Fourier-based interpretation and noise analysis of the moments of small-angle x-ray scattering in grating-based x-ray phase contrast imaging.

In grating-based x-ray phase contrast imaging, Fourier component analysis (FCA) is usually recognized as a gold standard to retrieve the contrasts including attenuation, phase and dark-field, since it is well-established on wave optics and is of high computational efficiency. Meanwhile, an alternative approach basing on the particle scattering theory is being developed and can provide similar contrasts with FCA by calculating multi-order moments of deconvolved small-angle x-ray scattering, so called as multi-order moment analysis (MMA). Although originated from quite different physics theories, the high consistency between the contrasts retrieved by FCA and MMA implies us that there may be some intrinsic connections between them, which has not been fully revealed to the best of our knowledge. In this work, we present a Fourier-based interpretation of MMA and conclude that the contrasts retrieved by MMA are actually the weighted compositions of Fourier coefficients, which means MMA delivers similar physical information as FCA. Based on the recognized cosine model, we also provide a truncated analytic MMA method, and its computational efficiency can be hundreds of times faster than the original deconvolution-based MMA method. Moreover, a noise analysis for our proposed truncated method is also conducted to further evaluate its performances. The results of numerical simulation and physical experiments support our analyses and conclusions.

Learning the Cost Function for Foothold Selection in a Quadruped Robot.

This paper is focused on designing a cost function of selecting a foothold for a physical quadruped robot walking on rough terrain. The quadruped robot is modeled with Denavit⁻Hartenberg (DH) parameters, and then a default foothold is defined based on the model. Time of Flight (TOF) camera is used to perceive terrain information and construct a 2.5D elevation map, on which the terrain features are detected. The cost function is defined as the weighted sum of several elements including terrain features and some features on the relative pose between the default foothold and other candidates. It is nearly impossible to hand-code the weight vector of the function, so the weights are learned using Supporting Vector Machine (SVM) techniques, and the training data set is generated from the 2.5D elevation map of a real terrain under the guidance of experts. Four candidate footholds around the default foothold are randomly sampled, and the expert gives the order of such four candidates by rotating and scaling the view for seeing clearly. Lastly, the learned cost function is used to select a suitable foothold and drive the quadruped robot to walk autonomously across the rough terrain with wooden steps. Comparing to the approach with the original standard static gait, the proposed cost function shows better performance.

Diagnosis of breast cancer based on microcalcifications using grating-based phase contrast CT.

OBJECTIVES: Microcalcifications are an important feature in the diagnosis of breast cancer, especially in the early stages. In this paper, a CT-based method is proposed to potentially distinguish benign and malignant breast diseases based on the distributions of microcalcifications using grating-based phase-contrast imaging on a conventional X-ray tube. METHODS: The method presented based on the ratio of dark-field signals to attenuation signals in CT images is compared with the existing method based on the ratio in projections, and the threshold for the classification of microcalcifications in the two types of breast diseases is obtained using our approach. The experiment was operated on paraffin-fixed specimens that originated from 20 female patients ranging from 27-65 years old. RESULTS: Compared with the method based on projection images (AUC = 0.87), the proposed method is more effective (AUC = 0.95) to distinguish the two types of diseases. The discrimination threshold of microcalcifications for the classification of diseases in CT images is found to be 3.78 based on the Youden index. CONCLUSIONS: The proposed method can be further developed to improve the early diagnosis and diagnostic accuracy and reduce the clinical misdiagnosis rate of breast cancer. KEY POINTS: • Microcalcifications are of special importance to indicate early breast cancer. • Grating-based phase-contrast imaging can improve the diagnosis of breast cancers. • The method described here can better classify benign and malignant breast diseases.

Virtual scatter modulation for X-ray CT scatter correction using primary modulator.

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.

Cardiac CT: A system architecture study.

BACKGROUND: We are interested in exploring dedicated, high-performance cardiac CT systems optimized to provide the best tradeoff between system cost, image quality, and radiation dose. OBJECTIVE: We sought to identify and evaluate a broad range of CT architectures that could provide an optimal, dedicated cardiac CT solution. METHODS: We identified and evaluated thirty candidate architectures using consistent design choices. We defined specific evaluation metrics related to cost and performance. We then scored the candidates versus the defined metrics. Lastly, we applied a weighting system to combine scores for all metrics into a single overall score for each architecture. CT experts with backgrounds in cardiovascular radiology, x-ray physics, CT hardware and CT algorithms performed the scoring and weighting. RESULTS: We found nearly a twofold difference between the most and the least promising candidate architectures. Architectures employed by contemporary commercial diagnostic CT systems were among the highest-scoring candidates. We identified six architectures that show sufficient promise to merit further in-depth analysis and comparison. CONCLUSION: Our results suggest that contemporary diagnostic CT system architectures outperform most other candidates that we evaluated, but the results for a few alternatives were relatively close. We selected six representative high-scoring candidates for more detailed design and further comparative evaluation.

Fast kV-switching and dual-layer flat-panel detector enabled cone-beam CT joint spectral imaging.

Purpose. Fast kV-switching (FKS) and dual-layer flat-panel detector (DL-FPD) technologies have been actively studied as promising dual-energy spectral imaging solutions for FPD-based cone-beam computed tomography (CT). However, cone-beam CT (CBCT) spectral imaging is known to face challenges in obtaining accurate and robust material discrimination performance. That is because the energy separation by either FKS or DL-FPD, alone, is still limited, along with apparently unpaired signal levels in the effective low- and high-energy projections in real applications, not to mention the x-ray scatter in cone-beam scan which will make the material decomposition almost impossible if no correction is applied. To further improve CBCT spectral imaging capability, this work aims to promote a source-detector joint multi-energy spectral imaging solution which takes advantages of both FKS and DL-FPD, and to conduct a feasibility study on the first tabletop CBCT system with the joint spectral imaging capability developed.Methods. For CBCT, development of multi-energy spectral imaging can be jointly realized by using an x-ray source with a generator whose kilo-voltages can alternate in tens of Hertz (i.e. FKS), and a DL-FPD whose top- and bottom-layer projections corresponds to different effective energy levels. Thanks to the complimentary characteristics inherent in FKS and DL-FPD, the overall energy separation will be significantly better when compared with FKS or DL-FPD alone, and the x-ray photon detection efficiency will be also improved when compared with FKS alone. In this work, a noise performance analysis using the Cramér-Rao lower bound (CRLB) method is conducted. The CRLB for basis material after a projection-domain material decomposition is derived, followed by a set of numerical calculations of CRLBs, for the FKS, the DL-FPD and the joint solution, respectively. To compensate for the slightly angular mismatch between low- and high- projections in FKS, a dual-domain projection completion scheme is implemented. Afterwards material decomposition from the complete projection data is carried out by using the maximum-likelihood method, followed by reconstruction of basis material and virtual monochromatic images (VMI). In this work, the first FKS and DL-FPD jointly enabled multi-energy tabletop CBCT system, to the best of our knowledge, has been developed in our laboratory. To evaluate its spectral imaging performance, a set of physics experiments are conducted, where the multi-energy and head phantoms are scanned using the 80/105/130 kVp switching pairs and projection data are collected using a prototype DL-FPD, whose both top and bottom layer of panels are composed of 550µm of cesium iodine (CsI) scintillators with no intermediate metal filter in-between.Results. The numerical simulations show that the joint spectral imaging solution can lead to a significant improvement in energy separation and lower noise levels in most of material decomposition cases. The physics experiments confirmed the feasibility and superiority of the joint spectral imaging, whose CNRs in the selected regions of interest of the multi-energy phantom were boosted by an average improvement of 21.9%, 20.4% for water basis images and 32.8%, 62.8% for iodine images when compared with that of the FKS and DL-FPD, respectively. For the head phantom case, the joint spectral imaging can effectively reduce the streaking artifacts as well, and the standard deviation in the selected regions of interest are reduced by an average decrement of 19.5% and 8.1% for VMI when compared with that of the FKS and DL-FPD, respectively.Conclusions. A feasibility study of the joint spectral imaging solution for CBCT by utilizing both the FKS and DL-FPD was conducted, with the first tabletop CBCT system having such a capability being developed, which exhibits improved CNR and is more effective in avoiding streaking artifacts as expected.

Multi-energy blended CBCT spectral imaging and scatter-decoupled material decomposition using a spectral modulator with flying focal spot (SMFFS).

BACKGROUND: Cone-beam CT (CBCT) has been extensively employed in industrial and medical applications, such as image-guided radiotherapy and diagnostic imaging, with a growing demand for quantitative imaging using CBCT. However, conventional CBCT can be easily compromised by scatter and beam hardening artifacts, and the entanglement of scatter and spectral effects introduces additional complexity. PURPOSE: The intertwined scatter and spectral effects within CBCT pose significant challenges to the quantitative performance of spectral imaging. In this work, we present the first attempt to develop a stationary spectral modulator with flying focal spot (SMFFS) technology as a promising, low-cost approach to accurately solving the x-ray scattering problem and physically enabling spectral imaging in a unified framework, and with no significant misalignment in data sampling of spectral projections. METHODS: To deal with the intertwined scatter-spectral challenge, we propose a novel scatter-decoupled material decomposition (SDMD) method for SMFFS, which consists of four steps in total, including (1) spatial resolution-preserved and noise-suppressed multi-energy "residual" projection generation free from scatter, based on a hypothesis of scatter similarity; (2) first-pass material decomposition from the generated multi-energy residual projections in non-penumbra regions, with a structure similarity constraint to overcome the increased noise and penumbra effect; (3) scatter estimation for complete data; and (4) second-pass material decomposition for complete data by using a multi-material spectral correction method. Monte Carlo simulations of a pure-water cylinder phantom with different focal spot deflections are conducted to validate the scatter similarity hypothesis. Both numerical simulations using a clinical abdominal CT dataset, and physics experiments on a tabletop CBCT system using a Gammex multi-energy CT phantom and an anthropomorphic chest phantom, are carried out to demonstrate the feasibility of CBCT spectral imaging with SMFFS and our proposed SDMD method. RESULTS: Monte Carlo simulations show that focal spot deflections within a range of 2 mm share quite similar scatter distributions overall. Numerical simulations demonstrate that SMFFS with SDMD method can achieve better material decomposition and CT number accuracy with fewer artifacts. In physics experiments, for the Gammex phantom, the average error of the mean values ( E RMSE ROI $E^{\text{ROI}}_{\text{RMSE}}$ ) in selected regions of interest (ROIs) of virtual monochromatic image (VMI) at 70 keV is 8 HU in SMFFS cone-beam (CB) scan, and 19 and 210 HU in sequential 80/120 kVp (dual kVp, DKV) CB scan with and without scatter correction, respectively. For the chest phantom, the E RMSE ROI $E^{\text{ROI}}_{\text{RMSE}}$ in selected ROIs of VMIs is 12 HU for SMFFS CB scan, and 15 and 438 HU for sequential 80/140 kVp CB scan with and without scatter correction, respectively. Also, the non-uniformity among selected regions of the chest phantom is 14 HU for SMFFS CB scan, and 59 and 184 HU for the DKV CB scan with and without a traditional scatter correction method, respectively. CONCLUSIONS: We propose a SDMD method for CBCT with SMFFS. Our preliminary results show that SMFFS can enable spectral imaging with simultaneous scatter correction for CBCT and effectively improve its quantitative imaging performance.

An analytical form of ring artifact correction for computed tomography based on directional gradient domain optimization.

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.

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.

Deep-Learning-Based Metal Artefact Reduction With Unsupervised Domain Adaptation Regularization for Practical CT Images.

CT metal artefact reduction (MAR) methods based on supervised deep learning are often troubled by domain gap between simulated training dataset and real-application dataset, i.e., methods trained on simulation cannot generalize well to practical data. Unsupervised MAR methods can be trained directly on practical data, but they learn MAR with indirect metrics and often perform unsatisfactorily. To tackle the domain gap problem, we propose a novel MAR method called UDAMAR based on unsupervised domain adaptation (UDA). Specifically, we introduce a UDA regularization loss into a typical image-domain supervised MAR method, which mitigates the domain discrepancy between simulated and practical artefacts by feature-space alignment. Our adversarial-based UDA focuses on a low-level feature space where the domain difference of metal artefacts mainly lies. UDAMAR can simultaneously learn MAR from simulated data with known labels and extract critical information from unlabeled practical data. Experiments on both clinical dental and torso datasets show the superiority of UDAMAR by outperforming its supervised backbone and two state-of-the-art unsupervised methods. We carefully analyze UDAMAR by both experiments on simulated metal artefacts and various ablation studies. On simulation, its close performance to the supervised methods and advantages over the unsupervised methods justify its efficacy. Ablation studies on the influence from the weight of UDA regularization loss, UDA feature layers, and the amount of practical data used for training further demonstrate the robustness of UDAMAR. UDAMAR provides a simple and clean design and is easy to implement. These advantages make it a very feasible solution for practical CT MAR.

Dual-energy head cone-beam CT using a dual-layer flat-panel detector: Hybrid material decomposition and a feasibility study.

BACKGROUND: Flat panel detector (FPD) based cone-beam computed tomography (CT) has made tremendous progress in the last two decades, with many new and advanced medical and industrial applications keeping emerging from diagnostic imaging and image guidance for radiotherapy and interventional surgery. The current cone-beam CT (CBCT), however, is still suboptimal for head CT scan which requires a high standard of image quality. While the dual-layer FPD technology is under extensive development and is promising to further advance CBCT from qualitative anatomic imaging to quantitative dual-energy CT, its potential of enabling head CBCT applications has not yet been fully investigated. PURPOSE: The relatively moderate energy separation from the dual-layer FPD and the overall low signal level especially at the bottom-layer detector, could raise significant challenges in performing high-quality dual-energy material decomposition (MD). In this work, we propose a hybrid, physics and model guided, MD algorithm that attempts to fully use the detected x-ray signals and prior-knowledge behind head CBCT using dual-layer FPD. METHODS: Firstly, a regular projection-domain MD is performed as initial results of our approach and for comparison as conventional method. Secondly, based on the combined projection, a dual-layer multi-material spectral correction (dMMSC) is applied to generate beam hardening free images. Thirdly, the dMMSC corrected projections are adopted as a physics-model based guidance to generate a hybrid MD. A set of physics experiments including fan-beam scan and cone-beam scan using a head phantom and a Gammex Multi-Energy CT phantom are conducted to validate our proposed approach. RESULTS: The combined reconstruction could reduce noise by about 10% with no visible resolution degradation. The fan-beam studies on the Gammex phantom demonstrated an improved MD performance, with the averaged iodine quantification error for the 5-15 mg/ml iodine inserts reduced from about 5.6% to 3.0% by the hybrid method. On fan-beam scan of the head phantom, our proposed hybrid MD could significantly reduce the streak artifacts, with CT number nonuniformity (NU) in the selected regions of interest (ROIs) reduced from 23 Hounsfield Units (HU) to 4.2 HU, and the corresponding noise suppressed from 31 to 6.5 HU. For cone-beam scan, after scatter correction (SC) and cone-beam artifact reduction (CBAR), our approach can also significantly improve image quality, with CT number NU in the selected ROI reduced from 24.2 to 6.6 HU and the noise level suppressed from 22.1 to 8.2 HU. CONCLUSIONS: Our proposed physics and model guided hybrid MD for dual-layer FPD based head CBCT can significantly improve the robustness of MD and suppress the low-signal artifact. This preliminary feasibility study also demonstrated that the dual-layer FPD is promising to enable head CBCT spectral imaging.

Empirical cupping correction for CT scanners with primary modulation (ECCP).

PURPOSE: X-ray CT measures the attenuation of polychromatic x-rays through an object. The raw data acquired, which are the negative logarithm of the relative x-ray intensity behind the patient, must undergo water precorrection to linearize the measurement and to convert them into line integrals that are ready for reconstruction. The function to linearize the measured projection data depends on the detected spectrum of the ray. This spectrum may vary as a function of the detector position, e.g., in cases where the heel effect becomes relevant, where a bow-tie filter introduces channel-dependent beam hardening, or where a primary modulator is used to modulate the primary intensity of the spectrum. METHODS: The authors propose a new approach that allows to handle these effects in a highly convenient way. Their new empirical cupping correction for primary modulation (ECCP) corrects for artifacts, such as cupping artifacts or ring artifacts, which are induced by nonlinearities in the projection data due to spatially varying pre- or postfiltration of the x-rays. To do so, ECCP requires only a simple scan of a homogeneous phantom of nearly arbitrary shape. Based on this information, coefficients of a polynomial series are calculated and stored for later use. RESULTS: Physical measurements demonstrate the quality of the precorrection that can be achieved using ECCP to remove the cupping artifacts and to obtain well-calibrated CT values even in cases of strong primary modulation. A combination of ECCP with analytical techniques yielding a hybrid cupping correction method is possible and allows for channel-dependent correction functions. CONCLUSION: The proposed ECCP method is a very effective and easy to incorporate approach that compensates for even strong detector channel-dependent changes of the detected spectrum. © 2011 American Association of Physicists in Medicine.

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.

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.

Fluence adaptation for contrast-based dose optimization in x-ray phase-contrast imaging.

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.

An analysis of scatter characteristics in x-ray CT spectral correction.

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.

Modulator design for x-ray scatter correction using primary modulation: material selection.

PURPOSE: An optimal material selection for primary modulator is proposed in order to minimize beam hardening of the modulator in x-ray cone-beam computed tomography (CBCT). Recently, a measurement-based scatter correction method using primary modulation has been developed and experimentally verified. In the practical implementation, beam hardening of the modulator blocker is a limiting factor because it causes inconsistency in the primary signal and therefore degrades the accuracy of scatter correction. METHODS: This inconsistency can be purposely assigned to the effective transmission factor of the modulator whose variation as a function of object filtration represents the magnitude of beam hardening of the modulator. In this work, the authors show that the variation reaches a minimum when the K-edge of the modulator material is near the mean energy of the system spectrum. Accordingly, an optimal material selection can be carried out in three steps. First, estimate and evaluate the polychromatic spectrum for a given x-ray system including both source and detector; second, calculate the mean energy of the spectrum and decide the candidate materials whose K-edge energies are near the mean energy; third, select the optimal material from the candidates after considering both the magnitude of beam hardening and the physical and chemical properties. RESULTS: A tabletop x-ray CBCT system operated at 120 kVp is used to validate the material selection method in both simulations and experiments, from which the optimal material for this x-ray system is then chosen. With the transmission factor initially being 0.905 and 0.818, simulations show that erbium provides the least amount of variation as a function of object filtrations (maximum variations are 2.2% and 4.3%, respectively, only one-third of that for copper). With different combinations of aluminum and copper filtrations (simulating a range of object thicknesses), measured overall variations are 2.5%, 1.0%, and 8.6% for 25.4 microm of copper, erbium, and tungsten, respectively. With and without 300 microm of copper in the beam, the measured variations for 25.4 microm of copper, erbium, and tungsten, 1 mm of aluminum, as well as 406 microm of copper, are 1.8%, 0.2%, 5.5%, 1.9%, and 7.5%, respectively. CONCLUSIONS: The spatial variation in the effective transmission factor of the modulator blocker due to beam hardening caused by the modulator itself reaches a minimum when the K-edge of the modulator material is near the mean energy of the spectrum. An optimal modulator material selection using the K-edge discontinuity is therefore proposed.

Shading correction for on-board cone-beam CT in radiation therapy using planning MDCT images.

PURPOSE: Applications of cone-beam CT (CBCT) to image-guided radiationtherapy (IGRT) are hampered by shading artifacts in the reconstructed images. These artifacts are mainly due to scatter contamination in the projections but also can result from uncorrected beam hardening effects as well as nonlinearities in responses of the amorphous silicon flat panel detectors. While currently, CBCT is mainly used to provide patient geometry information for treatment setup, more demanding applications requiring high-quality CBCT images are under investigation. To tackle these challenges, many CBCT correction algorithms have been proposed; yet, a standard approach still remains unclear. In this work, we propose a shading correction method for CBCT that addresses artifacts from low-frequency projection errors. The method is consistent with the current workflow of radiation therapy. METHODS: With much smaller inherent scatter signals and more accurate detectors, diagnostic multidetector CT (MDCT) provides high quality CT images that are routinely used for radiation treatment planning. Using the MDCT image as "free" prior information, we first estimate the primary projections in the CBCT scan via forward projection of the spatially registered MDCT data. Since most of the CBCT shading artifacts stem from low-frequency errors in the projections such as scatter, these errors can be accurately estimated by low-pass filtering the difference between the estimated and raw CBCT projections. The error estimates are then subtracted from the raw CBCT projections. Our method is distinct from other published correction methods that use the MDCT image as a prior because it is projection-based and uses limited patient anatomical information from the MDCT image. The merit of CBCT-based treatment monitoring is therefore retained. RESULTS: The proposed method is evaluated using two phantom studies on tabletop systems. On the Catphan 600 phantom, our approach reduces the reconstruction error from 348 Hounsfield unit (HU) without correction to 4 HU around the object center after correction, and from 375 HU to 17 HU in the high-contrast regions. In the selected regions of interest (ROIs), the average image contrast is increased by a factor of 3.3. When noise suppression is implemented, the proposed correction substantially improves the contrast-to-noise ratio (CNR) and therefore the visibility of low-contrast objects, as seen in a more challenging pelvis phantom study. Besides a significant improvement in image uniformity, a low-contrast object of approximately 25 HU, which is otherwise buried in the shading artifacts, can be clearly identified after the proposed correction due to a CNR increase of 3.1. Compared to a kernel-based scatter correction method coupled with an analytical beam hardening correction, our approach also shows an overall improved performance with some residual artifacts. CONCLUSIONS: By providing effective shading correction, our approach has the potential to improve the accuracy of more advanced CBCT-based clinical applications for IGRT, such as tumor delineation and dose calculation.

Scatter correction method for x-ray CT using primary modulation: phantom studies.

PURPOSE: Scatter correction is a major challenge in x-ray imaging using large area detectors. Recently, the authors proposed a promising scatter correction method for x-ray computed tomography (CT) using primary modulation. Proof of concept was previously illustrated by Monte Carlo simulations and physical experiments on a small phantom with a simple geometry. In this work, the authors provide a quantitative evaluation of the primary modulation technique and demonstrate its performance in applications where scatter correction is more challenging. METHODS: The authors first analyze the potential errors of the estimated scatter in the primary modulation method. On two tabletop CT systems, the method is investigated using three phantoms: A Catphan 600 phantom, an anthropomorphic chest phantom, and the Catphan 600 phantom with two annuli. Two different primary modulators are also designed to show the impact of the modulator parameters on the scatter correction efficiency. The first is an aluminum modulator with a weak modulation and a low modulation frequency, and the second is a copper modulator with a strong modulation and a high modulation frequency. RESULTS: On the Catphan 600 phantom in the first study, the method reduces the error of the CT number in the selected regions of interest (ROIs) from 371.4 to 21.9 Hounsfield units (HU); the contrast to noise ratio also increases from 10.9 to 19.2. On the anthropomorphic chest phantom in the second study, which represents a more difficult case due to the high scatter signals and object heterogeneity, the method reduces the error of the CT number from 327 to 19 HU in the selected ROIs and from 31.4% to 5.7% on the overall average. The third study is to investigate the impact of object size on the efficiency of our method. The scatter-to-primary ratio estimation error on the Catphan 600 phantom without any annulus (20 cm in diameter) is at the level of 0.04, it rises to 0.07 and 0.1 on the phantom with an elliptical annulus (30 cm in the minor axis and 38 cm in the major axis) and with a circular annulus (38 cm in diameter). CONCLUSIONS: On the three phantom studies, good scatter correction performance of the proposed method has been demonstrated using both image comparisons and quantitative analysis. The theory and experiments demonstrate that a strong primary modulation that possesses a low transmission factor and a high modulation frequency is preferred for high scatter correction accuracy.

A dual-domain deep learning-based reconstruction method for fully 3D sparse data helical CT.

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.