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.

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.

CT-based synthetic iodine map generation using conditional denoising diffusion probabilistic model.

BACKGROUND: Iodine maps, derived from image-processing of contrast-enhanced dual-energy computed tomography (DECT) scans, highlight the differences in tissue iodine intake. It finds multiple applications in radiology, including vascular imaging, pulmonary evaluation, kidney assessment, and cancer diagnosis. In radiation oncology, it can contribute to designing more accurate and personalized treatment plans. However, DECT scanners are not commonly available in radiation therapy centers. Additionally, the use of iodine contrast agents is not suitable for all patients, especially those allergic to iodine agents, posing further limitations to the accessibility of this technology. PURPOSE: The purpose of this work is to generate synthetic iodine map images from non-contrast single-energy CT (SECT) images using conditional denoising diffusion probabilistic model (DDPM). METHODS: One-hundered twenty-six head-and-neck patients' images were retrospectively investigated in this work. Each patient underwent non-contrast SECT and contrast DECT scans. Ground truth iodine maps were generated from contrast DECT scans using commercial software syngo.via installed in the clinic. A conditional DDPM was implemented in this work to synthesize iodine maps. Three-fold cross-validation was conducted, with each iteration selecting the data from 42 patients as the test dataset and the remainder as the training dataset. Pixel-to-pixel generative adversarial network (GAN) and CycleGAN served as reference methods for evaluating the proposed DDPM method. RESULTS: The accuracy of the proposed DDPM was evaluated using three quantitative metrics: mean absolute error (MAE) (1.039 ± 0.345 mg/mL), structural similarity index measure (SSIM) (0.89 ± 0.10) and peak signal-to-noise ratio (PSNR) (25.4 ± 3.5 db) respectively. Compared to the reference methods, the proposed technique showcased superior performance across the evaluated metrics, further validated by the paired two-tailed t-tests. CONCLUSION: The proposed conditional DDPM framework has demonstrated the feasibility of generating synthetic iodine map images from non-contrast SECT images. This method presents a potential clinical application, which is providing accurate iodine contrast map in instances where only non-contrast SECT is accessible.

Deep learning-based fast volumetric imaging using kV and MV projection images for lung cancer radiotherapy: A feasibility study.

PURPOSE: The long acquisition time of CBCT discourages repeat verification imaging, therefore increasing treatment uncertainty. In this study, we present a fast volumetric imaging method for lung cancer radiation therapy using an orthogonal 2D kV/MV image pair. METHODS: The proposed model is a combination of 2D and 3D networks. The proposed model consists of five major parts: (1) kV and MV feature extractors are used to extract deep features from the perpendicular kV and MV projections. (2) The feature-matching step is used to re-align the feature maps to their projection angle in a Cartesian coordinate system. By using a residual module, the feature map can focus more on the difference between the estimated and ground truth images. (3) In addition, the feature map is downsized to include more global semantic information for the 3D estimation, which is useful to reduce inhomogeneity. By using convolution-based reweighting, the model is able to further increase the uniformity of image. (4) To reduce the blurry noise of generated 3D volume, the Laplacian latent space loss calculated via the feature map that is extracted via specifically-learned Gaussian kernel is used to supervise the network. (5) Finally, the 3D volume is derived from the trained model. We conducted a proof-of-concept study using 50 patients with lung cancer. An orthogonal kV/MV pair was generated by ray tracing through CT of each phase in a 4D CT scan. Orthogonal kV/MV pairs from nine respiratory phases were used to train this patient-specific model while the kV/MV pair of the remaining phase was held for model testing. RESULTS: The results are based on simulation data and phantom results from a real Linac system. The mean absolute error (MAE) values achieved by our method were 57.5 HU and 77.4 HU within body and tumor region-of-interest (ROI), respectively. The mean achieved peak-signal-to-noise ratios (PSNR) were 27.6 dB and 19.2 dB within the body and tumor ROI, respectively. The achieved mean normalized cross correlation (NCC) values were 0.97 and 0.94 within the body and tumor ROI, respectively. A phantom study demonstrated that the proposed method can accurately re-position the phantom after shift. It is also shown that the proposed method using both kV and MV is superior to current method using kV or MV only in image quality. CONCLUSION: These results demonstrate the feasibility and accuracy of our proposed fast volumetric imaging method from an orthogonal kV/MV pair, which provides a potential solution for daily treatment setup and verification of patients receiving radiation therapy for lung cancer.

Inter-fraction deformable image registration using unsupervised deep learning for CBCT-guided abdominal radiotherapy.

Objective. CBCTs in image-guided radiotherapy provide crucial anatomy information for patient setup and plan evaluation. Longitudinal CBCT image registration could quantify the inter-fractional anatomic changes, e.g. tumor shrinkage, and daily OAR variation throughout the course of treatment. The purpose of this study is to propose an unsupervised deep learning-based CBCT-CBCT deformable image registration which enables quantitative anatomic variation analysis.Approach.The proposed deformable registration workflow consists of training and inference stages that share the same feed-forward path through a spatial transformation-based network (STN). The STN consists of a global generative adversarial network (GlobalGAN) and a local GAN (LocalGAN) to predict the coarse- and fine-scale motions, respectively. The network was trained by minimizing the image similarity loss and the deformable vector field (DVF) regularization loss without the supervision of ground truth DVFs. During the inference stage, patches of local DVF were predicted by the trained LocalGAN and fused to form a whole-image DVF. The local whole-image DVF was subsequently combined with the GlobalGAN generated DVF to obtain the final DVF. The proposed method was evaluated using 100 fractional CBCTs from 20 abdominal cancer patients in the experiments and 105 fractional CBCTs from a cohort of 21 different abdominal cancer patients in a holdout test.Main Results. Qualitatively, the registration results show good alignment between the deformed CBCT images and the target CBCT image. Quantitatively, the average target registration error calculated on the fiducial markers and manually identified landmarks was 1.91 ± 1.18 mm. The average mean absolute error, normalized cross correlation between the deformed CBCT and target CBCT were 33.42 ± 7.48 HU, 0.94 ± 0.04, respectively.Significance. In summary, an unsupervised deep learning-based CBCT-CBCT registration method is proposed and its feasibility and performance in fractionated image-guided radiotherapy is investigated. This promising registration method could provide fast and accurate longitudinal CBCT alignment to facilitate inter-fractional anatomic changes analysis and prediction.

Image-Domain Material Decomposition for Dual-energy CT using Unsupervised Learning with Data-fidelity Loss.

BACKGROUND: Dual-energy CT (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.

One-step Iterative Estimation of Effective Atomic Number and Electron Density for Dual Energy CT.

Dual-energy computed tomography (DECT) is a promising technology that has shown a number of clinical advantages over conventional X-ray CT, such as improved material identification, artifact suppression, etc. For proton therapy treatment planning, besides material-selective images, maps of effective atomic number (Z) and relative electron density to that of water ($\rho_e$) can also be achieved and further employed to improve stopping power ratio accuracy and reduce range uncertainty. In this work, we propose a one-step iterative estimation method, which employs multi-domain gradient $L_0$-norm minimization, for Z and $\rho_e$ maps reconstruction. The algorithm was implemented on GPU to accelerate the predictive procedure and to support potential real-time adaptive treatment planning. The performance of the proposed method is demonstrated via both phantom and patient studies.

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 to implement data acquisition via sophisticated schemes, for example, 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 computed tomography (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.

Magnetic resonance imaging contrast enhancement synthesis using cascade networks with local supervision.

PURPOSE: Gadolinium-based contrast agents (GBCAs) are widely administrated in MR imaging for diagnostic studies and treatment planning. Although GBCAs are generally thought to be safe, various health and environmental concerns have been raised recently about their use in MR imaging. The purpose of this work is to derive synthetic contrast enhance MR images from unenhanced counterpart images, thereby eliminating the need for GBCAs, using a cascade deep learning workflow that incorporates contour information into the network. METHODS AND MATERIALS: The proposed workflow consists of two sequential networks: (1) a retina U-Net, which is first trained to derive semantic features from the non-contrast MR images in representing the tumor regions; and (2) a synthesis module, which is trained after the retina U-Net to take the concatenation of the semantic feature maps and non-contrast MR image as input and to generate the synthetic contrast enhanced MR images. After network training, only the non-contrast enhanced MR images are required for the input in the proposed workflow. The MR images of 369 patients from the multimodal brain tumor segmentation challenge 2020 (BraTS2020) dataset were used in this study to evaluate the proposed workflow for synthesizing contrast enhanced MR images (200 patients for five-fold cross-validation and 169 patients for hold-out test). Quantitative evaluations were conducted by calculating the normalized mean absolute error (NMAE), structural similarity index measurement (SSIM), and Pearson correlation coefficient (PCC). The original contrast enhanced MR images were considered as the ground truth in this analysis. RESULTS: The proposed cascade deep learning workflow synthesized contrast enhanced MR images that are not visually differentiable from the ground truth with and without supervision of the tumor contours during the network training. Difference images and profiles of the synthetic contrast enhanced MR images revealed that intensity differences could be observed in the tumor region if the contour information was not incorporated in network training. Among the hold-out test patients, mean values and standard deviations of the NMAE, SSIM, and PCC were 0.063±0.022, 0.991±0.007 and 0.995±0.006, respectively, for the whole brain; and were 0.050±0.025, 0.993±0.008 and 0.999±0.003, respectively, for the tumor contour regions. Quantitative evaluations with five-fold cross-validation and hold-out test showed that the calculated metrics can be significantly enhanced (p-values ≤ 0.002) with the tumor contour supervision in network training. CONCLUSION: The proposed workflow was able to generate synthetic contrast enhanced MR images that closely resemble the ground truth images from non-contrast enhanced MR images when the network training included tumor contours. These results suggest that it may be possible to minimize the use of GBCAs in cranial MR imaging studies.

Synthesizing high-resolution magnetic resonance imaging using parallel cycle-consistent generative adversarial networks for fast magnetic resonance imaging.

PURPOSE: The common practice in acquiring the magnetic resonance (MR) images is to obtain two-dimensional (2D) slices at coarse locations while keeping the high in-plane resolution in order to ensure enough body coverage while shortening the MR scan time. The aim of this study is to propose a novel method to generate HR MR images from low-resolution MR images along the longitudinal direction. In order to address the difficulty of collecting paired low- and high-resolution MR images in clinical settings and to gain the advantage of parallel cycle consistent generative adversarial networks (CycleGANs) in synthesizing realistic medical images, we developed a parallel CycleGANs based method using a self-supervised strategy. METHODS AND MATERIALS: The proposed workflow consists of two parallely trained CycleGANs to independently predict the HR MR images in the two planes along the directions that are orthogonal to the longitudinal MR scan direction. Then, the final synthetic HR MR images are generated by fusing the two predicted images. MR images, including T1-weighted (T1), contrast enhanced T1-weighted (T1CE), T2-weighted (T2), and T2 Fluid Attenuated Inversion Recovery (FLAIR), of the multimodal brain tumor segmentation challenge 2020 (BraTS2020) dataset were processed to evaluate the proposed workflow along the cranial-caudal (CC), lateral, and anterior-posterior directions. Institutional collected MR images were also processed for evaluation of the proposed method. The performance of the proposed method was investigated via both qualitative and quantitative evaluations. Metrics of normalized mean absolute error (NMAE), peak signal-to-noise ratio (PSNR), edge keeping index (EKI), structural similarity index measurement (SSIM), information fidelity criterion (IFC), and visual information fidelity in pixel domain (VIFP) were calculated. RESULTS: It is shown that the proposed method can generate HR MR images visually indistinguishable from the ground truth in the investigations on the BraTS2020 dataset. In addition, the intensity profiles, difference images and SSIM maps can also confirm the feasibility of the proposed method for synthesizing HR MR images. Quantitative evaluations on the BraTS2020 dataset shows that the calculated metrics of synthetic HR MR images can all be enhanced for the T1, T1CE, T2, and FLAIR images. The enhancements in the numerical metrics over the low-resolution and bi-cubic interpolated MR images, as well as those genearted with a comparative deep learning method, are statistically significant. Qualitative evaluation of the synthetic HR MR images of the clinical collected dataset could also confirm the feasibility of the proposed method. CONCLUSIONS: The proposed method is feasible to synthesize HR MR images using self-supervised parallel CycleGANs, which can be expected to shorten MR acquisition time in clinical practices.

On the Conditioning of Spectral Channelization (Energy Binning) and Its Impact on Multi-Material Decomposition Based Spectral Imaging in Photon-Counting CT.

OBJECTIVE: The conditioning (well-posedness) of basis materials (functions) and spectral channelization play important roles in determining the performance of spectral imaging (material specific imaging and virtual monochromatic imaging/analysis) in photon-counting CT. Aimed at further understanding the fundamentals of photon-counting spectral CT and providing guidelines on its design and implementation, we propose a singular value decomposition (SVD) and analysis based approach in this work to assess the conditioning of spectral channelization and its impact on the performance of spectral imaging under both ideal and realistic detector spectral response. METHODS: Via simulation studies, in which the geometry of photon-counting CT is similar to a clinical CT, the condition number acquired via SVD and analysis is employed to assess the conditioning of spectral channelization in photon-counting CT and its impact on the performance of spectral imaging. The simulation study runs over two- and three-material decom-position based spectral imaging (material specific imaging and virtual monochromatic imaging/analysis over the energy range [18] [150] keV). Under both ideal and realistic detector spectral response, a specially designed phantom that mimics the soft and bony tissues in the head is utilized to quantitatively reveal the relationship between the conditioning (condition number) of spectral channelization and the performance (mainly noise and contrast-to-noise ratio) of spectral imaging in photon-counting CT. The simulation study is also extended over the cases wherein up to 50% spectral overlapping occurs. RESULTS: The results show that, under ideal detector spectral response, the condition number of spectral channelization reaches the minimum while no overlapping occurs in spectral channels. The condition number of spectral channelization increments with increasing spectral overlapping in the channels. The distortion in detector's spectral response induced by scattering, charge-sharing and fluorescent escaping results in spectral overlapping in spectral channels and thus degrades the conditioning (larger condition number) of spectral channelization. Respectively, the noise increases and contrast-to-noise ratio decreases in material- specific imaging and virtual monochromatic imaging/analysis, while the condition number of spectral channelization increments with increasing spectral overlapping. CONCLUSION: The SVD and analysis based approach can be utilized to systematically analyze the conditioning of spectral channelization and its impact on the performance of spectral imaging in photon-counting CT. SIGNIFICANCE: The approach proposed by us brings innovation and has significance. In addition to providing information for insightful understanding of the fundamentals, the approach proposed in this study and the data obtained so far may provide guidelines on the implementation of spectral imaging in photon-counting CT and energy-integration CT as well, along with its applicability to other x-ray related imaging modalities such as radiography and tomosynthesis.

Principal Component Analysis in Projection and Image Domains-Another Form of Spectral Imaging in Photon-Counting CT.

OBJECTIVE: We explore the feasibility of principal component analysis (PCA) as a form of spectral imaging in photon-counting CT. METHODS: Using the data acquired by a prototype system and simulated by computer, we investigate the feasibility of spectral imaging in photon-counting CT via PCA for feature extraction and study the impacts made by data standardization and de-noising on its performance. RESULTS: The PCA in the projection domain maintains the data consistence that is essential for tomographic image reconstruction and performs virtually the same as that in the image domain. The first three primary components account for more than 99.99% covariance of the data. Within anticipation, the contrast-to-noise ratio (CNR) between the target and background in the first principal component image can be larger than that in the image generated from the data acquired in each energy bin. More importantly, the CNR in the first principal component image may be larger than that in the image formed by the summed data acquired in all energy bins (i.e., the conventional polychromatic CT image). In addition, de-noising can not only reduce the noise in images but also improve the effectiveness/efficiency of PCA in feature extraction. CONCLUSION: The PCA in either projection or image domain provides another form of spectral imaging in photon-counting CT that fits the essential requirements on spectral imaging in true color. SIGNIFICANCE: The verification of PCA's feasibility in CT as a form spectral imaging and observation of its potential superiority in CNR over conventional polychromatic CT are meaningful in theory and practice.

High through-plane resolution CT imaging with self-supervised deep learning.

CT images for radiotherapy planning are usually acquired in thick slices to reduce the imaging dose, especially for pediatric patients, and to lessen the need for contouring and treatment planning on more slices. However, low through-plane resolution may degrade the accuracy of dose calculations. In this paper, a self-supervised deep learning workflow is proposed to synthesize high through-plane resolution CT images by learning from their high in-plane resolution features. The proposed workflow was designed to facilitate neural networks to learn the mapping from low-resolution (LR) to high-resolution (HR) images in the axial plane. During the inference step, the HR sagittal and coronal images were generated by feeding two parallel-trained neural networks with the respective LR sagittal and coronal images to the trained neural networks. The CT simulation images of a cohort of 75 patients with head and neck cancer (1 mm slice thickness) and 200 CT images of a cohort of 20 lung cancer patients (3 mm slice thickness) were retrospectively investigated in a cross-validation manner. The HR images generated with the proposed method were qualitatively (visual quality, image intensity profiles and preliminary observer study) and quantitatively (mean absolute error, edge keeping index, structural similarity index measurement, information fidelity criterion and visual information fidelity in pixel domain) inspected, while taking the original CT images of the head and neck and lung cancer patients as the reference. The qualitative results showed the capability of the proposed method for generating high through-plane resolution CT images with data from both groups of cancer patients. All the improvements in the measure metrics were confirmed to be statistically significant with paired two-samplet-test analysis. The innovative point of the work is that the proposed deep learning workflow for CT image generation with high through-plane resolution in radiotherapy is self-supervised, meaning that it does not rely on ground truth CT images to train the network. In addition, the assumption that the in-plane HR information can supervise the through-plane HR generation is confirmed. We hope that this will inspire more research on this topic to further improve the through-plane resolution of medical images.

Content-oriented sparse representation (COSR) for CT denoising with preservation of texture and edge.

PURPOSE: Denoising has been a challenging research subject in medical imaging, since the suppression of noise conflicts with the preservation of texture and edges. To address this challenge, we develop a content-oriented sparse representation (COSR) method for denoising in computed tomography (CT). METHODS: An image is segmented into a number of content areas and each of them consists of similar material. Having been ex-painted, each content area is sparsely coded using the dictionary learnt from patches extracted from the corresponding content area. By constraining sparsity, noise is suppressed and the final image is formed by aggregating all denoised content areas. The performance of COSR method is examined with images simulated by computer and generated by multidetector row CT (MDCT), cone beam CT (CBCT), and micro-CT, in which water phantom, anthropomorphic phantom, a human subject, and a small animal are engaged, using the figures of merit, such as standard division (SD), contrast to noise ratio (CNR), and thresholded edge keeping index (EKIth ) and structural similarity index (SSIM). In addition, the optimization of performance by parameter tuning is also investigated. RESULTS: Quantitatively gauged by metrics of noise, EKIth and SSIM, the performance evaluation shows that the proposed COSR method is effective in denoising (>50% reduction in noise) while it outperforms the conventional sparse representation method in preservation of texture and edge by ~20% (gauged by SSIM). It has also been shown that the COSR method is tolerable to inaccuracy in content area segmentation and variation in dictionary learning. Moreover, the computational efficiency of COSR can be substantially improved using prelearnt dictionaries. CONCLUSIONS: The COSR method would find its utility in clinical and preclinical applications, such as low-dose CT, image segmentation, registration, and computer-aided diagnosis. The proposal of COSR denoising is of innovation and significance in the theory and practice of denoising in medical imaging. A demonstration code package is available at https://github.com/xiehq/COSR.

On the data acquisition, image reconstruction, cone beam artifacts, and their suppression in axial MDCT and CBCT - A review.

PURPOSE: In the clinic, computed tomography (CT) has evolved into an essential modality for diagnostic imaging by multidetector row CT (MDCT) and image guided intervention by cone beam CT (CBCT). Recognizing the increasing importance of axial MDCT/CBCT in clinical and preclinical applications, and the existence of CB artifacts in MDCT/CBCT images, we provide a review of CB artifacts' root causes, rendering mechanisms and morphology, and possible solutions for elimination and/or reduction of the artifacts. METHODS: By examining the null space in Radon and Fourier domain, the root cause of CB artifacts (i.e., data insufficiency) in axial MDCT/CBCT is analytically investigated, followed by a review of the data sufficiency conditions and the "circle +" source trajectories. The rendering mechanisms and morphology of CB artifacts in axial MDCT/CBCT and their special cases (e.g., half/short scan and full scan with latitudinally displaced detector) are then analyzed, followed by a survey of the potential solutions to suppress the artifacts. The phenomenon of imaged zone indention and its variation over FBP, BPF/DBPF, two-pass and iterative CB reconstruction algorithms and/or schemes are discussed in detail. RESULTS: An interdomain examination of the null space provides an insightful understanding of the root cause of CB artifacts in axial MDCT/CBCT. The decomposition of CB artifacts rendering mechanisms facilitates understanding of the artifacts' behavior under different conditions and the potential solutions to suppress them. An inspection of the imaged zone intention phenomenon provides guidance on the design and implementation of CB image reconstruction algorithms and schemes for CB artifacts suppression in axial MDCT/CBCT. CONCLUSIONS: With increasing importance of axial MDCT/CBCT in clinical and preclinical applications, this review article can update the community with in-depth information and clarification on the latest progress in dealing with CB artifacts and thus increase clinical/preclinical confidence.

Optimization of data acquisition in axial CT under the framework of sampling on lattice for suppression of aliasing artifacts with algorithmic detector interlacing.

PURPOSE: We present the methodology for analyzing and optimizing the sampling structure of projection data acquisition in axial multidetector CT (MDCT) and cone beam CT (CBCT) under the framework of sampling on lattice. Specifically, we propose and evaluate the scheme of interlaced detector cell binning for suppression of longitudinal aliasing artifacts. In addition, we investigate the proposed scheme's capability of mitigating shift variation in spatial resolution and possibility of improving CB image reconstruction accuracy. METHODS: Under the framework of sampling on lattice, the proposed scheme is evaluated using an axial MDCT with its architecture similar to that of state-of-the-art CT scanners for diagnostic imaging in the clinic. The widely used FDK algorithm is adopted for image reconstruction, in which either horizontal/latitudinal or vertical/longitudinal interpolation is used for lining-up of projection data between interlaced detector cells. Using a spiral clock phantom, the capability of suppressing aliasing artifacts and possibility of improving reconstruction accuracy is quantitatively investigated. The in-plane spatial resolution, as assessed by the modulation transfer function (MTF), and its shift-variant property are quantitatively assessed using wire phantoms, while the through-plane spatial resolution and its shift-variant behavior are assessed by the slice sensitivity profile (SSP) using thin foil phantoms. RESULTS: The preliminary results show that the interlaced detector cell binning can suppress longitudinal aliasing artifacts effectively, while the shift variation in spatial resolution and reconstruction inaccuracy can be mitigated moderately. In addition, the direction, along which the interpolation is carried out to line up projection data between the interlaced detector cells for image reconstruction, plays a significant role in determining the in-plane and through-plane spatial resolution. CONCLUSIONS: The scheme of interlaced detector cell binning with longitudinal interpolation for data lining-up is an effective solution for suppression of longitudinal aliasing artifacts in axial MDCT and CBCT.

Grating-based x-ray differential phase contrast imaging with twin peaks in phase-stepping curves-phase retrieval and dewrapping.

PURPOSE: X-ray differential phase contrast CT implemented with Talbot interferometry employs phase-stepping to extract information of x-ray attenuation, phase shift, and small-angle scattering. Since inaccuracy may exist in the absorption grating G2 due to an imperfect fabrication, the effective period of G2 can be as large as twice the nominal period, leading to a phenomenon of twin peaks that differ remarkably in their heights. In this work, the authors investigate how to retrieve and dewrap the phase signal from the phase-stepping curve (PSC) with the feature of twin peaks for x-ray phase contrast imaging. METHODS: Based on the paraxial Fresnel-Kirchhoff theory, the analytical formulae to characterize the phenomenon of twin peaks in the PSC are derived. Then an approach to dewrap the retrieved phase signal by jointly using the phases of the first- and second-order Fourier components is proposed. Through an experimental investigation using a prototype x-ray phase contrast imaging system implemented with Talbot interferometry, the authors evaluate and verify the derived analytic formulae and the proposed approach for phase retrieval and dewrapping. RESULTS: According to theoretical analysis, the twin-peak phenomenon in PSC is a consequence of combined effects, including the inaccuracy in absorption grating G2, mismatch between phase grating and x-ray source spectrum, and finite size of x-ray tube's focal spot. The proposed approach is experimentally evaluated by scanning a phantom consisting of organic materials and a lab mouse. The preliminary data show that compared to scanning G2 over only one single nominal period and correcting the measured phase signal with an intuitive phase dewrapping method that is being used in the field, stepping G2 over twice its nominal period and dewrapping the measured phase signal with the proposed approach can significantly improve the quality of x-ray differential phase contrast imaging in both radiograph and CT. CONCLUSIONS: Using the phase retrieval and dewrapping methods proposed to deal with the phenomenon of twin peaks in PSCs and phase wrapping, the performance of grating-based x-ray differential phase contrast radiography and CT can be significantly improved.

Reducing radiation dose in grating based x-ray phase contrast CT with twin-peaks in its phase stepping curves.

PURPOSE: Differential phase contrast CT has been recognized as an x-ray imaging method with the potential to greatly improve the differentiation of soft tissues. Talbot interferometry has been one of the promising solutions allowing implementation with commercially available x-ray tubes with a polychromatic spectrum. Mainly due to imperfections in grating fabrication and the polychromatic spectrum of x-ray beam, a twin-peaks phenomenon may exist in phase stepping curves (PSCs) and degrade the performance of phase retrieval. The authors have previously proposed a Fourier analysis based method for phase retrieval in the scenario wherein the twin-peaks phenomenon occurs in PSCs. In this work, the authors propose a 5-step algebraic method for phase retrieval and investigate the potential of reducing radiation dose while both the Fourier and algebraic methods are being utilized for phase retrieval. METHODS: The algebraic method to deal with the twin-peaks phenomenon, in which a set of linear equations with five unknown variables is needed for phase retrieval, is an extension of the so-called 3-step method that has been used in the scenario wherein only single-peak exists in the PSCs. In addition to a numerical phantom, two sets of experimental data (a phantom made of organic materials and a small animal) acquired by a prototype differential phase contrast CT system are employed to evaluate the performance of the Fourier and algebraic phase retrieval methods and their potential in radiation dose reduction. RESULTS: The evaluation by both numerical phantom and experimental data shows that the algebraic method works as well as the Fourier method in phase retrieval if the twin-peaks phenomenon in the PSCs is appropriately dealt with. In addition, while the radiation dose associated with data acquisition is being reduced via fewer phase shifting steps, the algebraic method can maintain a better performance compared to the Fourier method. CONCLUSIONS: Along with the Fourier method, the proposed 5-step algebraic method can cope with the twin-peaks phenomenon in phase retrieval. With decreased phase shifting steps and thus radiation dose, the proposed algebraic method performs better than the Fourier method, providing a practical solution for implementation of grating based differential phase contrast CT.

Time-frequency analysis of non-stationary fusion plasma signals using an improved Hilbert-Huang transform.

An improved Hilbert-Huang transform method is developed to the time-frequency analysis of non-stationary signals in tokamak plasmas. Maximal overlap discrete wavelet packet transform rather than wavelet packet transform is proposed as a preprocessor to decompose a signal into various narrow-band components. Then, a correlation coefficient based selection method is utilized to eliminate the irrelevant intrinsic mode functions obtained from empirical mode decomposition of those narrow-band components. Subsequently, a time varying vector autoregressive moving average model instead of Hilbert spectral analysis is performed to compute the Hilbert spectrum, i.e., a three-dimensional time-frequency distribution of the signal. The feasibility and effectiveness of the improved Hilbert-Huang transform method is demonstrated by analyzing a non-stationary simulated signal and actual experimental signals in fusion plasmas.