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

Estimation of Proton Stopping Power Ratio and Mean Excitation Energy Using Electron Density and Its Applications via Machine Learning Approach

Purpose

The purpose of this study was to develop a simple flexible method for accurate estimation of stopping power ratio (SPR) and mean excitation energy (I) using relative electron density (ρ e).

Materials and Methods

The model was formulated using empirical relationships between SPR, mean excitation energy I, and relative electron density. Some examples were implemented, and a comparison was carried out using other existing methods. The needed coefficients in the model were estimated using optimization tools. Basis vector method (BVM) and Hunemohr and Saito (H-S) method were applied to estimate the ρ e used in the application section. 80 kVp and 150 kVpSn were used as low and high energy, respectively, for the implementation of dual-energy methods.

Results

All the examples of the proposed method considered have modeling error that is ≤0.32% and testing root mean square error (RMSE) ≤0.92% for SPR with a mean error close to 0.00%. The method was able to achieve modeling RMSE of 2.12% for mean excitation energy with room for improvement. Similar or better results were achieved in application to BVM.

Conclusion

The method showed robustness in application by achieving lower testing error than other presented methods in most cases. It achieved accurate estimation which can be improved using the machine learning algorithm since it is flexible to implement in terms of the function (model) degree and tissue classification.

MB-DECTNet: a model-based unrolling network for accurate 3D dual-energy CT reconstruction from clinically acquired helical scans

Objective.Over the past several decades, dual-energy CT (DECT) imaging has seen significant advancements due to its ability to distinguish between materials. DECT statistical iterative reconstruction (SIR) has exhibited potential for noise reduction and enhanced accuracy. However, its slow convergence and substantial computational demands render the elapsed time for 3D DECT SIR often clinically unacceptable. The objective of this study is to accelerate 3D DECT SIR while maintaining subpercentage or near-subpercentage accuracy.Approach.We incorporate DECT SIR into a deep-learning model-based unrolling network for 3D DECT reconstruction (MB-DECTNet), which can be trained end-to-end. This deep learning-based approach is designed to learn shortcuts between initial conditions and the stationary points of iterative algorithms while preserving the unbiased estimation property of model-based algorithms. MB-DECTNet comprises multiple stacked update blocks, each containing a data consistency layer (DC) and a spatial mixer layer, with the DC layer functioning as a one-step update from any traditional iterative algorithm.Main results.The quantitative results indicate that our proposed MB-DECTNet surpasses both the traditional image-domain technique (MB-DECTNet reduces average bias by a factor of 10) and a pure deep learning method (MB-DECTNet reduces average bias by a factor of 8.8), offering the potential for accurate attenuation coefficient estimation, akin to traditional statistical algorithms, but with considerably reduced computational costs. This approach achieves 0.13% bias and 1.92% mean absolute error and reconstructs a full image of a head in less than 12 min. Additionally, we show that the MB-DECTNet output can serve as an initializer for DECT SIR, leading to further improvements in results.Significance.This study presents a model-based deep unrolling network for accurate 3D DECT reconstruction, achieving subpercentage error in estimating virtual monoenergetic images for a full head at 60 and 150 keV in 30 min, representing a 40-fold speedup compared to traditional approaches. These findings have significant implications for accelerating DECT SIR and making it more clinically feasible.

Motion-compensated scheme for sequential scanned statistical iterative dual-energy CT reconstruction

Objective.Dual-energy computed tomography (DECT) has been widely used to reconstruct numerous types of images due its ability to better discriminate tissue properties. Sequential scanning is a popular dual-energy data acquisition method as it requires no specialized hardware. However, patient motion between two sequential scans may lead to severe motion artifacts in DECT statistical iterative reconstructions (SIR) images. The objective is to reduce the motion artifacts in such reconstructions.Approach.We propose a motion-compensation scheme that incorporates a deformation vector field into any DECT SIR. The deformation vector field is estimated via the multi-modality symmetric deformable registration method. The precalculated registration mapping and its inverse or adjoint are then embedded into each iteration of the iterative DECT algorithm.Main results.Results from a simulated and clinical case show that the proposed framework is capable of reducing motion artifacts in DECT SIRs. Percentage mean square errors in regions of interest in the simulated and clinical cases were reduced from 4.6% to 0.5% and 6.8% to 0.8%, respectively. A perturbation analysis was then performed to determine errors in approximating the continuous deformation by using the deformation field and interpolation. Our findings show that errors in our method are mostly propagated through the target image and amplified by the inverse matrix of the combination of the Fisher information and Hessian of the penalty term.Significance.We have proposed a novel motion-compensation scheme to incorporate a 3D registration method into the joint statistical iterative DECT algorithm in order to reduce motion artifacts caused by inter-scan motion, and successfully demonstrate that interscan motion corrections can be integrated into the DECT SIR process, enabling accurate imaging of radiological quantities on conventional SECT scanners, without significant loss of either computational efficiency or accuracy.

Towards subpercentage uncertainty proton stopping-power mapping via dual-energy CT: Direct experimental validation and uncertainty analysis of a statistical iterative image reconstruction method

PURPOSE

To assess the potential of a joint dual-energy computerized tomography (CT) reconstruction process (statistical image reconstruction method built on a basis vector model (JSIR-BVM)) implemented on a 16-slice commercial CT scanner to measure high spatial resolution stopping-power ratio (SPR) maps with uncertainties of less than 1%.

METHODS

JSIR-BVM was used to reconstruct images of effective electron density and mean excitation energy from dual-energy CT (DECT) sinograms for 10 high-purity samples of known density and atomic composition inserted into head and body phantoms. The measured DECT data consisted of 90 and 140 kVp axial sinograms serially acquired on a Philips Brilliance Big Bore CT scanner without beam-hardening corrections. The corresponding SPRs were subsequently measured directly via ion chamber measurements on a MEVION S250 superconducting synchrocyclotron and evaluated theoretically from the known sample compositions and densities. Deviations of JSIR-BVM SPR values from their theoretically calculated and directly measured ground-truth values were evaluated for our JSIR-BVM method and our implementation of the Hünemohr-Saito (H-S) DECT image-domain decomposition technique for SPR imaging. A thorough uncertainty analysis was then performed for five different scenarios (comparison of JSIR-BVM stopping-power ratio/stopping power (SPR/SP) to International Commission on Radiation Measurements and Units benchmarks; comparison of JSIR-BVM SPR to measured benchmarks; and uncertainties in JSIR-BVM SPR/SP maps for patients of unknown composition) per the Joint Committee for Guides in Metrology and the Guide to Expression of Uncertainty in Measurement, including the impact of uncertainties in measured photon spectra, sample composition and density, photon cross section and I-value models, and random measurement uncertainty. Estimated SPR uncertainty for three main tissue groups in patients of unknown composition and the weighted proportion of each tissue type for three proton treatment sites were then used to derive a composite range uncertainty for our method.

RESULTS

Mean JSIR-BVM SPR estimates deviated by less than 1% from their theoretical and directly measured ground-truth values for most inserts and phantom geometries except for high-density Delrin and Teflon samples with SPR error relative to proton measurements of 1.1% and -1.0% (head phantom) and 1.1% and -1.1% (body phantom). The overall root-mean-square (RMS) deviations over all samples were 0.39% and 0.52% (head phantom) and 0.43% and 0.57% (body phantom) relative to theoretical and directly measured ground-truth SPRs, respectively. The corresponding RMS (maximum) errors for the image-domain decomposition method were 2.68% and 2.73% (4.68% and 4.99%) for the head phantom and 0.71% and 0.87% (1.37% and 1.66%) for the body phantom. Compared to H-S SPR maps, JSIR-BVM yielded 30% sharper and twofold sharper images for soft tissues and bone-like surrogates, respectively, while reducing noise by factors of 6 and 3, respectively. The uncertainty (coverage factor k = 1) of the DECT-to-benchmark values comparison ranged from 0.5% to 1.5% and is dominated by scanning-beam photon-spectra uncertainties. An analysis of the SPR uncertainty for patients of unknown composition showed a JSIR-BVM uncertainty of 0.65%, 1.21%, and 0.77% for soft-, lung-, and bony-tissue groups which led to a composite range uncertainty of 0.6-0.9%.

CONCLUSIONS

Observed JSIR-BVM SPR estimation errors were all less than 50% of the estimated k = 1 total uncertainty of our benchmarking experiment, demonstrating that JSIR-BVM high spatial resolution, low-noise SPR mapping is feasible and is robust to variations in the geometry of the scanned object. In contrast, the much larger H-S SPR estimation errors are dominated by imaging noise and residual beam-hardening artifacts. While the uncertainties characteristic of our current JSIR-BVM implementation can be as large as 1.5%, achieving < 1% total uncertainty is feasible by improving the accuracy of scanner-specific scatter-profile and photon-spectrum estimates. With its robustness to beam-hardening artifact, image noise, and variations in phantom size and geometry, JSIR-BVM has the potential to achieve high spatial-resolution SPR mapping with subpercentage accuracy and estimated uncertainty in the clinical setting.

Experimental implementation of a joint statistical image reconstruction method for proton stopping power mapping from dual-energy CT data

PURPOSE

To experimentally commission a dual-energy CT (DECT) joint statistical image reconstruction (JSIR) method, which is built on a linear basis vector model (BVM) of material characterization, for proton stopping power ratio (SPR) estimation.

METHODS

The JSIR-BVM method builds on the relationship between the energy-dependent photon attenuation coefficients and the proton stopping power via a pair of BVM component weights. The two BVM component images are simultaneously reconstructed from the acquired DECT sinograms and then used to predict the electron density and mean excitation energy (I-value), which are required by the Bethe equation for SPR computation. A post-reconstruction image-based DECT method, which utilizes the two separate CT images reconstructed via the scanner's software, was implemented for comparison. The DECT measurement data were acquired on a Philips Brilliance scanner at 90 and 140 kVp for two phantoms of different sizes. Each phantom contains 12 different soft and bony tissue surrogates with known compositions. The SPR estimation results were compared to the reference values computed from the known compositions. The difference of the computed water equivalent path lengths (WEPL) across the phantoms between the two methods was also compared.

RESULTS

The overall root-mean-square (RMS) of SPR estimation error of the JSIR-BVM method are 0.33% and 0.37% for the head- and body-sized phantoms, respectively, and all SPR estimates of the test samples are within 0.7% of the reference ground truth. The image-based method achieves overall RMS errors of 2.35% and 2.50% for the head- and body-sized phantoms, respectively. The JSIR-BVM method also reduces the pixel-wise random variation by 4-fold to 6-fold within homogeneous regions compared to the image-based method. The average differences between the JSIR-BVM method and the image-based method are 0.54% and 1.02% for the head- and body-sized phantoms, respectively.

CONCLUSION

By taking advantage of an accurate polychromatic CT data model and a model-based DECT statistical reconstruction algorithm, the JSIR-BVM method accounts for both systematic bias and random noise in the acquired DECT measurement data. Therefore, the JSIR-BVM method achieves good accuracy and precision on proton SPR estimation for various tissue surrogates and object sizes. In contrast, the experimentally achievable accuracy of the image-based method may be limited by the uncertainties in the image formation process. The result suggests that the JSIR-BVM method has the potential for more accurate SPR prediction compared to post-reconstruction image-based methods in clinical settings.

Impact of joint statistical dual-energy CT reconstruction of proton stopping power images: Comparison to image- and sinogram-domain material decomposition approaches

PURPOSE

The purpose of this study was to assess the performance of a novel dual-energy CT (DECT) approach for proton stopping power ratio (SPR) mapping that integrates image reconstruction and material characterization using a joint statistical image reconstruction (JSIR) method based on a linear basis vector model (BVM). A systematic comparison between the JSIR-BVM method and previously described DECT image- and sinogram-domain decomposition approaches is also carried out on synthetic data.

METHODS

The JSIR-BVM method was implemented to estimate the electron densities and mean excitation energies (I-values) required by the Bethe equation for SPR mapping. In addition, image- and sinogram-domain DECT methods based on three available SPR models including BVM were implemented for comparison. The intrinsic SPR modeling accuracy of the three models was first validated. Synthetic DECT transmission sinograms of two 330 mm diameter phantoms each containing 17 soft and bony tissues (for a total of 34) of known composition were then generated with spectra of 90 and 140 kVp. The estimation accuracy of the reconstructed SPR images were evaluated for the seven investigated methods. The impact of phantom size and insert location on SPR estimation accuracy was also investigated.

RESULTS

All three selected DECT-SPR models predict the SPR of all tissue types with less than 0.2% RMS errors under idealized conditions with no reconstruction uncertainties. When applied to synthetic sinograms, the JSIR-BVM method achieves the best performance with mean and RMS-average errors of less than 0.05% and 0.3%, respectively, for all noise levels, while the image- and sinogram-domain decomposition methods show increasing mean and RMS-average errors with increasing noise level. The JSIR-BVM method also reduces statistical SPR variation by sixfold compared to other methods. A 25% phantom diameter change causes up to 4% SPR differences for the image-domain decomposition approach, while the JSIR-BVM method and sinogram-domain decomposition methods are insensitive to size change.

CONCLUSION

Among all the investigated methods, the JSIR-BVM method achieves the best performance for SPR estimation in our simulation phantom study. This novel method is robust with respect to sinogram noise and residual beam-hardening effects, yielding SPR estimation errors comparable to intrinsic BVM modeling error. In contrast, the achievable SPR estimation accuracy of the image- and sinogram-domain decomposition methods is dominated by the CT image intensity uncertainties introduced by the reconstruction and decomposition processes.

Algorithm-enabled partial-angular-scan configurations for dual-energy CT

PURPOSE

We seek to investigate an optimization-based one-step method for image reconstruction that explicitly compensates for nonlinear spectral response (i.e., the beam-hardening effect) in dual-energy CT, to investigate the feasibility of the one-step method for enabling two dual-energy partial-angular-scan configurations, referred to as the short- and half-scan configurations, on standard CT scanners without involving additional hardware, and to investigate the potential of the short- and half-scan configurations in reducing imaging dose and scan time in a single-kVp-switch full-scan configuration in which two full rotations are made for collection of dual-energy data.

METHODS

We use the one-step method to reconstruct images directly from dual-energy data through solving a nonconvex optimization program that specifies the images to be reconstructed in dual-energy CT. Dual-energy full-scan data are generated from numerical phantoms and collected from physical phantoms with the standard single-kVp-switch full-scan configuration, whereas dual-energy short- and half-scan data are extracted from the corresponding full-scan data. Besides visual inspection and profile-plot comparison, the reconstructed images are analyzed also in quantitative studies based upon tasks of linear-attenuation-coefficient and material-concentration estimation and of material differentiation.

RESULTS

Following the performance of a computer-simulation study to verify that the one-step method can reconstruct numerically accurately basis and monochromatic images of numerical phantoms, we reconstruct basis and monochromatic images by using the one-step method from real data of physical phantoms collected with the full-, short-, and half-scan configurations. Subjective inspection based upon visualization and profile-plot comparison reveals that monochromatic images, which are used often in practical applications, reconstructed from the full-, short-, and half-scan data are largely visually comparable except for some differences in texture details. Moreover, quantitative studies based upon tasks of linear-attenuation-coefficient and material-concentration estimation and of material differentiation indicate that the short- and half-scan configurations yield results in close agreement with the ground-truth information and that of the full-scan configuration.

CONCLUSIONS

The one-step method considered can compensate effectively for the nonlinear spectral response in full- and partial-angular-scan dual-energy CT. It can be exploited for enabling partial-angular-scan configurations on standard CT scanner without involving additional hardware. Visual inspection and quantitative studies reveal that, with the one-step method, partial-angular-scan configurations considered can perform at a level comparable to that of the full-scan configuration, thus suggesting the potential of the two partial-angular-scan configurations in reducing imaging dose and scan time in the standard single-kVp-switch full-scan CT in which two full rotations are performed. The work also yields insights into the investigation and design of other nonstandard scan configurations of potential practical significance in dual-energy CT.

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

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 method based on l¹-l¹ norm constraints, wherein we impose first l¹-norm sparsity on the voxel time series (temporal data) in the transformed domain and the second l¹-norm sparsity on the successive difference of the same temporal data. Hence, we name the proposed method as Double Temporal Sparsity based Reconstruction (DTSR) method. 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 methods, the DTSR method shows promising potential with an improvement of 10-12 dB in PSNR with acceleration factors upto 3.5 on resting state fMRI data. Simulation results on real data demonstrate that DTSR method can be used to acquire accelerated fMRI with accurate detection of RSNs.

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

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 mPFM 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.

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

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, CaCl2 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 (2010)]. 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.