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The cosine-model analysis (CMA) method and the small angle x-ray scattering (SAXS) method are two major types of information retrieval algorithms, commonly utilized in x-ray phase-contrast imaging with a grating interferometer. However, there are significant differences between the two methods in algorithm implementation, and the existing literature has not completely revealed their intrinsic relationship. In this paper, we theoretically derive and experimentally verify the intrinsic connections between CMA and SAXS, and it is seen that SAXS can be interpreted well by the cosine-model assumption of CMA. To validate our analysis of the scattering distribution when applying the cosine model to the convolution used in SAXS, we applied a deconvolution process into CMA before using the Fourier transform to get the three contrasts. Furthermore, the principal component analysis (PCA) is introduced in this work, and two PCA-based retrieval algorithms are presented in order to simplify the iteration process of deconvolution in SAXS or to obtain absorption and dark-field signals instead of the Fourier transform in CMA. Applying a quantitative structural similarity (SSIM) index and a profile analysis to the results of an ex vivo mammography, it is proved that retrieved images via CMA and SAXS are consistent with each other (SSIM values are 1.0000, 0.9845 and 0.9767 respectively), and that the extra deconvolution process applied into CMA shows a good performance and our analytical analysis of the scattering distribution is valid when applying the cosine model to the convolution used in SAXS. Besides, it is concluded that PCA shows almost the same performance with the Fourier transform (SSIM values are 1.0000 for both absorption and dark-field images), and the simplified SAXS-analogous method works well with higher efficiency in computation and better stability relative to the original SAXS, while maintaining the similar level of image quality (SSIM values are 1.0000, 0.9839 and 0.9781 respectively).

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.

Purpose: To quantitatively evaluate and compare six proposed system architectures for cardiac CT scanning., Methods: Starting from the clinical requirements for cardiac CT, we defined six dedicated cardiac CT architectures. We selected these architectures based on a previous screening study and defined them in sufficient detail to comprehensively analyze their cost and performance. We developed rigorous comparative evaluation methods for the most important aspects of performance and cost, and we applied these evaluation criteria to the defined cardiac CT architectures., Results: We found that CT system architectures based on the third-generation geometry provide nearly linear performance improvement versus the increased cost of additional beam lines (i.e., source-detector pairs), although similar performance improvement could be achieved with advanced motion-correction algorithms. The third-generation architectures outperform even the most promising of the proposed architectures that deviate substantially from the traditional CT system architectures., Conclusion: This work confirms the validity of the current trend in commercial CT scanner design. However, we anticipate that over time, CT hardware and software technologies will evolve, the relative importance of the performance criteria will change, the relative costs of components will vary, some of the remaining challenges will be addressed, and perhaps new candidate architectures will be identified; therefore, the conclusion of a comparative analysis like this may change. The evaluation methods that we used can provide a framework for other researchers to analyze their own proposed CT architectures., (© 2017 American Association of Physicists in Medicine.)

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.

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.

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. [ABSTRACT FROM AUTHOR]

Purpose: Applications of cone-beam CT (CBCT) to image-guided radiation therapy (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 ∼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. [ABSTRACT FROM AUTHOR]