Image-domain material decomposition for dual-energy CT using unsupervised learning with data-fidelity loss

BACKGROUND

Dual-energy computed tomography (DECT) and material decomposition play vital roles in quantitative medical imaging. However, the decomposition process may suffer from significant noise amplification, leading to severely degraded image signal-to-noise ratios (SNRs). While existing iterative algorithms perform noise suppression using different image priors, these heuristic image priors cannot accurately represent the features of the target image manifold. Although deep learning-based decomposition methods have been reported, these methods are in the supervised-learning framework requiring paired data for training, which is not readily available in clinical settings.

PURPOSE

This work aims to develop an unsupervised-learning framework with data-measurement consistency for image-domain material decomposition in DECT.

METHODS

The proposed framework combines iterative decomposition and deep learning-based image prior in a generative adversarial network (GAN) architecture. In the generator module, a data-fidelity loss is introduced to enforce the measurement consistency in material decomposition. In the discriminator module, the discriminator is trained to differentiate the low-noise material-specific images from the high-noise images. In this scheme, paired images of DECT and ground-truth material-specific images are not required for the model training. Once trained, the generator can perform image-domain material decomposition with noise suppression in a single step.

RESULTS

In the simulation studies of head and lung digital phantoms, the proposed method reduced the standard deviation (SD) in decomposed images by 97% and 91% from the values in direct inversion results. It also generated decomposed images with structural similarity index measures (SSIMs) greater than 0.95 against the ground truth. In the clinical head and lung patient studies, the proposed method suppressed the SD by 95% and 93% compared to the decomposed images of matrix inversion.

CONCLUSIONS

Since the invention of DECT, noise amplification during material decomposition has been one of the biggest challenges, impeding its quantitative use in clinical practice. The proposed method performs accurate material decomposition with efficient noise suppression. Furthermore, the proposed method is within an unsupervised-learning framework, which does not require paired data for model training and resolves the issue of lack of ground-truth data in clinical scenarios.

Optimizing dual-energy CT technique for iodine-based contrast-to-noise ratio, a theoretical study

BACKGROUND

Dual-energy CT (DECT) systems provide valuable material-specific information by simultaneously acquiring two spectral measurements, resulting in superior image quality and contrast-to-noise ratio (CNR) while reducing radiation exposure and contrast agent usage. The selection of DECT scan parameters, including x-ray tube settings and fluence, is critical for the stability of the reconstruction process and hence the overall image quality.

PURPOSE

The goal of this study is to propose a systematic theoretical method for determining the optimal DECT parameters for minimal noise and maximum CNR in virtual monochromatic images (VMIs) for fixed subject size and total radiation dose.

METHODS

The noise propagation in the process of projection based material estimation from DECT measurements is analyzed. The main components of the study are the mean pixel variances for the sinogram and monochromatic image and the CNR, which were shown to depend on the Jacobian matrix of the sinograms-to-DECT measurements map. Analytic estimates for the mean sinogram and monochromatic image pixel variances and the CNR as functions of tube potentials, fluence, and VMI energy are derived, and then used in a virtual phantom experiment as an objective function for optimizing the tube settings and VMI energy to minimize the image noise and maximize the CNR.

RESULTS

It was shown that DECT measurements corresponding to kV settings that maximize the square of Jacobian determinant values over a domain of interest lead to improved stability of basis material reconstructions. Instances of non-uniqueness in DECT were addressed, focusing on scenarios where the Jacobian determinant becomes zero within the domain of interest despite significant spectral separation. The presence of non-uniqueness can lead to singular solutions during the inversion of sinograms-to-DECT measurements, underscoring the importance of considering uniqueness properties in parameter selection. Additionally, the optimal VMI energy and tube potentials for maximal CNR was determined. When the x-ray beam filter material was fixed at 2 mm of aluminum and the photon fluence for low and high kV scans were considered equal, the tube potential pair of 60/120 kV led to the maximal iodine CNR in the VMI at 53 keV.

CONCLUSIONS

Optimizing DECT scan parameters to maximize the CNR can be done in a systematic way. Also, choosing the parameters that maximize the Jacobian determinant over the set of expected line integrals leads to more stable reconstructions due to the reduced amplification of the measurement noise. Since the values of the Jacobian determinant depend strongly on the imaging task, careful consideration of all of the relevant factors is needed when implementing the proposed framework.

Prototyping optimization-based image reconstructions from limited-angular-range data in dual-energy CT

Image reconstruction from data collected over full-angular range (FAR) in dual-energy CT (DECT) is well-studied. There exists interest in DECT with advanced scan configurations in which data are collected only over limited-angular ranges (LARs) for meeting unique workflow needs in certain practical imaging applications, and thus in the algorithm development for image reconstruction from such LAR data. The objective of the work is to investigate and prototype image reconstructions in DECT with LAR scans. We investigate and prototype optimization programs with various designs of constraints on the directional-total-variations (DTVs) of virtual monochromatic images and/or basis images, and derive the DTV algorithms to numerically solve the optimization programs for achieving accurate image reconstruction from data collected in a slew of different LAR scans. Using simulated and real data acquired with low- and high-kV spectra over LARs, we conduct quantitative studies to demonstrate and evaluate the optimization programs and their DTV algorithms developed. As the results of the numerical studies reveal, while the DTV algorithms yield images of visual quality and quantitative accuracy comparable to that of the existing algorithms from FAR data, the former reconstruct images with improved visualization, reduced artifacts, and also enhanced quantitative accuracy when applied to LAR data in DECT. Optimization-based, one-step algorithms, including the DTV algorithms demonstrated, can be developed for quantitative image reconstruction from spectral data collected over LARs of extents that are considerably smaller than the FAR in DECT. The theoretical and numerical results obtained can be exploited for prototyping designs of optimization-based reconstructions and LAR scans in DECT, and they may also yield insights into the development of reconstruction procedures in practical DECT applications. The approach and algorithms developed can naturally be applied to investigating image reconstruction from LAR data in multi-spectral and photon-counting CT.

Constrained one-step material decomposition reconstruction of head CT data from a silicon photon-counting prototype

BACKGROUND

Spectral CT material decomposition provides quantitative information but is challenged by the instability of the inversion into basis materials. We have previously proposed the constrained One-Step Spectral CT Image Reconstruction (cOSSCIR) algorithm to stabilize the material decomposition inversion by directly estimating basis material images from spectral CT data. cOSSCIR was previously investigated on phantom data.

PURPOSE

This study investigates the performance of cOSSCIR using head CT datasets acquired on a clinical photon-counting CT (PCCT) prototype. This is the first investigation of cOSSCIR for large-scale, anatomically complex, clinical PCCT data. The cOSSCIR decomposition is preceded by a spectrum estimation and nonlinear counts correction calibration step to address nonideal detector effects.

METHODS

Head CT data were acquired on an early prototype clinical PCCT system using an edge-on silicon detector with eight energy bins. Calibration data of a step wedge phantom were also acquired and used to train a spectral model to account for the source spectrum and detector spectral response, and also to train a nonlinear counts correction model to account for pulse pileup effects. The cOSSCIR algorithm optimized the bone and adipose basis images directly from the photon counts data, while placing a grouped total variation (TV) constraint on the basis images. For comparison, basis images were also reconstructed by a two-step projection-domain approach of Maximum Likelihood Estimation (MLE) for decomposing basis sinograms, followed by filtered backprojection (MLE + FBP) or a TV minimization algorithm (MLE + TVmin ) to reconstruct basis images. We hypothesize that the cOSSCIR approach will provide a more stable inversion into basis images compared to two-step approaches. To investigate this hypothesis, the noise standard deviation in bone and soft-tissue regions of interest (ROIs) in the reconstructed images were compared between cOSSCIR and the two-step methods for a range of regularization constraint settings.

RESULTS

cOSSCIR reduced the noise standard deviation in the basis images by a factor of two to six compared to that of MLE + TVmin , when both algorithms were constrained to produce images with the same TV. The cOSSCIR images demonstrated qualitatively improved spatial resolution and depiction of fine anatomical detail. The MLE + TVmin algorithm resulted in lower noise standard deviation than cOSSCIR for the virtual monoenergetic images (VMIs) at higher energy levels and constraint settings, while the cOSSCIR VMIs resulted in lower noise standard deviation at lower energy levels and overall higher qualitative spatial resolution. There were no statistically significant differences in the mean values within the bone region of images reconstructed by the studied algorithms. There were statistically significant differences in the mean values within the soft-tissue region of the reconstructed images, with cOSSCIR producing mean values closer to the expected values.

CONCLUSIONS

The cOSSCIR algorithm, combined with our previously proposed spectral model estimation and nonlinear counts correction method, successfully estimated bone and adipose basis images from high resolution, large-scale patient data from a clinical PCCT prototype. The cOSSCIR basis images were able to depict fine anatomical details with a factor of two to six reduction in noise standard deviation compared to that of the MLE + TVmin two-step approach.

Noise correlation and its impact on the performance of multi-material decomposition-based spectral imaging in photon-counting CT

PURPOSE

It has been known that noise correlation plays an important role in the determination of the performance of spectral imaging based on two-material decomposition (2-MD). To further understand the basics of spectral imaging in photon-counting CT toward optimal design and implementation, we study the noise correlation in multi-MD (m-MD) and its impact on the performance of spectral imaging.

METHOD

We derive the equations that characterize the noise and noise correlation in the material-specific (basis) images in m-MD, followed by a simulation study to verify the derived equations and study the noise correlation's impact on the performance of spectral imaging. Using a specially designed digital phantom, the study of noise correlation runs over the cases of two-, three-, and four-MD (2-MD, 3-MD, and 4-MD). Then, the noise correlation's impact on the performance of spectral imaging in photon-counting CT is investigated, using a modified Shepp-Logan phantom.

RESULTS

The results in 2-MD show that, in-line with what has been reported in the literature, the noise correlation coefficient between the material-specific images corresponding to the basis materials approaches -1. The results in m-MD (m ≥ 3) are more complicated and interesting, as the noise correlation coefficients between a pair of the material-specific images alternate between ±1, and so do in the case of 4-MD. The m-MD data show that the noise in virtual monochromatic imaging (a form of spectral imaging) is moderate even though the noises in material-specific (basis) images vary drastically.

CONCLUSIONS

The observation of noise correlation in 3-MD, 4-MD, and beyond (i.e., m-MD) is informative to the community. The relationship between noise correlation and the performance of spectral imaging revealed in this work may help clinical medical physicists understand the fundamentals of spectral imaging based on MD and optimize the performance of spectral imaging in photon-counting CT and other X-ray imaging modalities.

Photon-counting CT via interleaved/gapped spectral channels: Feasibility and imaging performance

PURPOSE

Compared to energy-integration, photon-counting x-ray detection facilitates the spectral channelization (energy binning) in spectral CT and thus offers the opportunity of implementing data acquisition via sophisticated schemes, e.g., gapping or interleaving in spectral channels. In this article, we report our investigation of the performance of material decomposition based spectral imaging in photon-counting CT implemented in such data acquisition schemes, and their comparison with the benchmark scheme and other schemes without spectral gapping or interleaving.

MATERIALS AND METHODS

Using a deliberately designed anthropomorphic head phantom that mimics the intracranial soft tissues and bony structures, a simulation study is carried out with the focus on two-material decomposition-based spectral imaging in photon-counting CT, under both ideal and realistic detector spectral responses. The projection data are acquired in four spectral channels, and then are sorted to implement the schemes of gapping ((ch₁ , ch₃ ); (ch₂ , ch₄ ); (ch₁ , ch₄ )) and interleaving ((ch₁ , ch₃ )+(ch₂ , ch₄ ); (ch₁ , ch₄ )+(ch₂ , ch₃ ); ((ch₁ +ch₃ ), (ch₂ +ch₄ )); ((ch₁ +ch₄ ), (ch₂ +ch₃ ))) in spectral channels, in addition to the benchmark scheme ((ch₁ +ch₂ ), (ch₃ +ch₄ )) and other conventional schemes (ch₁ , ch₂ ), (ch₂ , ch₃ ) and (ch₃ , ch₄ ), where 'ch' denotes channel, '+' denote addition, and (·,·) the operation of material decomposition and image reconstruction. Using the contrast-to-noise ratio between targeted regions of interest as the figure of merit, we study the performance of spectral imaging (material specific and virtual monochromatic) associated with these spectral channelization schemes.

RESULTS

Under ideal detector spectral response, the scheme (ch₁ , ch₄ ) outperforms the benchmark scheme ((ch₁ +ch₂ ), (ch₃ +ch₄ )) and others in gapped and/or interleaved spectral channelization in material specific imaging, while the interleaved scheme (ch₁ , ch₄ )+(ch₂ , ch₃ ) performs the best in virtual monochromatic imaging. Notably, only about half x-ray dose is utilized in the scheme (ch₁ , ch₄ ) for image formation. Under realistic detector spectral response, the difference in imaging performance over all spectral channelization schemes diminishes, along with degradation in each scheme's individual performance. The results suggest that (i) different strategy in spectral channelization may have to be exercised in material specific imaging and virtual monochromatic imaging, respectively, and (ii) the spectral distortion in realistic detector's response due to charge-sharing, Compton scattering and fluorescent escaping should be mitigated as much as possible.

CONCLUSION

The spectral channelization schemes and associated imaging performance reported herein are novel and thus informative to the community, which may further the understanding of physical fundamentals and design principles for material decomposition based spectral imaging in photon-counting CT and other x-ray related imaging modalities. This article is protected by copyright. All rights reserved.

On the conditioning of basis materials and its impact on multimaterial decomposition-based spectral imaging in photon-counting CT

PURPOSE

Material-specific imaging and virtual monochromatic imaging/analysis are the two forms of spectral imaging in CT implemented via either energy-integration or photon-counting data acquisition. Aimed at further understanding the fundamentals and providing guidelines on its design and implementation, we quantitatively investigate the conditioning (sufficiency in dimensionality, well-posedness in basis functions, and matching of K-edge materials) of basis materials and its impact on the performance of spectral imaging in photon-counting CT.

MATERIALS AND METHODS

Initially, singular value decomposition (SVD) is employed to investigate the dimensionality of material space for multimaterial decomposition-based spectral imaging in photon-counting CT over the energy range [18 150] keV. Then, the SVD is extended to study the well-posedness of basis functions, its relationship with the dimensionality of materials to be imaged, and its impact on imaging performance. A number of phantoms are designed to mimic the soft and bony tissues in the head and contrast enhancement materials (iodine and gadolinium). Simulation studies, in which the geometry of photon-counting CT is similar to a clinical CT, are carried out to evaluate and verify the proposed approach of conditioning analysis and the relationship between the conditioning of basis materials and the performance of spectral imaging in photon-counting CT.

RESULTS

The preliminary data show that the dimensionality of biological tissues, including both soft and bony tissues, is effectively equal to two. The dimensionality increments with inclusion of K-edge materials into the materials to be imaged. The well-posedness of basis functions depends on the correlation between the functions and impacts the noise in material decomposition substantially, but affects the noise in virtual monochromatic imaging/analysis moderately. If a K-edge material is in the materials to be imaged, the same K-edge material has to be one of the basis materials, but its concentration does not affect the accuracy of material decomposition significantly. Moreover, inclusion of K-edge material into the basis material makes the tuning of correlation among the basis functions feasible and thus improves the performance of spectral imaging in photon-counting CT.

CONCLUSION

The extension of SVD for systematic analysis of multimaterial decomposition-based spectral imaging in photon-counting CT is of innovation and significance. In addition to providing more information on the fundamentals, the approach used in this study and the data obtained so far may provide guidelines on the implementation of spectral imaging in either photon-counting or energy-integration CT, as well as other x-ray-related imaging modalities such as radiography and tomosynthesis.