i.e., Multiple Networks Overlaying (MNetO). In two architectures, we introduce a Swin Transformer (ST) block to the generator of pix2pixGAN to extract both local and global features from DBP images at the same time. We investigate two architectures from different networks, FOV sizes, pixel sizes, number of projections, geometric magnification, and processing time. Experimental results show that two architectures can both recover images. OSNet outperforms BPF in various scenarios. For the different networks, ST-pix2pixGAN is superior to pix2pixGAN and CycleGAN. MNetO exhibits a few artifacts due to the differences among the multiple models, but any one of its models is suitable for imaging the exterior edge in a certain direction.Comment: 13 pages, 13 figure