Energy-dependent Attenuation Coefficients Research Articles

Metal artifact reduction method based on a constrained beam-hardening estimator for polychromatic x-ray CT

Beam hardening in x-ray computed tomography (CT) is inevitable because of the polychromatic x-ray spectrum and energy-dependent attenuation coefficients of materials, leading to the underestimation of artifacts arising from projection data, especially on metal regions. State-of-the-art research on beam-hardening artifacts is based on a numerical method that recursively performs CT reconstruction, which leads to a heavy computational burden. To address this computational issue, we propose a constrained beam-hardening estimator that provides an efficient numerical solution via a linear combination of two images reconstructed only once during the entire process. The proposed estimator reflects the geometry of metal objects and physical characteristics of beam hardening during the transmission of polychromatic x-rays through a material. Most of the associated parameters are numerically obtained from an initial uncorrected CT image and forward projection transformation without additional optimization procedures. Only the unknown parameter related to beam-hardening artifacts is fine-tuned by linear optimization, which is performed only in the reconstruction image domain. The proposed approach was systematically assessed using numerical simulations and phantom data for qualitative and quantitative comparisons. Compared with existing sinogram inpainting-based and model-based approaches, the proposed scheme in conjunction with the constrained beam-hardening estimator not only provided improved image quality in areas surrounding the metal but also achieved fast beam-hardening correction owing to the analytical reconstruction structure. This work may have significant implications in improving dose calculation accuracy or target volume delineation for treatment planning in radiotherapy.

A new approach for reducing beam hardening artifacts in polychromatic X-ray computed tomography using more accurate prior image.

Metal artifacts severely degrade CT image quality in clinical diagnosis, which are difficult to removed, especially for the beam hardening artifacts. The metal artifact reduction (MAR) based on prior images are the most frequently-used methods. However, there exists a lot misclassification in most prior images caused by absence of prior information such as the spectrum distribution of X-ray beam source, especially many or big metal included. The purpose of this work is to find a more accurate prior image to improve image quality. The proposed method comprise of following four steps. First, the metal image is segmented by thresholding an initial image, where the metal traces are identified in the initial projection data using the forward projection of the metal image. Second, the accurate absorbent model of certain metal image is calculated according to the spectrum distribution of certain X-ray beam source and energy-dependent attenuation coefficients of metal. Then, a new metal image is reconstructed by the general analytical reconstruction algorithm such as filtered back projection (FPB). The prior image is obtained by segmenting the difference image between the initial image and the new metal image into air, tissue and bone. Finally, the initial projection data are normalized by dividing the projection data of prior image pixel to pixel, the corrected image is obtained by interpolation, denormalization and reconstruction. Some clinical images with dental fillings and knee prostheses are used to evaluate the proposed algorithm and normalized metal artifact reduction (NMAR) and linear interpolation (LI) method. The results demonstrate the artifacts can be reduced efficiently by the proposed method. The proposed method could obtain an exact prior image using the prior information about X-ray beam source and energy-dependent attenuation coefficients of metal. As a result, the better performance of reducing beam hardening artifacts can be improved, even though there were many or big implants. Moreover, the process of the proposed method is rather simple and little extra calculation burden is necessary. It has superiorities over other algorithms when include big or many implants.

Beam Hardening Correction Using Cone Beam Consistency Conditions.

The polychromatic X-ray spectrum and the energy-dependent attenuation coefficient of materials cause beam hardening artifacts in CT reconstructed volumes. These artifacts appear as cupping and streak artifacts depending on the material composition and the geometry of the imaged object. CT scanners employ projection linearization to transform polychromatic attenuation to monochromatic attenuation using a polynomial model. Polynomial coefficients are computed during calibration or using prior information such as X-ray spectrum and attenuation properties of the materials. In this paper, we are presenting a novel method to correct beam hardening artifacts by enforcing cone beam consistency conditions on the projection data. We used consistency conditions derived from Grangeat's fundamental relation between cone beam projection data and 3-D Radon transform. The optimal polynomial coefficients for artifact reduction are iteratively estimated by minimizing the inconsistency of a set of projection pairs. The results from simulated and real datasets show the visible reduction of artifacts. Our studies also demonstrate the robustness of the algorithm when the projections are perturbed with other physical measurement and geometrical errors. The proposed method requires neither calibration nor prior information like X-ray spectrum, attenuation properties of the materials and detector response. The algorithm can be used for beam hardening correction in clinical, pre-clinical, and industrial CT systems.

Reduce beam hardening artifacts ofpolychromatic X-ray computed tomography by an iterative approximation approach.

The beam hardening artifact is one of most important modalities of metal artifact for polychromatic X-ray computed tomography (CT), which can impair the image quality seriously. An iterative approach is proposed to reduce beam hardening artifact caused by metallic components in polychromatic X-ray CT. According to Lambert-Beer law, the (detected) projections can be expressed as monotonic nonlinear functions of element geometry projections, which are the theoretical projections produced only by the pixel intensities (image grayscale) of certain element (component). With help of a prior knowledge on spectrum distribution of X-ray beam source and energy-dependent attenuation coefficients, the functions have explicit expressions. Newton-Raphson algorithm is employed to solve the functions. The solutions are named as the synthetical geometry projections, which are the nearly linear weighted sum of element geometry projections with respect to mean of each attenuation coefficient. In this process, the attenuation coefficients are modified to make Newton-Raphson iterative functions satisfy the convergence conditions of fixed pointed iteration(FPI) so that the solutions will approach the true synthetical geometry projections stably. The underlying images are obtained using the projections by general reconstruction algorithms such as the filtered back projection (FBP). The image gray values are adjusted according to the attenuation coefficient means to obtain proper CT numbers. Several examples demonstrate the proposed approach is efficient in reducing beam hardening artifacts and has satisfactory performance in the term of some general criteria. In a simulation example, the normalized root mean square difference (NRMSD) can be reduced 17.52% compared to a newest algorithm. Since the element geometry projections are free from the effect of beam hardening, the nearly linear weighted sum of them, the synthetical geometry projections, are almost free from the effect of beam hardening. By working out the synthetical geometry projections, the proposed approach becomes quite efficient in reducing beam hardening artifacts.

Material decomposition with the multi-energy attenuation coefficient ratio by using a multiple discriminant analysis

The objective of this study was to develop a spectral CT system using a photon counting detector and to decompose materials by applying a multiple discriminant analysis (MDA) to the energy-dependent attenuation coefficient ratios. We imaged cylindrical phantoms of Polymethyl methacrylate (PMMA) with four holes filled with calcium chloride, iodine, and gold nanoparticle contrast agents. The attenuation coefficients were measured via reconstructed multi-energy images, and the linear attenuation ratio was used for material identification. The MDA projection matrix, determined from training phantoms, was used to identify the four materials in the testing phantoms. For quantification purposes, the relationships between the attenuation coefficients at multiple energy bins and the concentrations were characterized by using the least-squares method for each material. The mean identification accuracy for each of the three materials were 0.94 ± 0.09 for iodine, 0.96 ± 0.07 for gold nanoparticles, and 0.92 ± 0.05 for calcium chloride. The mean quantification errors were 1.90 ± 1.58% for iodine, 3.85 ± 3.13% for gold nanoparticle, and 3.40 ± 2.62% for calcium chloride. The developed multi-energy CT system based on the photon-counting detector with MDA can precisely decompose the four materials.

Metal Artifact Reduction for Polychromatic X-ray CT Based on a Beam-Hardening Corrector

This paper proposes a new method to correct beam hardening artifacts caused by the presence of metal in polychromatic X-ray computed tomography (CT) without degrading the intact anatomical images. Metal artifacts due to beam-hardening, which are a consequence of X-ray beam polychromaticity, are becoming an increasingly important issue affecting CT scanning as medical implants become more common in a generally aging population. The associated higher-order beam-hardening factors can be corrected via analysis of the mismatch between measured sinogram data and the ideal forward projectors in CT reconstruction by considering the known geometry of high-attenuation objects. Without prior knowledge of the spectrum parameters or energy-dependent attenuation coefficients, the proposed correction allows the background CT image (i.e., the image before its corruption by metal artifacts) to be extracted from the uncorrected CT image. Computer simulations and phantom experiments demonstrate the effectiveness of the proposed method to alleviate beam hardening artifacts.

X-ray and neutron attenuation correction factors for spherical samples

A method is derived to calculate the attenuation correction factors for elastic or inelastic X-ray or neutron scattering experiments using a spherical sample. The method can be applied to a sphere that is either fully or partially illuminated by an incident beam of rectangular cross-sectional area. The required input parameters are the energy-dependent attenuation coefficients, the radius of the sphere and the dimensions of the incident beam. In-plane scattering is assumed.

Build-up Factors for Medium Energy Neutrons up to 400 MeV

Neutron build-up factors were calculated for attenuation calculations for medium energy neutrons by the point kernel method. Neutron transport calculations were made by ANISN for concrete and iron shields with the DLC-87 multigroup cross section data. Energy-dependent attenuation coefficients were deduced from the obtained attenuation curves of source group neutrons. Neutron dose build-up factors were then calculated from the total dose equivalent data using the attenuation coefficients of the source neutrons. Characteristics of the build-up factors obtained were tested for a double layered shield, a concrete shield with variation in atomic composition and a finite thickness shield. An empirical fit to the energy spectra was also given