Fourier Properties of Symmetric-Geometry Computed Tomography and Its Linogram Reconstruction With Neural Network

Method for expanding the field-of-view of micro-CT imaging using array micro-focus X-ray source

Micro-computed tomography (micro-CT) is a critical high-resolution, non-destructive testing technique. However, its field-of-view (FOV) is constrained by the detector size, which limits the ability to perform high-resolution imaging of larger objects. To overcome this limitation, we developed a method for expanding the FOV of micro-CT imaging using an array micro-focus X-ray source based on electron beam scanning (EBMCT). This innovative approach expands the FOV by allowing X-rays to traverse different regions of the object through focal array scanning. Due to the unique scanning methodology of EBMCT, the resulting projections exhibits redundancy and truncation issues. For this reason, we propose a weighting distribution strategy based on trigonometric functions to smooth the projections, effectively mitigating the effects of redundancy and truncation on the reconstructed images. Furthermore, by combining the geometric structure of EBMCT and the weighting function, we derive a two-dimensional analytical reconstruction algorithm (Weighted multi-sources filtering back-projection, w-MSFBP) and a three-dimensional approximate reconstruction algorithm (Weighted multi-sources Feldkamp-Davis-Kress, w-MSFDK) for EBMCT reconstruction. Simulation and physical experiment results show that EBMCT can expand the FOV by more than two times while maintaining high resolution. Additionally, both the w-MSFBP and w-MSFDK algorithms accurately reconstruct two-dimensional and three-dimensional structures of the scanned objects. By effectively expanding the FOV of micro-CT, EBMCT provides valuable insights for the research and design of large FOV micro-CT systems.

Generalized-equiangular geometry CT: Concept and shift-invariant FBP algorithms

BACKGROUND

With advanced x-ray source and detector technologies being continuously developed, non-traditional CT geometries have been widely explored. Generalized-Equiangular Geometry CT (GEGCT) architecture, in which an x-ray source might be positioned radially far away from the focus of arced detector array that is equiangularly spaced, is of importance in many novel CT systems and designs.

PURPOSE

GEGCT, unfortunately, has no theoretically exact and shift-invariant analytical image reconstruction algorithm in general. In this study, to obtain fast and accurate reconstruction from GEGCT and to promote its system design and optimization, an in-depth investigation on a group of approximate Filtered Back-Projection (FBP) algorithms with a variety of weighting strategies has been conducted.

METHODS

The architecture of GEGCT is first presented and characterized by using a normalized-radial-offset distance (NROD). Next, shift-invariant weighted FBP-type algorithms are derived in a unified framework, with pre-filtering, filtering, and post-filtering weights, for both fixed and dynamic NROD configurations. Three viable weighting strategies are then presented including a classic one developed by Besson in the literature and two new ones generated from a curvature fitting and from an empirical formula, where all of the three weights can be expressed as certain functions of NROD. After that, an analysis of reconstruction accuracy is conducted with a wide range of NROD. Finally, the weighted FBP algorithm for GEGCT is extended to a three-dimensional form in the case of cone-beam scan with a cylindrical detector array.

RESULTS

Theoretical analysis and numerical study show that weights in the shift-invariant FBP algorithms can guarantee highly accurate reconstruction for GEGCT. A simulation of Shepp-Logan phantom and a GEGCT scan of lung mimicked by using a clinical lung CT dataset both demonstrate that FBP reconstructions with Besson and polynomial weights can achieve excellent image quality, with Peak Signal to Noise Ratio and Structural Similarity being at the same level as that from the standard equiangular fan-beam CT scan. Reconstruction of a cylinder object with multiple contrasts from simulated GEGCT scan with dynamic NROD is also highly consistent with fixed ones when using the Besson and polynomial weights, with root mean square error less than 7 hounsfield units, demonstrating the robustness and flexibility of the presented FBP algorithms. In terms of resolution, the direct FBP methods for GEGCT could achieve 1.35 lp/mm of spatial resolution at 10% modulation transfer functions point, higher than that of the rebinning method which can only reach 1.14 lp/mm. Moreover, 3D reconstructions of a disc phantom reveal that a greater value of NROD for GEGCT will bring less cone beam artifacts as expected.

CONCLUSIONS

We propose the concept of GEGCT and investigate the feasibility of using shift-invariant weighted FBP-type algorithms for reconstruction from GEGCT data without rebinning. A comprehensive analysis and phantom studies have been conducted to validate the effectiveness of proposed weighting strategies in a wide range of NROD for GEGCT with fixed and dynamic NROD.

Dual-scale similarity-guided cycle generative adversarial network for unsupervised low-dose CT denoising

Removing the noise in low-dose CT (LDCT) is crucial to improving the diagnostic quality. Previously, many supervised or unsupervised deep learning-based LDCT denoising algorithms have been proposed. Unsupervised LDCT denoising algorithms are more practical than supervised ones since they do not need paired samples. However, unsupervised LDCT denoising algorithms are rarely used clinically due to their unsatisfactory denoising ability. In unsupervised LDCT denoising, the lack of paired samples makes the direction of gradient descent full of uncertainty. On the contrary, paired samples used in supervised denoising allow the parameters of networks to have a clear direction of gradient descent. To bridge the gap in performance between unsupervised and supervised LDCT denoising, we propose dual-scale similarity-guided cycle generative adversarial network (DSC-GAN). DSC-GAN uses similarity-based pseudo-pairing to better accomplish unsupervised LDCT denoising. We design a Vision Transformer-based global similarity descriptor and a residual neural network-based local similarity descriptor for DSC-GAN to effectively describe the similarity between two samples. During training, pseudo-pairs, i.e., similar LDCT samples and normal-dose CT (NDCT) samples, dominate parameter updates. Thus, the training can achieve equivalent effect as training with paired samples. Experiments on two datasets demonstrate that DSC-GAN beats the state-of-the-art unsupervised algorithms and reaches a level close to supervised LDCT denoising algorithms.

Sam's Net: A Self-Augmented Multistage Deep-Learning Network for End-to-End Reconstruction of Limited Angle CT

Limited angle reconstruction is a typical ill-posed problem in computed tomography (CT). Given incomplete projection data, images reconstructed by conventional analytical algorithms and iterative methods suffer from severe structural distortions and artifacts. In this paper, we proposed a self-augmented multi-stage deep-learning network (Sam's Net) for end-to-end reconstruction of limited angle CT. With the merit of the alternating minimization technique, Sam's Net integrates multi-stage self-constraints into cross-domain optimization to provide additional constraints on the manifold of neural networks. In practice, a sinogram completion network (SCNet) and artifact suppression network (ASNet), together with domain transformation layers constitute the backbone for cross-domain optimization. An online self-augmentation module was designed following the manner defined by alternating minimization, which enables a self-augmented learning procedure and multi-stage inference manner. Besides, a substitution operation was applied as a hard constraint for the solution space based on the data fidelity and a learnable weighting layer was constructed for data consistency refinement. Sam's Net forms a new framework for ill-posed reconstruction problems. In the training phase, the self-augmented procedure guides the optimization into a tightened solution space with enriched diverse data distribution and enhanced data consistency. In the inference phase, multi-stage prediction can improve performance progressively. Extensive experiments with both simulated and practical projections under 90-degree and 120-degree fan-beam configurations validate that Sam's Net can significantly improve the reconstruction quality with high stability and robustness.

X-ray source translation based computed tomography (STCT)

Micro computed tomography (µCT) allows the noninvasive visualization and 3D reconstruction of internal structures of objects with high resolution. However, the current commercial µCT system relatively rotates the source-detector or objects to collect projections, referred as RCT in this paper, and has difficulties in imaging large objects with high resolutions because fabrication of large-area, inexpensive flat-panel detectors remains a challenge. In this paper, we proposed a source translation based CT (STCT) for imaging large objects with high resolution to get rid of the limitation of the detector size, where the field of view is primarily determined by the source translation distance. To compensate for the deficiency of incomplete data in STCT, we introduced multi-scanning STCT (mSTCT), from which the projections theoretically meet the conditions required for accurate reconstructions. Theoretical and numerical studies showed that mSTCT has the ability to accurately image large objects without any visible artifacts. Numerical simulations also indicated that mSTCT has a potential capability to precisely image the region of interest (ROI) inside objects, which remains a challenge in RCT due to truncated projections. In addition, an experimental platform for mSTCT has been established, from which the 2D and 3D reconstructed results demonstrated its feasibility for µCT applications. Moreover, STCT also has a great potential for security inspection and product screening by using two perpendicular STCTs, with advantages of low-cost equipment and high-speed examination.

Densely sampled spectral modulation for x-ray CT using a stationary modulator with flying focal spot: a conceptual and feasibility study of scatter and spectral correction

PURPOSE

Modulation of the x-ray source in computed tomography (CT) by a designated filter to achieve a desired distribution of photon flux has been greatly advanced in recent years. In this work, we present a densely sampled spectral modulation (DSSM) as a promising low-cost solution to quantitative CT imaging in the presence of scatter. By leveraging a special stationary filter (namely a spectral modulator) and a flying focal spot, DSSM features a strong correlation in the scatter distributions across focal spot positions and sees no substantial projection sparsity or misalignment in data sampling, making it possible to simultaneously correct for scatter and spectral effects in a unified framework.

METHODS

The concept of DSSM is first introduced, followed by an analysis of the design and benefits of using the stationary spectral modulator with a flying focal spot (SMFFS) that dramatically changes the data sampling and its associated data processing. With an assumption that the scatter distributions across focal spot positions have strong correlation, a scatter estimation and spectral correction algorithm from DSSM is then developed, where a dual-energy modulator along with two flying focal spot positions is of interest. Finally, a phantom study on a tabletop cone-beam CT system is conducted to understand the feasibility of DSSM by SMFFS, using a copper modulator and by moving the x-ray tube position in the X direction to mimic the flying focal spot.

RESULTS

Based on our analytical analysis of the DSSM by SMFFS, the misalignment of low- and high-energy projection rays can be reduced by a factor of more than 10 when compared with a stationary modulator only. With respect to modulator design, metal materials such as copper, molybdenum, silver, and tin could be good candidates in terms of energy separation at a given attenuation of photon flux. Physical experiments using a Catphan phantom as well as an anthropomorphic chest phantom demonstrate the effectiveness of DSSM by SMFFS with much better CT number accuracy and less image artifacts. The root mean squared error was reduced from 297.9 to 6.5 Hounsfield units (HU) for the Catphan phantom and from 409.3 to 39.2 HU for the chest phantom.

CONCLUSIONS

The concept of DSSM using a SMFFS is proposed. Phantom results on its scatter estimation and spectral correction performance validate our main ideas and key assumptions, demonstrating its potential and feasibility for quantitative CT imaging.