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Background: Ring artifact is a common problem in Computed Tomography (CT), which can lead to inaccurate diagnoses and treatment plans. It can be caused by various factors such as detector imperfections, anti-scatter grids, or other nonuniform filters placed in the x-ray beam. Physics-based corrections for these x-ray source and detector non-uniformity, in general cannot completely get rid of the ring artifacts. Therefore, there is a need for a robust method that can effectively remove ring artifacts in the image domain while preserving details., Purpose: This study aims to develop an effective method for removing ring artifacts from reconstructed CT images., Methods: The proposed method starts by converting the reconstructed CT image containing ring artifacts into polar coordinates, thereby transforming these artifacts into stripes. Relative Total Variation is used to extract the image's overall structural information. For the efficient restoration of intricate details, we introduce Directional Gradient Domain Optimization (DGDO) and design objective functions that make use of both the image's gradient and its overall structure. Subsequently, we present an efficient analytical algorithm to minimize these objective functions. The image obtained through DGDO is then transformed back into Cartesian coordinates, finalizing the ring artifact correction process., Results: Through a series of synthetic and real-world experiments, we have effectively demonstrated the prowess of our proposed method in the correction of ring artifacts while preserving intricate details in reconstructed CT images. In a direct comparison, our method has exhibited superior visual quality compared to several previous approaches. These results underscore the remarkable potential of our approach for enhancing the overall quality and clinical utility of CT imaging., Conclusions: The proposed method offers an analytical solution for removing ring artifacts from CT images while preserving details. As ring artifacts are a common problem in CT imaging, this method has high practical value in the medical field. The proposed method can improve image quality and reduce the difficulty of disease diagnosis, thereby contributing to better patient care., (© 2024 American Association of Physicists in Medicine.)

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.

Purpose: X-ray phase-contrast imaging (XPCI) can provide multiple contrasts with great potentials for clinical and industrial applications, including conventional attenuation, phase contrast, and dark field. Grating-based imaging (GBI) and edge-illumination (EI) are two promising types of XPCI as the conventional x-ray sources can be directly utilized. For the GBI and EI systems, the phase-stepping acquisition with multiple exposures at a constant fluence is usually adopted in the literature.This work, however, attempts to challenge such a constant fluence concept during the phase-stepping process and proposes a fluence adaptation mechanism for dose reduction., Method: Given the importance of patient radiation dose for clinical applications, numerous studies have tried to reduce patient dose in XPCI by altering imaging system designs, data acquisition, and information retrieval. Recently, analytic multiorder moment analysis has been proposed to improve the computing efficiency. In these algorithms, multiple contrasts can be calculated by summing together the weighted phase-stepping curves (PSCs) with some kernel functions, which suggests us that the raw data at different steps have different contributions for the noise in retrieved contrasts. Therefore, it is possible to improve the noise performance by adjusting the fluence distribution during the phase-stepping process directly. Based on analytic retrieval formulas and the Gaussian noise model for detected signals, we derived an optimal adaptive fluence distribution, which is proportional to the absolute weighting kernel functions and the root of original sample PSCs acquired under the constant fluence. Considering that the original sample PSC might be unavailable, we proposed two practical forms for the GBI and EI systems, which are also able to reduce the contrast noise when comparing with the constant fluence distribution. Since the kernel functions are target contrast-dependent, our proposed fluence adaptation mechanism provides a way of realizing a contrast-based dose optimization while keeping the same noise level., Results: To validate our analyses, simulations and experiments are conducted for the GBI and EI systems. Simulated results demonstrate that the dose reduction ratio between our proposed fluence distributions and the typical constant one can be about 20% for the phase contrast, which is consistent with our theoretical predictions. Although the experimental noise reduction ratios are a little smaller than the theoretical ones, low-dose experiments observe better noise performance by our proposed method. Our simulated results also give out the effective ranges of the parameters of the PSCs, such as the visibility in the GBI, the standard deviation, and the mean value in the EI, providing a guidance for the use of our proposed approach in practice., Conclusions: In this paper, we propose a fluence adaptation mechanism for contrast-based dose optimization in XPCI, which can be applied to the GBI and EI systems. Our proposed method explores a new direction for dose reduction, and may also be further extended to other types of XPCI systems and information retrieval algorithms., (© 2021 American Association of Physicists in Medicine.)

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., (© 2021 American Association of Physicists in Medicine.)

X-ray scatter remains a major physics challenge in volumetric computed tomography (CT), whose physical and statistical behaviors have been commonly leveraged in order to eliminate its impact on CT image quality. In this work, we conduct an in-depth derivation of how the scatter distribution and scatter to primary ratio (SPR) will change during the spectral correction, leading to an interesting finding on the property of scatter. Such a characterization of scatter's behavior provides an analytic approach of compensating for the SPR as well as approximating the change of scatter distribution after spectral correction, even though both of them might be significantly distorted as the linearization mapping function in spectral correction could vary a lot from one detector pixel to another. We conduct an evaluation of SPR compensations (SPRCs) on a Catphan phantom and an anthropomorphic chest phantom to validate the characteristics of scatter. In addition, this scatter property is also directly adopted into CT imaging using a spectral modulator with flying focal spot technology (SMFFS) as an example to demonstrate its potential in practical applications. For cone-beam CT (CBCT) scans at both 80 and 120 kVp, CT images with accurate CT numbers can be achieved after spectral correction followed by the appropriate SPRC based on our presented scatter property. In the case of the SMFFS based CBCT scan of the Catphan phantom at 120 kVp, after a scatter correction using an analytic algorithm derived from the scatter property, CT image quality was significantly improved, with the averaged root mean square error reduced from 297.9 to 6.5 Hounsfield units., (© 2021 Institute of Physics and Engineering in Medicine.)

Helical CT has been widely used in clinical diagnosis. In this work, we focus on a new prototype of helical CT, equipped with sparsely spaced multidetector and multi-slit collimator (MSC) in the axis direction. This type of system can not only lower radiation dose, and suppress scattering by MSC, but also cuts down the manufacturing cost of the detector. The major problem to overcome with such a system, however, is that of insufficient data for reconstruction. Hence, we propose a deep learning-based function optimization method for this ill-posed inverse problem. By incorporating a Radon inverse operator, and disentangling each slice, we significantly simplify the complexity of our network for 3D reconstruction. The network is composed of three subnetworks. Firstly, a convolutional neural network (CNN) in the projection domain is constructed to estimate missing projection data, and to convert helical projection data to 2D fan-beam projection data. This is follwed by the deployment of an analytical linear operator to transfer the data from the projection domain to the image domain. Finally, an additional CNN in the image domain is added for further image refinement. These three steps work collectively, and can be trained end to end. The overall network is trained on a simulated CT dataset based on eight patients from the American Association of Physicists in Medicine (AAPM) Low Dose CT Grand Challenge. We evaluate the trained network on both simulated datasets and clinical datasets. Extensive experimental studies have yielded very encouraging results, based on both visual examination and quantitative evaluation. These results demonstrate the effectiveness of our method and its potential for clinical usage. The proposed method provides us with a new solution for a fully 3D ill-posed problem.

In this work, we investigate the Fourier properties of a symmetric-geometry computed tomography (SGCT) with linearly distributed source and detector in a stationary configuration. A linkage between the 1D Fourier Transform of a weighted projection from SGCT and the 2D Fourier Transform of a deformed object is established in a simple mathematical form (i.e., the Fourier slice theorem for SGCT). Based on its Fourier slice theorem and its unique data sampling in the Fourier space, a Linogram-based Fourier reconstruction method is derived for SGCT. We demonstrate that the entire Linogram reconstruction process can be embedded as known operators into an end-to-end neural network. As a learning-based approach, the proposed Linogram-Net has capability of improving CT image quality for non-ideal imaging scenarios, a limited-angle SGCT for instance, through combining weights learning in the projection domain and loss minimization in the image domain. Numerical simulations and physical experiments on an SGCT prototype platform showed that our proposed Linogram-based method can achieve accurate reconstruction from a dual-SGCT scan and can greatly reduce computational complexity when compared with the filtered backprojection type reconstruction. The Linogram-Net achieved accurate reconstruction when projection data are complete and significantly suppressed image artifacts from a limited-angle SGCT scan mimicked by using a clinical CT dataset, with the average CT number error in the selected regions of interest reduced from 67.7 Hounsfield Units (HU) to 28.7 HU, and the average normalized mean square error of overall images reduced from 4.21e-3 to 2.65e-3.

Purpose: Inverse-geometry computed tomography (IGCT) could have great potential in medical applications and security inspections, and has been actively investigated in recent years. In this work, we explore a special architecture of IGCT in a stationary configuration: symmetric-geometry computed tomography (SGCT), where the x-ray source and detector are linearly distributed in a symmetric design. A direct filtered backprojection (FBP)-type algorithm is developed to analytically reconstruct images from the SGCT projections., Methods: In our proposed SGCT system, a big number of x-ray source points equally distributed along a straight-line trajectory will sequentially fire in an ultra-fast manner in one side, and an equispaced detector whose total length is comparable to that of the source will continuously collect data in the opposite side, as the object to be scanned moves into the imaging plane. We firstly present the overall design of SGCT. An FBP-type reconstruction algorithm is then derived for this unique imaging configuration. With finite length of x-ray source and detector arrays, projection data from one segment of SGCT scan are insufficient for an exact reconstruction. As a result, in practical applications, dual-SGCT scan whose detector segments are placed perpendicular to each other, is of particular interest and is proposed. Two segments of SGCT together can make sure that the passing rays cover at least 180 degrees for each and every point if carefully designed. In general, however, there exists a data redundancy problem for a dual-SGCT. So a weighting strategy is developed to maximize the use of projection data collected while avoid image artifacts. In addition, we further extend the fan-beam SGCT to cone beam and obtain a Feldkamp-Davis-Kress (FDK)-type reconstruction algorithm. Finally, we conduct a set of experimental studies both in simulation and on a prototype SGCT system and validate our proposed methods., Results: A simulation study using the Shepp-Logan head phantom confirms that CT images can be exactly reconstructed from dual-SGCT scan and that our proposed weighting strategy is able to handle the data redundancy properly. Compared with the rebinning-to-parallel-beam method using the forward projection of an abdominal CT dataset, our proposed method is seen to be less sensitive to data truncation. Our algorithm can achieve 10.64 lp/cm of spatial resolution at 50% modulation transfer functions point, higher than that of the rebinning method which can only reach at 9.42 lp/cm even with extremely fine interpolation. Real experiments of a cylindrical object on a prototype SGCT further prove the effectiveness and practicability of the direct FBP method proposed, with similar level of noise performance to rebinning algorithm., Conclusions: A new concept of SGCT with linearly distributed source and detector is investigated in this work, in which spinning of sources and detectors is no longer needed during data acquisition, simplifying its system design, development, and manufacturing. A direct FBP-type algorithm is developed for analytical reconstruction from SGCT projection data. Numerical and real experiments validate our method and show that exact CT image can be reconstructed from dual-SGCT scan, where data redundancy problem can be solved by our proposed weighting function., (© 2020 American Association of Physicists in Medicine.)

Purpose: Grating-based x-ray phase-contrast imaging (GPCI) is a promising technique for clinical applications as it can provide two newly emerging imaging modalities (differential phase-contrast and dark-field contrast) in addition to the conventional absorption contrast. As far, phase-stepping strategy is the most commonly used approach in GPCI to indirectly acquire differential phase-contrast and dark-field contrast. It is known that the obtained phase-stepping curves (PSCs) have the cosine property and the convolution property, leading to two types of information retrieval approaches in literature: the Fourier component analysis and the multi-order moment analysis. The purpose of this paper is to derive a new property of PSCs and apply the property to noise optimization for information retrieval., Methods: Based on the cosine expression of the flat PSC without the sample and the well-established convolution relationship between the flat PSC and the sample PSC, we reveal an important integral property of PSCs: the inner product of PSCs and an arbitrary function contains only zero-order and first-order components in the Fourier series. Furthermore, we apply the property to the direct multi-order moment analysis and propose a set of generalized forms including an optimal one in the presence of noise., Results: To validate the effectiveness of our analysis, we compared the simulated and real experiment results retrieved by the original direct multi-order moment analysis with the ones retrieved by our proposed noise-optimal form. A significant improvement of noise performance by our method is observed and the improvement ratio in differential phase-contrast is consistent with our theoretical calculation (39.2%)., Conclusions: In this paper, we reveal a new integral property of the acquired PSCs with and without samples in GPCI, which can be applied to information retrieval approaches like the direct multi-order moment analysis. Then we optimize these approaches to improve the noise performance, offering great potentials of dose reduction in practical applications., (© 2019 American Association of Physicists in Medicine.)

X-ray computed tomography (CT) scatter correction using primary modulator has been continuously developed over the past years, with progress in improving the performance of scatter correction. In this work, we further advance the primary modulator technique towards practical applications where the spectral nonuniformity caused by the modulator continues to be a challenging problem. A physics-based spectral compensation algorithm is proposed to adaptively correct for the spectral nonuniformity, and hence to reduce the resultant ring artifacts on reconstructed CT images. First, an initial spectrum of the CT system without the primary modulator is modeled using an understanding of x-ray CT physics, and optimized by an expectation maximization method; then, the optimized estimation of the initial spectrum is utilized to adaptively calculate the effective modulator thickness from measured transmissions of the primary modulator at each detector element, leading to a set of new spectra that is able to capture the nonuniform spectral distribution of the primary modulator; finally, using the modulator-modeled spectrum, a beam hardening mapping function is generated and beam hardening correction is applied to CT projections. A CatPhan600 phantom and an anthropomorphic thorax phantom were scanned with three different primary modulators to evaluate the approach. For the Catphan phantom, the spectral compensation algorithm efficiently removes the ring (and band) artifacts that otherwise dominate the reconstructed CT image. For the three modulators with nominal copper thickness of 52.5, 105 and 210 [Formula: see text]m, our method reduces the CT number nonuniformity from 147.9, 436.2 and 696.4 Hounsfield units (HU) to 14.6, 26.2 and 13.6 HU, respectively, close to that of the reference image (i.e. 7.5 HU). For the thorax phantom, the ring artifacts are also suppressed significantly on the transaxial image; on the sagittal image, the alternating black-and-white patterns are largely removed, with the CT number nonuniformity being reduced from 282.0 HU to 38.5 HU.

A new scatter estimation algorithm with a concept of virtual scatter modulation for X-ray scatter correction using primary modulator is proposed to reduce the aliasing errors in the estimated scatter. Virtual scatter modulation can be realized through dividing the measured primary-modulated image by the measured modulation function. After the division, the aggravation of the aliasing of primary due to the non-uniformity of the modulation function is largely transferred to that of scatter. Since scatter in general has less high frequencies than primary does, the aggravation of its aliasing is expected to be weaker, and therefore the overall aliasing can be reduced. A CatPhan©600 phantom and an anthropomorphic thorax phantom are scanned on a tabletop X-ray cone-beam computed tomography system to validate our proposed algorithm. On the Catphan phantom, the oscillations that are clearly observed in the central region of the Catphan scatter profile estimated using the original primary-modulation algorithm, are mostly eliminated with the proposed scatter modulation algorithm, leading to less residual artifacts and better CT number uniformity in the reconstructed image. Compared with 38.9 HU of CT nonuniformity in a selected uniform region when the primary-modulation algorithm is used, the new algorithm significantly reduces it to 4.5 HU, reaching the same level of uniformity as the ground truth reference. On the thorax phantom, overall better CT number uniformity is also achieved.