Attenuation coefficients of body tissues using principal-components analysis

Weaver, John B.; Huddleston, Alan L.

doi:10.1118/1.595759

Cited by 31 publications

(26 citation statements)

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“…Equations (13) and (14) show that the CRLB combines the effects of the attenuation coefficients of the object materials, since these are used as basis functions, and the detector noise covariance.…”

Section: C the Crlb For An Energy Selective X-ray Imaging Systemmentioning

confidence: 99%

“…(13) using Eq. (14) to compute the derivatives in the second term. The data were processed with the A-space method with a basis set consisting of the attenuation coefficients of bone and soft tissue for the two function case and adding either the attenuation coefficient of adipose tissue or the contrast agent as the third basis function.…”

Section: E Simulations Of Increase In Crlbmentioning

confidence: 99%

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Dimensionality and noise in energy selective x‐ray imaging

Alvarez¹

2013

Medical Physics

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Purpose:To develop and test a method to quantify the effect of dimensionality on the noise in energy selective x-ray imaging. Methods: The Cramèr-Rao lower bound (CRLB), a universal lower limit of the covariance of any unbiased estimator, is used to quantify the noise. It is shown that increasing dimensionality always increases, or at best leaves the same, the variance. An analytic formula for the increase in variance in an energy selective x-ray system is derived. The formula is used to gain insight into the dependence of the increase in variance on the properties of the additional basis functions, the measurement noise covariance, and the source spectrum. The formula is also used with computer simulations to quantify the dependence of the additional variance on these factors. Simulated images of an object with three materials are used to demonstrate the trade-off of increased information with dimensionality and noise. The images are computed from energy selective data with a maximum likelihood estimator. Results: The increase in variance depends most importantly on the dimension and on the properties of the additional basis functions. With the attenuation coefficients of cortical bone, soft tissue, and adipose tissue as the basis functions, the increase in variance of the bone component from two to three dimensions is 1.4 × 10 3 . With the soft tissue component, it is 2.7 × 10 4 . If the attenuation coefficient of a high atomic number contrast agent is used as the third basis function, there is only a slight increase in the variance from two to three basis functions, 1.03 and 7.4 for the bone and soft tissue components, respectively. The changes in spectrum shape with beam hardening also have a substantial effect. They increase the variance by a factor of approximately 200 for the bone component and 220 for the soft tissue component as the soft tissue object thickness increases from 1 to 30 cm. Decreasing the energy resolution of the detectors increases the variance of the bone component markedly with three dimension processing, approximately a factor of 25 as the resolution decreases from 100 to 3 bins. The increase with two dimension processing for adipose tissue is a factor of two and with the contrast agent as the third material for two or three dimensions is also a factor of two for both components. The simulated images show that a maximum likelihood estimator can be used to process energy selective x-ray data to produce images with noise close to the CRLB. Conclusions:The method presented can be used to compute the effects of the object attenuation coefficients and the x-ray system properties on the relationship of dimensionality and noise in energy selective x-ray imaging systems.

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Section: C the Crlb For An Energy Selective X-ray Imaging Systemmentioning

confidence: 99%

Section: E Simulations Of Increase In Crlbmentioning

confidence: 99%

Dimensionality and noise in energy selective x‐ray imaging

Alvarez¹

2013

Medical Physics

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“…7(a)], we compute some more objective image quality measures as well. The metrics we chose are: -divergence, since that is the metric over which our objective function is defined; mean percent bias (MPB); mean percent squared error (MPSE); and mean percent absolute error (MPAE) (28) (29) (30) where indexes the pixels in the region of interest, denotes the true image (from which the data was computed), denotes the image estimate, and denotes the average pixel value in the region of interest of the true image.…”

Section: A Quantifying Algorithm Performancementioning

confidence: 99%

“…We model as a linear combination of a small number of constituent substances (such as bone, fat, or aluminum) (3) where are the known linear attenuation coefficients (in mm ) at photon energy of the base substance in its pure form, and is the relative density of substance at pixel [26]- [28] (4)…”

Section: Data Modelmentioning

confidence: 99%

Pose estimation of known objects during transmission tomographic image reconstruction

Murphy

Yan

O'Sullivan

et al. 2006

IEEE Trans. Med. Imaging

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We address the problem of image formation in transmission tomography when metal objects of known composition and shape, but unknown pose, are present in the scan subject. Using an alternating minimization (AM) algorithm, derived from a model in which the detected data are viewed as Poisson-distributed photon counts, we seek to eliminate the streaking artifacts commonly seen in filtered back projection images containing high-contrast objects. We show that this algorithm, which minimizes the I-divergence (or equivalently, maximizes the log-likelihood) between the measured data and model-based estimates of the means of the data, converges much faster when knowledge of the high-density materials (such as brachytherapy applicators or prosthetic implants) is exploited. The algorithm incorporates a steepest descent-based method to find the position and orientation (collectively called the pose) of the known objects. This pose is then used to constrain the image pixels to their known attenuation values, or, for example, to form a mask on the "missing" projection data in the shadow of the objects. Results from two-dimensional simulations are shown in this paper. The extension of the model and methods used to three dimensions is outlined.

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“…The choice of basis material has been discussed previously by Weaver and Huddleston, 28 who used principal components analysis. However, the choice of water as the boundary material between low-Z and high-Z mixtures was suggested by Williamson et al 16 For our study, a water and polystyrene pair was selected for soft tissues (low-Z materials), while a water and aqueous CaCl 2 solution (23% concentration) pair was chosen for bony tissues (high-Z materials).…”

Section: A Basis Vector Modelmentioning

confidence: 99%

A linear, separable two-parameter model for dual energy CT imaging of proton stopping power computation

2016

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Purpose: To evaluate the accuracy and robustness of a simple, linear, separable, two-parameter model (basis vector model, BVM) in mapping proton stopping powers via dual energy computed tomography (DECT) imaging. Methods: The BVM assumes that photon cross sections (attenuation coefficients) of unknown materials are linear combinations of the corresponding radiological quantities of dissimilar basis substances (i.e., polystyrene, CaCl 2 aqueous solution, and water). The authors have extended this approach to the estimation of electron density and mean excitation energy, which are required parameters for computing proton stopping powers via the Bethe-Bloch equation. The authors compared the stopping power estimation accuracy of the BVM with that of a nonlinear, nonseparable photon cross section Torikoshi parametric fit model (VCU tPFM) as implemented by the authors and by Yang et al.["Theoretical variance analysis of single-and dual-energy computed tomography methods for calculating proton stopping power ratios of biological tissues," Phys. Med. Biol. 55, 1343-1362]. Using an idealized monoenergetic DECT imaging model, proton ranges estimated by the BVM, VCU tPFM, and Yang tPFM were compared to International Commission on Radiation Units and Measurements (ICRU) published reference values. The robustness of the stopping power prediction accuracy of tissue composition variations was assessed for both of the BVM and VCU tPFM. The sensitivity of accuracy to CT image uncertainty was also evaluated. Results: Based on the authors' idealized, error-free DECT imaging model, the root-mean-square error of BVM proton stopping power estimation for 175 MeV protons relative to ICRU reference values for 34 ICRU standard tissues is 0.20%, compared to 0.23% and 0.68% for the Yang and VCU tPFM models, respectively. The range estimation errors were less than 1 mm for the BVM and Yang tPFM models, respectively. The BVM estimation accuracy is not dependent on tissue type and proton energy range. The BVM is slightly more vulnerable to CT image intensity uncertainties than the tPFM models. Both the BVM and tPFM prediction accuracies were robust to uncertainties of tissue composition and independent of the choice of reference values. This reported accuracy does not include the impacts of I-value uncertainties and imaging artifacts and may not be achievable on current clinical CT scanners. Conclusions: The proton stopping power estimation accuracy of the proposed linear, separable BVM model is comparable to or better than that of the nonseparable tPFM models proposed by other groups. In contrast to the tPFM, the BVM does not require an iterative solving for effective atomic number and electron density at every voxel; this improves the computational efficiency of DECT imaging when iterative, model-based image reconstruction algorithms are used to minimize noise and systematic imaging artifacts of CT images. C

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Attenuation coefficients of body tissues using principal-components analysis

Cited by 31 publications

References 0 publications

Dimensionality and noise in energy selective x‐ray imaging

Dimensionality and noise in energy selective x‐ray imaging

Pose estimation of known objects during transmission tomographic image reconstruction

A linear, separable two-parameter model for dual energy CT imaging of proton stopping power computation

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