Statistical sinogram restoration in dual-energy CT for PET attenuation correction

A dual-energy CT reconstruction method based on anchor network from dual quarter scans

Compared with conventional single-energy computed tomography (CT), dual-energy CT (DECT) provides better material differentiation but most DECT imaging systems require dual full-angle projection data at different X-ray spectra. Relaxing the requirement of data acquisition is an attractive research to promote the applications of DECT in wide range areas and reduce the radiation dose as low as reasonably achievable. In this work, we design a novel DECT imaging scheme with dual quarter scans and propose an efficient method to reconstruct the desired DECT images from the dual limited-angle projection data. We first study the characteristics of limited-angle artifacts under dual quarter scans scheme, and find that the negative and positive artifacts of DECT images are complementarily distributed in image domain because the corresponding X-rays of high- and low-energy scans are symmetric. Inspired by this finding, a fusion CT image is generated by integrating the limited-angle DECT images of dual quarter scans. This strategy enhances the true image information and suppresses the limited-angle artifacts, thereby restoring the image edges and inner structures. Utilizing the capability of neural network in the modeling of nonlinear problem, a novel Anchor network with single-entry double-out architecture is designed in this work to yield the desired DECT images from the generated fusion CT image. Experimental results on the simulated and real data verify the effectiveness of the proposed method. This work enables DECT on imaging configurations with half-scan and largely reduces scanning angles and radiation doses.

A Locally Weighted Linear Regression Look-Up Table-Based Iterative Reconstruction Method for Dual Spectral CT

OBJECTIVE

Compared with traditional computed tomography (CT), dual spectral CT (DSCT) exhibits superior material distinguishability and thus has broad prospects in industrial and medical fields. In iterative DSCT algorithms, accurately modeling forward-projection functions is crucial, but it is very difficult to analytically provide accurate functions.

METHODS

In this article, we propose a locally weighted linear regression look-up table-based (LWLR-LUT) iterative reconstruction method for DSCT. First, the proposed method uses LWLR to establish LUTs for the forward-projection functions through calibration phantoms, achieving good local information calibration. Second, the reconstructed images can be iteratively obtained through the established LUTs. The proposed method not only does not require knowledge of the X-ray spectra and the attenuation coefficients, but also implicitly accounts for some scattered radiation while fitting locally the forward-projection functions in the calibration space.

RESULTS

Both numerical simulations and real data experiments demonstrate that the proposed method can achieve highly accurate polychromatic forward-projection functions and greatly improve the quality of the images reconstructed from scattering-free and scattering projections.

CONCLUSION

The proposed method is simple and practical, and achieves good material decomposition effects for objects with different complex structures through simple calibration phantoms.

Exploring Dual-Energy CT Spectral Information for Machine Learning-Driven Lesion Diagnosis in Pre-Log Domain

In this study, we proposed a computer-aided diagnosis (CADx) framework under dual-energy spectral CT (DECT), which operates directly on the transmission data in the pre-log domain, called CADxDE, to explore the spectral information for lesion diagnosis. The CADxDE includes material identification and machine learning (ML) based CADx. Benefits from DECT's capability of performing virtual monoenergetic imaging with the identified materials, the responses of different tissue types (e.g., muscle, water, and fat) in lesions at each energy can be explored by ML for CADx. Without losing essential factors in the DECT scan, a pre-log domain model-based iterative reconstruction is adopted to obtain decomposed material images, which are then used to generate the virtual monoenergetic images (VMIs) at selected n energies. While these VMIs have the same anatomy, their contrast distribution patterns contain rich information along with the n energies for tissue characterization. Thus, a corresponding ML-based CADx is developed to exploit the energy-enhanced tissue features for differentiating malignant from benign lesions. Specifically, an original image-driven multi-channel three-dimensional convolutional neural network (CNN) and extracted lesion feature-based ML CADx methods are developed to show the feasibility of CADxDE. Results from three pathologically proven clinical datasets showed 4.01% to 14.25% higher AUC (area under the receiver operating characteristic curve) scores than the scores of both the conventional DECT data (high and low energy spectrum separately) and the conventional CT data. The mean gain >9.13% in AUC scores indicated that the energy spectral-enhanced tissue features from CADxDE have great potential to improve lesion diagnosis performance.

Direct Multi-Material Reconstruction via Iterative Proximal Adaptive Descent for Spectral CT Imaging

Spectral computed tomography (spectral CT) is a promising medical imaging technology because of its ability to provide information on material characterization and quantification. However, with an increasing number of basis materials, the nonlinearity of measurements causes difficulty in decomposition. In addition, noise amplification and beam hardening further reduce image quality. Thus, improving the accuracy of material decomposition while suppressing noise is pivotal for spectral CT imaging. This paper proposes a one-step multi-material reconstruction model as well as an iterative proximal adaptive decent method. In this approach, a proximal step and a descent step with adaptive step size are designed under the forward-backward splitting framework. The convergence analysis of the algorithm is further discussed according to the convexity of the optimization objective function. For simulation experiments with different noise levels, the peak signal-to-noise ratio (PSNR) obtained by the proposed method increases approximately 23 dB, 14 dB, and 4 dB compared to those of other algorithms. Magnified areas of thorax data further demonstrated that the proposed method has a better ability to preserve details in tissues, bones, and lungs. Numerical experiments verify that the proposed method efficiently reconstructed the material maps, and reduced noise and beam hardening artifacts compared with the state-of-the-art methods.

An improved iterative neural network for high-quality image-domain material decomposition in dual-energy CT

PURPOSE

Dual-energy computed tomography (DECT) has been widely used in many applications that need material decomposition. Image-domain methods directly decompose material images from high- and low-energy attenuation images, and thus, are susceptible to noise and artifacts on attenuation images. The purpose of this study is to develop an improved iterative neural network (INN) for high-quality image-domain material decomposition in DECT, and to study its properties.

METHODS

We propose a new INN architecture for DECT material decomposition. The proposed INN architecture uses distinct cross-material convolutional neural network (CNN) in image refining modules, and uses image decomposition physics in image reconstruction modules. The distinct cross-material CNN refiners incorporate distinct encoding-decoding filters and cross-material model that captures correlations between different materials. We study the distinct cross-material CNN refiner with patch-based reformulation and tight-frame condition.

RESULTS

Numerical experiments with extended cardiac-torso phantom and clinical data show that the proposed INN significantly improves the image quality over several image-domain material decomposition methods, including a conventional model-based image decomposition (MBID) method using an edge-preserving regularizer, a recent MBID method using pre-learned material-wise sparsifying transforms, and a noniterative deep CNN method. Our study with patch-based reformulations reveals that learned filters of distinct cross-material CNN refiners can approximately satisfy the tight-frame condition.

CONCLUSIONS

The proposed INN architecture achieves high-quality material decompositions using iteration-wise refiners that exploit cross-material properties between different material images with distinct encoding-decoding filters. Our tight-frame study implies that cross-material CNN refiners in the proposed INN architecture are useful for noise suppression and signal restoration. This article is protected by copyright. All rights reserved.

Deep learning based spectral CT imaging

Spectral computed tomography (CT) has attracted much attention in radiation dose reduction, metal artifacts removal, tissue quantification and material discrimination. The x-ray energy spectrum is divided into several bins, each energy-bin-specific projection has a low signal-noise-ratio (SNR) than the current-integrating counterpart, which makes image reconstruction a unique challenge. Traditional wisdom is to use prior knowledge based iterative methods. However, this kind of methods demands a great computational cost. Inspired by deep learning, here we first develop a deep learning based reconstruction method; i.e., U-net with L_p^p-norm, Total variation, Residual learning, and Anisotropic adaption (ULTRA). Specifically, we emphasize the various multi-scale feature fusion and multichannel filtering enhancement with a denser connection encoding architecture for residual learning and feature fusion. To address the image deblurring problem associated with the L₂²- loss, we propose a general L_p^p-loss, p>0. Furthermore, the images from different energy bins share similar structures of the same object, the regularization characterizing correlations of different energy bins is incorporated into the L_p^p- loss function, which helps unify the deep learning based methods with traditional compressed sensing based methods. Finally, the anisotropically weighted total variation is employed to characterize the sparsity in the spatial-spectral domain to regularize the proposed network In particular, we validate our ULTRA networks on three large-scale spectral CT datasets, and obtain excellent results relative to the competing algorithms. In conclusion, our quantitative and qualitative results in numerical simulation and preclinical experiments demonstrate that our proposed approach is accurate, efficient and robust for high-quality spectral CT image reconstruction.

An iterative reconstruction method based on monochromatic images for dual energy CT

PURPOSE

Dual-energy computed tomography (DECT) scans objects using two different X-ray spectra to acquire more information, which is also called dual spectral CT (DSCT) in some articles. Compared to traditional CT, DECT exhibits superior material distinguishability. Therefore, DECT can be widely used in the medical and industrial domains. However, owing to the nonlinearity and ill condition of DECT, studies are underway on DECT reconstruction to obtain high quality images and achieve fast convergence speed. Therefore, in this study, we propose an iterative reconstruction method based on monochromatic images (IRM-MI) to rapidly obtain high-quality images in DECT reconstruction.

METHODS

An IRM-MI is proposed for DECT. The proposed method converts DECT reconstruction problem from the basis material images decomposition to monochromatic images decomposition to significantly improve the convergence speed of DECT reconstruction by changing the coefficient matrix of the original equations to increase the angle of the high- and low-energy projection curves or reduce the condition number of the coefficient matrix. The monochromatic images were then decomposed into basis material images. Furthermore, we conducted numerical experiments to evaluate the performance of the proposed method.

RESULTS

The decomposition results of the simulated data and real data experiments confirmed the effectiveness of the proposed method. Compared to the extended algebraic reconstruction technique (E-ART) method, the proposed method exhibited a significant increase in the convergence speed by increasing the angle of polychromatic projection curves or decreasing the condition number of the coefficient matrix, when choosing the appropriate monochromatic images. Therefore, the proposed method is also advantageous in acquiring high quality and rapidly converged images.

CONCLUSIONS

We developed an iterative reconstruction method based on monochromatic images for the material decomposition for DECT. The numerical experiments using the proposed method validated its capability of decomposing the basis material images. Furthermore, the proposed method achieved faster convergence speed compared to the E-ART method.

An oblique projection modification technique (OPMT) for fast multispectral CT reconstruction

In x-ray multispectral (or photon-counting) computed tomography (MCT), the object of interest is scanned under multiple x-ray spectra, and it can acquire more information about the scanned object than conventional CT, in which only one x-ray spectrum is used. The obtained polychromatic projections are utilized to perform material-selective and energy-selective image reconstruction. Compared with the conventional single spectral CT, MCT has a superior material distinguishability. Therefore, it has wide potential applications in both medical and industrial areas. However, the nonlinearity and ill condition of the MCT problem make it difficult to get high-quality and fast convergence of images for existing MCT reconstruction algorithms. In this paper, we proposed an iterative reconstruction algorithm based on an oblique projection modification technique (OPMT) for fast basis material decomposition of MCT. In the case of geometric inconsistency, along the current x-ray path, the oblique projection modification direction not only relates to the polychromatic projection equation of the known spectrum, but it also comprehensively refers to the polychromatic projection equation information of the unknown spectra. Moreover, the ray-by-ray correction makes it applicable to geometrically consistent projection data. One feature of the proposed algorithm is its fast convergence speed. The OPMT considers the information from multiple polychromatic projection equations, which greatly speeds up the convergence of MCT reconstructed images. Another feature of the proposed algorithm is its high flexibility. The ray-by-ray correction will be suitable for any common MCT scanning mode. The proposed algorithm is validated with numerical experiments from both simulated and real data. Compared with the ASD-NC-POCS and E-ART algorithms, the proposed algorithm achieved high-quality reconstructed images while accelerating the convergence speed of them.

PET-enabled dual-energy CT: image reconstruction and a proof-of-concept computer simulation study

Standard dual-energy computed tomography (CT) uses two different x-ray energies to obtain energy-dependent tissue attenuation information to allow quantitative material decomposition. The combined use of dual-energy CT and positron emission tomography (PET) may provide a more comprehensive characterization of disease states in cancer and other diseases. However, the integration of dual-energy CT with PET is not trivial, either requiring costly hardware upgrades or increasing radiation exposure. This paper proposes a different dual-energy CT imaging method that is enabled by PET. Instead of using a second x-ray CT scan with a different energy, this method exploits time-of-flight PET image reconstruction via the maximum likelihood attenuation and activity (MLAA) algorithm to obtain a 511 keV gamma-ray attenuation image from PET emission data. The high-energy gamma-ray attenuation image is then combined with the low-energy x-ray CT of PET/CT to provide a pair of dual-energy CT images. A major challenge with the standard MLAA reconstruction is the high noise present in the reconstructed 511 keV attenuation map, which would not compromise the PET activity reconstruction too much but may significantly affect the performance of the gamma-ray attenuation image for material decomposition. To overcome the problem, we further propose a kernel MLAA algorithm to exploit the prior information from the available x-ray CT image. We conducted a computer simulation to test the concept and algorithm for the task of material decomposition. The simulation results demonstrate that this PET-enabled dual-energy CT method is promising for quantitative material decomposition. The proposed method can be readily implemented on time-of-flight PET/CT scanners to enable simultaneous PET and dual-energy CT imaging.

DECT-MULTRA: Dual-Energy CT Image Decomposition With Learned Mixed Material Models and Efficient Clustering

Dual-energy computed tomography (DECT) imaging plays an important role in advanced imaging applications due to its material decomposition capability. Image-domain decomposition operates directly on CT images using linear matrix inversion, but the decomposed material images can be severely degraded by noise and artifacts. This paper proposes a new method dubbed DECT-MULTRA for image-domain DECT material decomposition that combines conventional penalized weighted-least squares (PWLS) estimation with regularization based on a mixed union of learned transforms (MULTRA) model. Our proposed approach pre-learns a union of common-material sparsifying transforms from patches extracted from all the basis materials, and a union of cross-material sparsifying transforms from multi-material patches. The common-material transforms capture the common properties among different material images, while the cross-material transforms capture the cross-dependencies. The proposed PWLS formulation is optimized efficiently by alternating between an image update step and a sparse coding and clustering step, with both of these steps having closed-form solutions. The effectiveness of our method is validated with both XCAT phantom and clinical head data. The results demonstrate that our proposed method provides superior material image quality and decomposition accuracy compared to other competing methods.

Spectrum Estimation-Guided Iterative Reconstruction Algorithm for Dual Energy CT

X-ray spectrum plays a very important role in dual energy computed tomography (DECT) reconstruction. Because it is difficult to measure x-ray spectrum directly in practice, efforts have been devoted into spectrum estimation by using transmission measurements. These measurement methods are independent of the image reconstruction, which bring extra cost and are time consuming. Furthermore, the estimated spectrum mismatch would degrade the quality of the reconstructed images. In this paper, we propose a spectrum estimation-guided iterative reconstruction algorithm for DECT which aims to simultaneously recover the spectrum and reconstruct the image. The proposed algorithm is formulated as an optimization framework combining spectrum estimation based on model spectra representation, image reconstruction, and regularization for noise suppression. To resolve the multi-variable optimization problem of simultaneously obtaining the spectra and images, we introduce the block coordinate descent (BCD) method into the optimization iteration. Both the numerical simulations and physical phantom experiments are performed to verify and evaluate the proposed method. The experimental results validate the accuracy of the estimated spectra and reconstructed images under different noise levels. The proposed method obtains a better image quality compared with the reconstructed images from the known exact spectra and is robust in noisy data applications.

Iterative reconstruction for low dose dual energy CT using information-divergence constrained spectral redundancy information

Dual energy computed tomography (DECT) can improve the capability of differentiating different materials compared with conventional CT. However, due to non-negligible radiation exposure to patients, dose reduction has recently become a critical concern in CT imaging field. In this work, to reduce noise at the same time maintain DECT images quality, we present an iterative reconstruction algorithm for low-dose DECT images where in the objective function of the algorithm consists of a data-fidelity term and a regularization term. The former term is based on alpha-divergence to describe the statistical distribution of the DE sinogram data. And the latter term is based on the redundant information to reflect the prior information of the desired DECT images. For simplicity, the presented algorithm is termed as "AlphaD-aviNLM". To minimize the associative objective function, a modified proximal forward-backward splitting algorithm is proposed. Digital phantom, physical phantom, and patient data were utilized to validate and evaluate the presented AlphaD-aviNLM algorithm. The experimental results characterize the performance of the presented AlphaD-aviNLM algorithm. Speficically, in the digital phantom study, the presented AlphaD-aviNLM algorithm performs better than the PWLS-TV, PWLS-aviNLM, and AlphaD-TV with more than 49%, 34%, and 40% gains for the RMSE metric, 1.3%, 0.4%, and 0.7% gains for the FSIM metric and 13%, 8%, and 11% gains for the PSNR metric. In the physical phantom study, the presented AlphaD-aviNLM algorithm performs better than the PWLS-TV, PWLS-aviNLM, and AlphaD-TV with more than 0.55%, 0.07%, and 0.16% gains for the FSIM metric.

Joint Statistical Iterative Material Image Reconstruction for Spectral Computed Tomography Using a Semi-Empirical Forward Model

By acquiring tomographic measurements with several distinct photon energy spectra, spectral computed tomography (spectral CT) is able to provide additional material-specific information compared with conventional CT. This information enables the generation of material selective images, which have found various applications in medical imaging. However, material decomposition typically leads to noise amplification and a degradation of the signal-to-noise ratio. This is still a fundamental problem of spectral CT, especially for low-dose medical applications. Inspired by the success for low-dose conventional CT, several statistical iterative reconstruction algorithms for spectral CT have been developed. These algorithms typically rely on detailed knowledge about the spectrum and the detector response. Obtaining this knowledge is often difficult in practice, especially if photon counting detectors are used to acquire the energy specific information. In this paper, a new algorithm for joint statistical iterative material image reconstruction is presented. It relies on a semi-empirical forward model which is tuned by calibration measurements. This strategy allows to model spatially varying properties of the imaging system without requiring detailed prior knowledge of the system parameters. We employ an efficient optimization algorithm based on separable surrogate functions to accelerate convergence and reduce the reconstruction time. Numerical as well as real experiments show that our new algorithm leads to reduced statistical bias and improved image quality compared with projection-based material decomposition followed by analytical or iterative image reconstruction.

Locally linear constraint based optimization model for material decomposition

Dual spectral computed tomography (DSCT) has a superior material distinguishability than the conventional single spectral computed tomography (SSCT). However, the decomposition process is an illposed problem, which is sensitive to noise. Thus, the decomposed image quality is degraded, and the corresponding signal-to-noise ratio (SNR) is much lower than that of directly reconstructed image of SSCT. In this work, we establish a locally linear relationship between the decomposed results of DSCT and SSCT. Based on this constraint, we propose an optimization model for DSCT and develop an iterative method with image guided filtering. To further improve the image quality, we employ a preprocessing method based on the relative total variation regularization. Both numerical simulations and real experiments are performed, and the results confirm the effectiveness of our proposed approach.

Iterative reconstruction for dual energy CT with an average image-induced nonlocal means regularization

Reducing radiation dose in dual energy computed tomography (DECT) is highly desirable but it may lead to excessive noise in the filtered backprojection (FBP) reconstructed DECT images, which can inevitably increase the diagnostic uncertainty. To obtain clinically acceptable DECT images from low-mAs acquisitions, in this work we develop a novel scheme based on measurement of DECT data. In this scheme, inspired by the success of edge-preserving non-local means (NLM) filtering in CT imaging and the intrinsic characteristics underlying DECT images, i.e. global correlation and non-local similarity, an averaged image induced NLM-based (aviNLM) regularization is incorporated into the penalized weighted least-squares (PWLS) framework. Specifically, the presented NLM-based regularization is designed by averaging the acquired DECT images, which takes the image similarity within the two energies into consideration. In addition, the weighted least-squares term takes into account DECT data-dependent variance. For simplicity, the presented scheme was termed as 'PWLS-aviNLM'. The performance of the presented PWLS-aviNLM algorithm was validated and evaluated on digital phantom, physical phantom and patient data. The extensive experiments validated that the presented PWLS-aviNLM algorithm outperforms the FBP, PWLS-TV and PWLS-NLM algorithms quantitatively. More importantly, it delivers the best qualitative results with the finest details and the fewest noise-induced artifacts, due to the aviNLM regularization learned from DECT images. This study demonstrated the feasibility and efficacy of the presented PWLS-aviNLM algorithm to improve the DECT reconstruction and resulting material decomposition.

Use of dual-energy computed tomography to measure skeletal-wide marrow composition and cancellous bone mineral density

Temporal and spatial variations in bone marrow adipose tissue (MAT) can be indicative of several pathologies and confound current methods of assessing immediate changes in bone mineral remodeling. We present a novel dual-energy computed tomography (DECT) method to monitor MAT and marrow-corrected volumetric BMD (mcvBMD) throughout the body. Twenty-three cancellous skeletal sites in 20 adult female cadavers aged 40-80 years old were measured using DECT (80 and 140 kVp). vBMD was simultaneous recorded using QCT. MAT was further sampled using MRI. Thirteen lumbar vertebrae were then excised from the MRI-imaged donors and examined by microCT. After MAT correction throughout the skeleton, significant differences (p < 0.05) were found between QCT-derived vBMD and DECT-derived mcvBMD results. McvBMD was highly heterogeneous with a maximum at the posterior skull and minimum in the proximal humerus (574 and 0.7 mg/cc, respectively). BV/TV and BMC have a nearly significant correlation with mcvBMD (r = 0.545, p = 0.057 and r = 0.539, p = 0.061, respectively). MAT assessed by DECT showed a significant correlation with MRI MAT results (r = 0.881, p < 0.0001). Both DECT- and MRI-derived MAT had a significant influence on uncorrected vBMD (r = -0.86 and r = -0.818, p ≤ 0.0001, respectively). Conversely, mcvBMD had no correlation with DECT- or MRI-derived MAT (r = 0.261 and r = 0.067). DECT can be used to assess MAT while simultaneously collecting mcvBMD values at each skeletal site. MAT is heterogeneous throughout the skeleton, highly variable, and should be accounted for in longitudinal mcvBMD studies. McvBMD accurately reflects the calcified tissue in cancellous bone.

An extended simultaneous algebraic reconstruction technique (E-SART) for X-ray dual spectral computed tomography

X-ray dual spectral computed tomography (DSCT) scans the measured object with two different x-ray energy spectra and the collected polychromatic projections from this procedure can be used to perform basis material decomposition of the object. An iterative method E-ART was recently proposed to produce highly quantitative basis material images for DSCT, but it has the drawback of slow convergence and huge computational costs. Inspired by the E-ART method, this paper proposes an extended simultaneous algebraic reconstruction technique (E-SART) for the basis material decomposition of DSCT and an accelerating strategy for improve the convergence speed of the iterative reconstruction. Compared with the E-ART method, the proposed method has much faster convergence rate while at the same time it has better noise suppressing feature. The advantages of this method were verified by experiments in which the FORBILD thorax phantom was iteratively reconstructed from noise-free and noisy polychromatic projections. SCANNING 38:599-611, 2016. © 2016 Wiley Periodicals, Inc.

Positron Emission Tomography: Current Challenges and Opportunities for Technological Advances in Clinical and Preclinical Imaging Systems

Positron emission tomography (PET) imaging is based on detecting two time-coincident high-energy photons from the emission of a positron-emitting radioisotope. The physics of the emission, and the detection of the coincident photons, give PET imaging unique capabilities for both very high sensitivity and accurate estimation of the in vivo concentration of the radiotracer. PET imaging has been widely adopted as an important clinical modality for oncological, cardiovascular, and neurological applications. PET imaging has also become an important tool in preclinical studies, particularly for investigating murine models of disease and other small-animal models. However, there are several challenges to using PET imaging systems. These include the fundamental trade-offs between resolution and noise, the quantitative accuracy of the measurements, and integration with X-ray computed tomography and magnetic resonance imaging. In this article, we review how researchers and industry are addressing these challenges.

A practical material decomposition method for x-ray dual spectral computed tomography

X-ray dual spectral CT (DSCT) scans the measured object with two different x-ray spectra, and the acquired rawdata can be used to perform the material decomposition of the object. Direct calibration methods allow a faster material decomposition for DSCT and can be separated in two groups: image-based and rawdata-based. The image-based method is an approximative method, and beam hardening artifacts remain in the resulting material-selective images. The rawdata-based method generally obtains better image quality than the image-based method, but this method requires geometrically consistent rawdata. However, today's clinical dual energy CT scanners usually measure different rays for different energy spectra and acquire geometrically inconsistent rawdata sets, and thus cannot meet the requirement. This paper proposes a practical material decomposition method to perform rawdata-based material decomposition in the case of inconsistent measurement. This method first yields the desired consistent rawdata sets from the measured inconsistent rawdata sets, and then employs rawdata-based technique to perform material decomposition and reconstruct material-selective images. The proposed method was evaluated by use of simulated FORBILD thorax phantom rawdata and dental CT rawdata, and simulation results indicate that this method can produce highly quantitative DSCT images in the case of inconsistent DSCT measurements.

The Use of Anatomical Information for Molecular Image Reconstruction Algorithms: Attenuation/Scatter Correction, Motion Compensation, and Noise Reduction

PET and SPECT are important tools for providing valuable molecular information about patients to clinicians. Advances in nuclear medicine hardware technologies and statistical image reconstruction algorithms enabled significantly improved image quality. Sequentially or simultaneously acquired anatomical images such as CT and MRI from hybrid scanners are also important ingredients for improving the image quality of PET or SPECT further. High-quality anatomical information has been used and investigated for attenuation and scatter corrections, motion compensation, and noise reduction via post-reconstruction filtering and regularization in inverse problems. In this article, we will review works using anatomical information for molecular image reconstruction algorithms for better image quality by describing mathematical models, discussing sources of anatomical information for different cases, and showing some examples.

Using edge-preserving algorithm with non-local mean for significantly improved image-domain material decomposition in dual-energy CT

Increased noise is a general concern for dual-energy material decomposition. Here, we develop an image-domain material decomposition algorithm for dual-energy CT (DECT) by incorporating an edge-preserving filter into the Local HighlY constrained backPRojection reconstruction (HYPR-LR) framework. With effective use of the non-local mean, the proposed algorithm, which is referred to as HYPR-NLM, reduces the noise in dual-energy decomposition while preserving the accuracy of quantitative measurement and spatial resolution of the material-specific dual-energy images. We demonstrate the noise reduction and resolution preservation of the algorithm with an iodine concentrate numerical phantom by comparing the HYPR-NLM algorithm to the direct matrix inversion, HYPR-LR and iterative image-domain material decomposition (Iter-DECT). We also show the superior performance of the HYPR-NLM over the existing methods by using two sets of cardiac perfusing imaging data. The DECT material decomposition comparison study shows that all four algorithms yield acceptable quantitative measurements of iodine concentrate. Direct matrix inversion yields the highest noise level, followed by HYPR-LR and Iter-DECT. HYPR-NLM in an iterative formulation significantly reduces image noise and the image noise is comparable to or even lower than that generated using Iter-DECT. For the HYPR-NLM method, there are marginal edge effects in the difference image, suggesting the high-frequency details are well preserved. In addition, when the search window size increases from to , there are no significant changes or marginal edge effects in the HYPR-NLM difference images. The reference drawn from the comparison study includes: (1) HYPR-NLM significantly reduces the DECT material decomposition noise while preserving quantitative measurements and high-frequency edge information, and (2) HYPR-NLM is robust with respect to parameter selection.

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

We propose a new algorithm, called line integral alternating minimization (LIAM), for dual-energy X-ray CT image reconstruction. Instead of obtaining component images by minimizing the discrepancy between the data and the mean estimates, LIAM allows for a tunable discrepancy between the basis material projections and the basis sinograms. A parameter is introduced that controls the size of this discrepancy, and with this parameter the new algorithm can continuously go from a two-step approach to the joint estimation approach. LIAM alternates between iteratively updating the line integrals of the component images and reconstruction of the component images using an image iterative deblurring algorithm. An edge-preserving penalty function can be incorporated in the iterative deblurring step to decrease the roughness in component images. Images from both simulated and experimentally acquired sinograms from a clinical scanner were reconstructed by LIAM while varying the regularization parameters to identify good choices. The results from the dual-energy alternating minimization algorithm applied to the same data were used for comparison. Using a small fraction of the computation time of dual-energy alternating minimization, LIAM achieves better accuracy of the component images in the presence of Poisson noise for simulated data reconstruction and achieves the same level of accuracy for real data reconstruction.

Sinogram-based attenuation correction in PET/CT

In a typical positron emission tomography/computed tomography (PET/CT) system, the attenuation correction is necessary for PET image reconstruction, which involves a transformation from the CT Hounsfield units (HU) to its linear attenuation coefficient (LAC) at 511 keV. This transformation is usually aided by an empirical bilinear function, followed by the forward projection of the transformed attenuation image. In this paper, we propose a direct method that calculates attenuation factors from CT projections, without using a reconstructed CT image. In this method, the human body is considered as a mixture of three distinct components: air, water and bone. Then, we estimate the proportions of these three components along each x-ray path and restore the attenuation factor at 511 keV with the known water and bone LACs. Our numerical results show that the proposed method produces as accurate estimation as the conventional HU mapping method.

Material identification in x-ray microscopy and micro CT using multi-layer, multi-color scintillation detectors

We demonstrate that a dual-layer, dual-color scintillator construct for microscopic CT, originally proposed to increase sensitivity in synchrotron imaging, can also be used to perform material quantification and classification when coupled with polychromatic illumination. We consider two different approaches to data handling: (1) a data-domain material decomposition whose estimation performance can be characterized by the Cramer-Rao lower bound formalism but which requires careful calibration and (2) an image-domain material classification approach that is more robust to calibration errors. The data-domain analysis indicates that useful levels of SNR (>5) could be achieved in one second or less at typical bending magnet fluxes for relatively large amounts of contrast (several mm path length, such as in a fluid flow experiment) and at typical undulator fluxes for small amount of contrast (tens of microns path length, such as an angiography experiment). The tools introduced could of course be used to study and optimize parameters for a wider range of potential applications. The image domain approach was analyzed in terms of its ability to distinguish different elemental stains by characterizing the angle between the lines traced out in a two-dimensional space of effective attenuation coefficient in the front and back layer images. This approach was implemented at a synchrotron and the results were consistent with simulation predictions.

Spectral CT Image Restoration via an Average Image-Induced Nonlocal Means Filter

GOAL

Spectral computed tomography (SCT) images reconstructed by an analytical approach often suffer from a poor signal-to-noise ratio and strong streak artifacts when sufficient photon counts are not available in SCT imaging. In reducing noise-induced artifacts in SCT images, in this study, we propose an average image-induced nonlocal means (aviNLM) filter for each energy-specific image restoration.  Methods:  The present aviNLM algorithm exploits redundant information in the whole energy domain. Specifically, the proposed aviNLM algorithm yields the restored results by performing a nonlocal weighted average operation on the noisy energy-specific images with the nonlocal weight matrix between the target and prior images, in which the prior image is generated from all of the images reconstructed in each energy bin.  Results: Qualitative and quantitative studies are conducted to evaluate the aviNLM filter by using the data of digital phantom, physical phantom, and clinical patient data acquired from the energy-resolved and -integrated detectors, respectively. Experimental results show that the present aviNLM filter can achieve promising results for SCT image restoration in terms of noise-induced artifact suppression, cross profile, and contrast-to-noise ratio and material decomposition assessment. Conclusion and Significance: The present aviNLM algorithm has useful potential for radiation dose reduction by lowering the mAs in SCT imaging, and it may be useful for some other clinical applications, such as in myocardial perfusion imaging and radiotherapy.

Dual energy CT for attenuation correction with PET/CT

PURPOSE

The authors evaluate the energy dependent noise and bias properties of monoenergetic images synthesized from dual-energy CT (DECT) acquisitions. These monoenergetic images can be used to estimate attenuation coefficients at energies suitable for positron emission tomography (PET) and single-photon emission computed tomography (SPECT) imaging. This is becoming more relevant with the increased use of quantitative imaging by PET/CT and SPECT/CT scanners. There are, however, potential variations in the noise and bias of synthesized monoenergetic images as a function of energy.

METHODS

The authors used analytic approximations and simulations to estimate the noise and bias of synthesized monoenergetic images of water-filled cylinders with different shapes and the NURBS-based cardiac-torso (NCAT) phantom from 40 to 520 keV, the range of SPECT and PET energies. The dual-kVp spectra were based on the GE Lightspeed VCT scanner at 80 and 140 kVp with added filtration of 0.5 mm Cu. The authors evaluated strategies of noise suppression with sinogram smoothing and dose minimization with reduction of tube currents at the two kVp settings. The authors compared the impact of DECT-based attenuation correction with single-kVp CT-based attenuation correction on PET quantitation for the NCAT phantom for soft tissue and high-Z materials of bone and iodine contrast enhancement.

RESULTS

Both analytic calculations and simulations displayed the expected minimum noise value for a synthesized monoenergetic image at an energy between the mean energies of the two spectra. In addition the authors found that the normalized coefficient of variation in the synthesized attenuation map increased with energy but reached a plateau near 160 keV, and then remained constant with increasing energy up to 511 keV and beyond. The bias was minimal, as the linear attenuation coefficients of the synthesized monoenergetic images were within 2.4% of the known true values across the entire energy range. Compared with no sinogram smoothing, sinogram smoothing can dramatically reduce noise in the DECT-derived attenuation map. Through appropriate selection of tube currents for high and low kVp scans, DECT can deliver roughly the same amount of radiation dose as that of a single kVp CT scan, but could be used for PET attenuation correction with reduced bias in contrast agent regions by a factor of ≈ 2.6 and slightly reduced RMSE for the total image.

CONCLUSIONS

When DECT is used for attenuation correction at higher energies, there is a noise amplification that is dependent on the energy of the synthesized monoenergetic image of linear attenuation coefficients. Sinogram smoothing reduces the noise amplification in DECT-derived attenuation maps without increasing bias. With an appropriate selection of CT techniques, a DECT scan with the same radiation dose as a single CT scan can result in a PET image with improved quantitative accuracy.

A full-spectral Bayesian reconstruction approach based on the material decomposition model applied in dual-energy computed tomography

PURPOSE

Dual-energy computed tomography (DECT) makes it possible to get two fractions of basis materials without segmentation. One is the soft-tissue equivalent water fraction and the other is the hard-matter equivalent bone fraction. Practical DECT measurements are usually obtained with polychromatic x-ray beams. Existing reconstruction approaches based on linear forward models without counting the beam polychromaticity fail to estimate the correct decomposition fractions and result in beam-hardening artifacts (BHA). The existing BHA correction approaches either need to refer to calibration measurements or suffer from the noise amplification caused by the negative-log preprocessing and the ill-conditioned water and bone separation problem. To overcome these problems, statistical DECT reconstruction approaches based on nonlinear forward models counting the beam polychromaticity show great potential for giving accurate fraction images.

METHODS

This work proposes a full-spectral Bayesian reconstruction approach which allows the reconstruction of high quality fraction images from ordinary polychromatic measurements. This approach is based on a Gaussian noise model with unknown variance assigned directly to the projections without taking negative-log. Referring to Bayesian inferences, the decomposition fractions and observation variance are estimated by using the joint maximum a posteriori (MAP) estimation method. Subject to an adaptive prior model assigned to the variance, the joint estimation problem is then simplified into a single estimation problem. It transforms the joint MAP estimation problem into a minimization problem with a nonquadratic cost function. To solve it, the use of a monotone conjugate gradient algorithm with suboptimal descent steps is proposed.

RESULTS

The performance of the proposed approach is analyzed with both simulated and experimental data. The results show that the proposed Bayesian approach is robust to noise and materials. It is also necessary to have the accurate spectrum information about the source-detector system. When dealing with experimental data, the spectrum can be predicted by a Monte Carlo simulator. For the materials between water and bone, less than 5% separation errors are observed on the estimated decomposition fractions.

CONCLUSIONS

The proposed approach is a statistical reconstruction approach based on a nonlinear forward model counting the full beam polychromaticity and applied directly to the projections without taking negative-log. Compared to the approaches based on linear forward models and the BHA correction approaches, it has advantages in noise robustness and reconstruction accuracy.

Proximal ADMM for multi-channel image reconstruction in spectral X-ray CT

The development of spectral X-ray computed tomography (CT) using binned photon-counting detectors has received great attention in recent years and has enabled selective imaging of contrast agents loaded with K-edge materials. A practical issue in implementing this technique is the mitigation of the high-noise levels often present in material-decomposed sinogram data. In this work, the spectral X-ray CT reconstruction problem is formulated within a multi-channel (MC) framework in which statistical correlations between the decomposed material sinograms can be exploited to improve image quality. Specifically, a MC penalized weighted least squares (PWLS) estimator is formulated in which the data fidelity term is weighted by the MC covariance matrix and sparsity-promoting penalties are employed. This allows the use of any number of basis materials and is therefore applicable to photon-counting systems and K-edge imaging. To overcome numerical challenges associated with use of the full covariance matrix as a data fidelity weight, a proximal variant of the alternating direction method of multipliers is employed to minimize the MC PWLS objective function. Computer-simulation and experimental phantom studies are conducted to quantitatively evaluate the proposed reconstruction method.

Multi-material decomposition using statistical image reconstruction for spectral CT

Spectral computed tomography (CT) provides information on material characterization and quantification because of its ability to separate different basis materials. Dual-energy (DE) CT provides two sets of measurements at two different source energies. In principle, two materials can be accurately decomposed from DECT measurements. However, many clinical and industrial applications require three or more material images. For triple-material decomposition, a third constraint, such as volume conservation, mass conservation or both, is required to solve three sets of unknowns from two sets of measurements. The recently proposed flexible image-domain (ID) multi-material decomposition) method assumes each pixel contains at most three materials out of several possible materials and decomposes a mixture pixel by pixel. We propose a penalized-likelihood (PL) method with edge-preserving regularizers for each material to reconstruct multi-material images using a similar constraint from sinogram data. We develop an optimization transfer method with a series of pixel-wise separable quadratic surrogate (PWSQS) functions to monotonically decrease the complicated PL cost function. The PWSQS algorithm separates pixels to allow simultaneous update of all pixels, but keeps the basis materials coupled to allow faster convergence rate than our previous proposed material- and pixel-wise SQS algorithms. Comparing with the ID method using 2-D fan-beam simulations, the PL method greatly reduced noise, streak and cross-talk artifacts in the reconstructed basis component images, and achieved much smaller root mean square errors.

Model-Based Iterative Reconstruction for Dual-Energy X-Ray CT Using a Joint Quadratic Likelihood Model

Dual-energy X-ray CT (DECT) has the potential to improve contrast and reduce artifacts as compared to traditional CT. Moreover, by applying model-based iterative reconstruction (MBIR) to dual-energy data, one might also expect to reduce noise and improve resolution. However, the direct implementation of dual-energy MBIR requires the use of a nonlinear forward model, which increases both complexity and computation. Alternatively, simplified forward models have been used which treat the material-decomposed channels separately, but these approaches do not fully account for the statistical dependencies in the channels. In this paper, we present a method for joint dual-energy MBIR (JDE-MBIR), which simplifies the forward model while still accounting for the complete statistical dependency in the material-decomposed sinogram components. The JDE-MBIR approach works by using a quadratic approximation to the polychromatic log-likelihood and a simple but exact nonnegativity constraint in the image domain. We demonstrate that our method is particularly effective when the DECT system uses fast kVp switching, since in this case the model accounts for the inaccuracy of interpolated sinogram entries. Both phantom and clinical results show that the proposed model produces images that compare favorably in quality to previous decomposition-based methods, including FBP and other statistical iterative approaches.

Information-theoretic discrepancy based iterative reconstructions (IDIR) for polychromatic x-ray tomography

PURPOSE

X-ray photons generated from a typical x-ray source for clinical applications exhibit a broad range of wavelengths, and the interactions between individual particles and biological substances depend on particles' energy levels. Most existing reconstruction methods for transmission tomography, however, neglect this polychromatic nature of measurements and rely on the monochromatic approximation. In this study, we developed a new family of iterative methods that incorporates the exact polychromatic model into tomographic image recovery, which improves the accuracy and quality of reconstruction.

METHODS

The generalized information-theoretic discrepancy (GID) was employed as a new metric for quantifying the distance between the measured and synthetic data. By using special features of the GID, the objective function for polychromatic reconstruction which contains a double integral over the wavelength and the trajectory of incident x-rays was simplified to a paraboloidal form without using the monochromatic approximation. More specifically, the original GID was replaced with a surrogate function with two auxiliary, energy-dependent variables. Subsequently, the alternating minimization technique was applied to solve the double minimization problem. Based on the optimization transfer principle, the objective function was further simplified to the paraboloidal equation, which leads to a closed-form update formula. Numerical experiments on the beam-hardening correction and material-selective reconstruction were conducted to compare and assess the performance of conventional methods and the proposed algorithms.

RESULTS

The authors found that the GID determines the distance between its two arguments in a flexible manner. In this study, three groups of GIDs with distinct data representations were considered. The authors demonstrated that one type of GIDs that comprises "raw" data can be viewed as an extension of existing statistical reconstructions; under a particular condition, the GID is equivalent to the Poisson log-likelihood function. The newly proposed GIDs of the other two categories consist of log-transformed measurements, which have the advantage of imposing linearized penalties over multiple discrepancies. For all proposed variants of the GID, the aforementioned strategy was used to obtain a closed-form update equation. Even though it is based on the exact polychromatic model, the derived algorithm bears a structural resemblance to conventional methods based on the monochromatic approximation. The authors named the proposed approach as information-theoretic discrepancy based iterative reconstructions (IDIR). In numerical experiments, IDIR with raw data converged faster than previously known statistical reconstruction methods. IDIR with log-transformed data exhibited superior reconstruction quality and faster convergence speed compared with conventional methods and their variants.

CONCLUSIONS

The authors' new framework for tomographic reconstruction allows iterative inversion of the polychromatic data model. The primary departure from the traditional iterative reconstruction was the employment of the GID as a new metric for quantifying the inconsistency between the measured and synthetic data. The proposed methods outperformed not only conventional methods based on the monochromatic approximation but also those based on the polychromatic model. The authors have observed that the GID is a very flexible means to design an objective function for iterative reconstructions. Hence, the authors expect that the proposed IDIR framework will also be applicable to other challenging tasks.

Sparse angular CT reconstruction using non-local means based iterative-correction POCS

In divergent-beam computed tomography (CT), sparse angular sampling frequently leads to conspicuous streak artifacts. In this paper, we propose a novel non-local means (NL-means) based iterative-correction projection onto convex sets (POCS) algorithm, named as NLMIC-POCS, for effective and robust sparse angular CT reconstruction. The motivation for using NLMIC-POCS is that NL-means filtered image can produce an acceptable priori solution for sequential POCS iterative reconstruction. The NLMIC-POCS algorithm has been tested on simulated and real phantom data. The experimental results show that the presented NLMIC-POCS algorithm can significantly improve the image quality of the sparse angular CT reconstruction in suppressing streak artifacts and preserving the edges of the image.

Noise and Bias Properties of Monoenergetic Images from DECT used for Attenuation Correction with PET/CT and SPECT/CT

We evaluate the energy dependent noise and bias properties of monoenergetic images synthesized from dual-energy CT (DECT) acquisitions used to estimate attenuation coefficients at PET or SPECT energies. This is becoming more relevant with the increased used of quantitative imaging by PET/CT and SPECT/CT. There are, however, variations in the noise and bias properties of synthesized monoenergetic images as a function of energy. We used analytic approximations and simulations to estimate the bias and noise of synthesized monoenergetic images of a water-filled cylinder from 10 to 525 keV. The dual-energy spectra were based on the GE Lightspeed VCT scanner at 80 and 140 kVp. Both analytic calculations and simulations for increasing energy the relative noise plateaued near 140 keV (i.e. SPECT with (99m)Tc), and then remained constant with increasing energy up to 511 keV and beyond (i.e. PET). If DECT is being used for attenuation correction at higher energies, there is a noise amplification that is dependent on the energy of the synthesized monoenergetic image of linear attenuation coefficients. For SPECT and PET imaging the bias and noise levels of DECT based attenuation correction is unlikely to affect image quality.