Line Integral Alternating Minimization Algorithm for Dual-Energy X-Ray CT Image Reconstruction

Chen, Yaqi; O'Sullivan, Joseph A.; Politte, David G.; Evans, Joshua; Han, Dong; Whiting, Bruce R.; Williamson, Jeffrey F.

doi:10.1109/tmi.2015.2490658

Cited by 16 publications

(26 citation statements)

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“…However, all of these studies have been limited to the post reconstruction scenario where only spectrally averaged linear attenuation coefficients need to be accurately estimated. Our prior and current work demonstrate the potential of iterative statistical image‐reconstruction (SIR) algorithms, based on physically accurate spectral and scatter distribution measurements, to limit input errors to the < 0.5% level required to address the poorly conditioned problem of DECT low‐energy cross‐section mapping. For example, by using a polyenergetic alternating minimization (AM) reconstruction process was able to limit image‐nonuniformity errors to 0.3%, independently of phantom size and location therein using a commercial 16‐row CT scanner.…”

Section: Discussionmentioning

confidence: 85%

“…For example, by using a polyenergetic alternating minimization (AM) reconstruction process was able to limit image‐nonuniformity errors to 0.3%, independently of phantom size and location therein using a commercial 16‐row CT scanner. Our subsequent SIR extensions reconstruct the

()(, c_{1} (x), c_{2} (x))

image directly by operating jointly on unprocessed low‐ and high‐energy experimentally acquired sinograms . Such innovations would not be possible without the BVM model, which accurately and efficiently (due to its linearity and separability) supports estimation of monoenergetic linear attenuation coefficients.…”

Section: Discussionmentioning

confidence: 99%

“…For example, the DECT stoichiometric technique for postreconstruction mapping of electron density and mean excitation energy for proton therapy requires only that the model predict spectrally averaged linear attenuation coefficients in the diagnostic CT energy range. On the other hand, model‐based CT image‐reconstruction algorithms that incorporate higher order beam‐hardening corrections require that the model accurately predict monoenergetic linear attenuation coefficients across the entire diagnostic X‐ray energy range, while using QDECT to support Monte Carlo‐based treatment planning for low‐energy brachytherapy requires high accurate monoenergetic predictions down to 20 keV for partial cross‐sections, differential cross‐sections, and energy‐absorption coefficients as well as total linear attenuation coefficients …”

Section: Introductionmentioning

confidence: 99%

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Technical Note: On the accuracy of parametric two-parameter photon cross-section models in dual-energy CT applications

et al. 2017

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Purpose To evaluate and compare the theoretically achievable accuracy of two families of two-parameter photon cross-section models: basis vector model (BVM) and modified parametric fit model (mPFM). Method The modified PFM assumes that photoelectric absorption and scattering cross sections can be accurately represented by power functions in effective atomic number and/or energy plus the Klein-Nishina cross section, along with empirical corrections that enforce exact prediction of elemental cross sections. Two PFM variants were investigated: the widely used Torikoshi model (tPFM) and a more complex “VCU” variant (vPFM). For 43 standard soft and bony tissues and phantom materials, all consisting of elements with atomic number less than 20 (except iodine), we evaluated the theoretically achievable accuracy of tPFM and vPFM for predicting linear attenuation, photoelectric absorption, and energy absorption coefficients, and we compared it to a previously investigated separable, linear two-parameter model, BVM. Results For an idealized dual-energy computed tomography (DECT) imaging scenario, the cross-section mapping process demonstrates that BVM more accurately predicts photon cross sections of biological mixtures than either tPFM or vPFM. Maximum linear attenuation coefficient prediction errors were 15% and 5% for tPFM and BVM, respectively. The root-mean-square (RMS) prediction errors of total linear attenuation over the 20 keV to 1000 keV energy range of tPFM and BVM were 0.93% (tPFM) and 0.1% (BVM) for adipose tissue, 0.8% (tPFM) and 0.2% (BVM) for muscle tissue, and 1.6% (tPFM) and 0.2% (BVM) for cortical bone tissue. With exception of the thyroid and Teflon, the RMS error for photoelectric absorption and scattering coefficient was within 4% for the tPFM and 2% for the BVM. Neither model predicts the photon cross sections of thyroid tissue accurately, exhibiting relative errors as large as 20%. For the energy absorption coefficients prediction error, RMS errors for the BVM were less than 1.5%, while for the tPFM, the RMS errors were as large as 16%. Conclusion Compared to modified PFMs, BVM shows superior potential to support dual-energy CT cross-section mapping. In addition, the linear, separable BVM can be more efficiently deployed by iterative model-based DECT image reconstruction algorithms.

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Section: Discussionmentioning

confidence: 85%

()(, c_{1} (x), c_{2} (x))

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Technical Note: On the accuracy of parametric two-parameter photon cross-section models in dual-energy CT applications

et al. 2017

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“…ADMM is suitable for constrained optimization problems and is being used extensively since past few years [30,31,32,33]. This technique facilitates solution by decomposing the original objective function into multiple objective functions that are easy to solve.…”

Section: Algorithm Designmentioning

confidence: 99%

Double temporal sparsity based accelerated reconstruction of compressively sensed resting-state fMRI

Aggarwal

Gupta

2017

Computers in Biology and Medicine

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A number of reconstruction methods have been proposed recently for accelerated functional Magnetic Resonance Imaging (fMRI) data collection. However, existing methods suffer with the challenge of greater artifacts at high acceleration factors. This paper addresses the issue of accelerating fMRI collection via undersampled k -space measurements combined with the proposed Double Temporal Sparsity based Reconstruction (DTSR) method with the l 1 − l 1 norm constraint. The robustness of the proposed DTSR method has been thoroughly evaluated both at the subject level and at the group level on real fMRI data. Results are presented at various acceleration factors. Quantitative analysis in terms of Peak Signal-to-Noise Ratio (PSNR) and other metrics, and qualitative analysis in terms of reproducibility of brain Resting State Networks (RSNs) demonstrate that the proposed method is accurate and robust. In addition, the proposed DTSR method preserves brain networks that are important for studying fMRI data. Compared to the existing accelerated fMRI reconstruction methods, the DTSR method shows promising potential with an improvement of 10-12dB in PSNR with acceleration factors upto 3.5. Simulation results on real data demonstrate that DTSR method can be used to acquire accelerated fMRI with accurate detection of RSNs.

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“…5,18 Forward projections require an accurate estimation of linear attenuation coefficients, µ(x,E) at any energy E in the scanning spectrum and voxel x in the scan subject. The polyenergetic forward projectors used by the iterative QDECT techniques reported to date 5,18,19 have been based upon the linear, separable, closed basis vector model (BVM), 16 which was first introduced into the CT image reconstruction field by Alvarez and Macovski. 20 In this study, we propose an adaptation of the linear separable two-parameter DECT BVM model for estimating proton stopping powers.…”

Section: Introductionmentioning

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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Line Integral Alternating Minimization Algorithm for Dual-Energy X-Ray CT Image Reconstruction

Cited by 16 publications

References 50 publications

Technical Note: On the accuracy of parametric two-parameter photon cross-section models in dual-energy CT applications

Technical Note: On the accuracy of parametric two-parameter photon cross-section models in dual-energy CT applications

Double temporal sparsity based accelerated reconstruction of compressively sensed resting-state fMRI

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

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