Non-Local Low-Rank Cube-Based Tensor Factorization for Spectral CT Reconstruction

Multi-limited-angle spectral CT image reconstruction based on average image induced relative total variation model

In recent years, spectral computed tomography (CT) has attracted extensive attention. The purpose of this study is to achieve a low-cost and fast energy spectral CT reconstruction algorithm by implementing multi-limited-angle scans. General spectral CT projection data are collected over a full-angular range of 360 degrees. We simulate multi-source spectral CT by using a pair of X-ray source/detector. To speed up scanning, multi-limited-angle scanning was used in each energy channel. On this basis, an average image induced relative total variation (Aii-RTV) with multi-limited-angle spectral CT image reconstruction model is proposed. The iterative algorithm is used to solve Aii-RTV. Before iteration, the weighted average projection data of the multi-limited-angle energy spectral is carried out. In each step of the iterative algorithm flow is as follows: First, the relative total variation (RTV) reconstruction model is used to reconstruct the average image using average projection data. Then, the partial derivative of the average image is used to calculate the inherent variation in RTV model due to the integrity of the average image, and take its reciprocal as the weight coefficient of the windowing total variation of each energy channel reconstruction image. Finally, the average energy image is used to guide the multi-limited-angle projection data to reconstruct the image of each energy channel so as to suppress the limited-angle artifact of each energy channel image. In addition, we also discuss the influence of parameter selection on reconstructed image quality, which is important for regularization model. Through the reconstruction of multi-limited-angle spectral CT projection data, quantitative results and reconstructed images show that our algorithm has better performance than prior image constrained compressed sensing (PICCS) and RTV. The average PSNR of our reconstruction results in different channels was 35.6273, 4.533 and 2.301 higher than RTV (31.0943) and PICCS (33.3263), respectively.

LOQUAT: Low-Rank Quaternion Reconstruction for Photon-Counting CT

Photon-counting computed tomography (PCCT) may dramatically benefit clinical practice due to its versatility such as dose reduction and material characterization. However, the limited number of photons detected in each individual energy bin can induce severe noise contamination in the reconstructed image. Fortunately, the notable low-rank prior inherent in the PCCT image can guide the reconstruction to a denoised outcome. To fully excavate and leverage the intrinsic low-rankness, we propose a novel reconstruction algorithm based on quaternion representation (QR), called low-rank quaternion reconstruction (LOQUAT). First, we organize a group of nonlocal similar patches into a quaternion matrix. Then, an adjusted weighted Schatten-p norm (AWSN) is introduced and imposed on the matrix to enforce its low-rank nature. Subsequently, we formulate an AWSN-regularized model and devise an alternating direction method of multipliers (ADMM) framework to solve it. Experiments on simulated and real-world data substantiate the superiority of the LOQUAT technique over several state-of-the-art competitors in terms of both visual inspection and quantitative metrics. Moreover, our QR-based method exhibits lower computational complexity than some popular tensor representation (TR) based counterparts. Besides, the global convergence of LOQUAT is theoretically established under a mild condition. These properties bolster the robustness and practicality of LOQUAT, facilitating its application in PCCT clinical scenarios. The source code will be available at https://github.com/linzf23/LOQUAT.

Enhancing photon-counting computed tomography reconstruction via subspace dictionary learning and spatial sparsity regularization

Background

Photon-counting computed tomography (CT) is an advanced imaging technique that enables multi-energy imaging from a single scan. However, the limited photon count assigned to narrow energy bins leads to increased quantum noise in the reconstructed spectral images. To address this issue, leveraging the prior information in the spectral images is essential. This study aimed to develop an efficient algorithm that enhances image reconstruction quality by reducing noise levels and preserving image details.

Methods

To improve image reconstruction quality for photon-counting CT, we propose an algorithm based on the subspace-assisted multi-prior information, including global, nonlocal, and local priors, for spectral CT reconstruction. Specifically, the algorithm first maps spectral CT images, which exhibit global low-rank characteristics, to low-dimensional eigenimages using subspace decomposition. Then, similar image patches are extracted based on the manifold structure distance from highly correlated eigenimages in both spectral and spatial domains. These patches are stacked to form a nonlocal full-channel tensor group. Subsequently, non-convex structural sparsity is applied to this tensor group through adaptive dictionary learning, exploiting nonlocal similarity. Finally, the alternating direction method of multipliers (ADMM) is applied to solve the optimization model iteratively.

Results

The simulated walnut and real mouse data were applied to validate the effectiveness of the proposed method. In the simulation experiments, the proposed method reduced the root mean square error (RMSE) by 87.74%, 86.88%, 67.01%, 46.42%, and 13.51% compared to the respective state-of-the-art five comparison methods. The time taken for one iteration of the proposed algorithm was as low as 32.57 seconds, which was 92.07% less than framelet tensor nuclear norm [framelet tensor sparsity with block-matching method (FTNN)] method and 74.13% less than total variation regularization [tensor nonlocal similarity and local TV sparsity method (ITS_TV)] method, the other two tensor block-matching (BM)-based comparison methods. The material decomposition results in real mouse data further validated the accuracy of the proposed method for different materials.

Conclusions

The experimental results indicate that the proposed algorithm effectively reduces computational costs while improving the accuracy of image reconstruction and material decomposition, showing promising advantages over the compared method.

SOUL-Net: A Sparse and Low-Rank Unrolling Network for Spectral CT Image Reconstruction

Spectral computed tomography (CT) is an emerging technology, that generates a multienergy attenuation map for the interior of an object and extends the traditional image volume into a 4-D form. Compared with traditional CT based on energy-integrating detectors, spectral CT can make full use of spectral information, resulting in high resolution and providing accurate material quantification. Numerous model-based iterative reconstruction methods have been proposed for spectral CT reconstruction. However, these methods usually suffer from difficulties such as laborious parameter selection and expensive computational costs. In addition, due to the image similarity of different energy bins, spectral CT usually implies a strong low-rank prior, which has been widely adopted in current iterative reconstruction models. Singular value thresholding (SVT) is an effective algorithm to solve the low-rank constrained model. However, the SVT method requires a manual selection of thresholds, which may lead to suboptimal results. To relieve these problems, in this article, we propose a sparse and low-rank unrolling network (SOUL-Net) for spectral CT image reconstruction, that learns the parameters and thresholds in a data-driven manner. Furthermore, a Taylor expansion-based neural network backpropagation method is introduced to improve the numerical stability. The qualitative and quantitative results demonstrate that the proposed method outperforms several representative state-of-the-art algorithms in terms of detail preservation and artifact reduction.

Learned Tensor Neural Network Texture Prior for Photon-Counting CT Reconstruction

Photon-counting computed tomography (PCCT) reconstructs multiple energy-channel images to describe the same object, where there exists a strong correlation among different channel images. In addition, reconstruction of each channel image suffers photon count starving problem. To make full use of the correlation among different channel images to suppress the data noise and enhance the texture details in reconstructing each channel image, this paper proposes a tensor neural network (TNN) architecture to learn a multi-channel texture prior for PCCT reconstruction. Specifically, we first learn a spatial texture prior in each individual channel image by modeling the relationship between the center pixels and its corresponding neighbor pixels using a neural network. Then, we merge the single channel spatial texture prior into multi-channel neural network to learn the spectral local correlation information among different channel images. Since our proposed TNN is trained on a series of unpaired small spatial-spectral cubes which are extracted from one single reference multi-channel image, the local correlation in the spatial-spectral cubes is considered by TNN. To boost the TNN performance, a low-rank representation is also employed to consider the global correlation among different channel images. Finally, we integrate the learned TNN and the low-rank representation as priors into Bayesian reconstruction framework. To evaluate the performance of the proposed method, four references are considered. One is simulated images from ultra-high-resolution CT. One is spectral images from dual-energy CT. The other two are animal tissue and preclinical mouse images from a custom-made PCCT systems. Our TNN prior Bayesian reconstruction demonstrated better performance than other state-of-the-art competing algorithms, in terms of not only preserving texture feature but also suppressing image noise in each channel image.

Adaptive and Iterative Learning With Multi-Perspective Regularizations for Metal Artifact Reduction

Metal artifact reduction (MAR) is important for clinical diagnosis with CT images. The existing state-of-the-art deep learning methods usually suppress metal artifacts in sinogram or image domains or both. However, their performance is limited by the inherent characteristics of the two domains, i.e., the errors introduced by local manipulations in the sinogram domain would propagate throughout the whole image during backprojection and lead to serious secondary artifacts, while it is difficult to distinguish artifacts from actual image features in the image domain. To alleviate these limitations, this study analyzes the desirable properties of wavelet transform in-depth and proposes to perform MAR in the wavelet domain. First, wavelet transform yields components that possess spatial correspondence with the image, thereby preventing the spread of local errors to avoid secondary artifacts. Second, using wavelet transform could facilitate identification of artifacts from image since metal artifacts are mainly high-frequency signals. Taking these advantages of the wavelet transform, this paper decomposes an image into multiple wavelet components and introduces multi-perspective regularizations into the proposed MAR model. To improve the transparency and validity of the model, all the modules in the proposed MAR model are designed to reflect their mathematical meanings. In addition, an adaptive wavelet module is also utilized to enhance the flexibility of the model. To optimize the model, an iterative algorithm is developed. The evaluation on both synthetic and real clinical datasets consistently confirms the superior performance of the proposed method over the competing methods.

Prior image-based generative adversarial learning for multi-material decomposition in photon counting computed tomography

BACKGROUND

Photon counting detector computed tomography (PCD-CT) is a novel promising technique providing higher spatial resolution, lower radiation dose and greater energy spectrum differentiation, which create more possibilities to improve image quality. Multi-material decomposition is an attractive application for PCD-CT to identify complicated materials and provide accurate quantitative analysis. However, limited by the finite photon counting rate in each energy window of photon counting detector, the noise problem hinders the decomposition of high-quality basis material images.

METHODS

To address this issue, an end-to-end multi-material decomposition network based on prior images is proposed in this paper. First, the reconstructed images corresponding to the full spectrum with less noise are introduced as prior information to improve the overall signal-to-noise ratio of the data. Then, a generative adversarial network is designed to mine the relationship between reconstructed images and basis material images based on the information interaction of material decomposition. Furthermore, a weighted edge loss is introduced to adapt to the structural differences of different basis material images.

RESULTS

To verify the performance of the proposed method, simulation and real studies are carried out. In simulation study of structured fibro-glandular tissue model, the results show that the proposed method decreased the root mean square error by 67 % and 26 % on adipose, 66 % and 28 % on fibroglandular, 52 % and 8 % on calcification, compared to butterfly network and dual interactive Wasserstein generative adversarial network.

CONCLUSION

Experimentally, the proposed method shows certain advantages over other methods on noise suppression effect, detail retention ability and decomposition accuracy.

Phase retrieval via nonlocal complex-domain sparsity

Phase retrieval is indispensable for a number of coherent imaging systems. Owing to limited exposure, it is a challenge for traditional phase retrieval algorithms to reconstruct fine details in the presence of noise. In this Letter, we report an iterative framework for noise-robust phase retrieval with high fidelity. In the framework, we investigate nonlocal structural sparsity in the complex domain by low-rank regularization, which effectively suppresses artifacts caused by measurement noise. The joint optimization of sparsity regularization and data fidelity with forward models enables satisfying detail recovery. To further improve computational efficiency, we develop an adaptive iteration strategy that automatically adjusts matching frequency. The effectiveness of the reported technique has been validated for coherent diffraction imaging and Fourier ptychography, with ≈7 dB higher peak SNR (PSNR) on average, compared with conventional alternating projection reconstruction.

Image-spectral decomposition extended-learning assisted by sparsity for multi-energy computed tomography reconstruction

Background

Multi-energy computed tomography (CT) provides multiple channel-wise reconstructed images, and they can be used for material identification and k-edge imaging. Nonetheless, the projection datasets are frequently corrupted by various noises (e.g., electronic, Poisson) in the acquisition process, resulting in lower signal-noise-ratio (SNR) measurements. Multi-energy CT images have local sparsity, nonlocal self-similarity in spatial dimension, and correlation in spectral dimension.

Methods

In this paper, we propose an image-spectral decomposition extended-learning assisted by sparsity (IDEAS) method to fully exploit these intrinsic priors for multi-energy CT image reconstruction. Particularly, a nonlocal low-rank Tucker decomposition (TD) is employed to utilize the correlation and nonlocal self-similarity priors. Moreover, considering the advantages of multi-task tensor dictionary learning (TDL) in sparse representation, an adaptive spatial dictionary and an adaptive spectral dictionary are trained during the iterative reconstruction process. Furthermore, a weighted total variation (TV) regularization term is employed to encourage local sparsity.

Results

Numerical simulation, physical phantom, and preclinical mouse experiments are performed to validate the proposed IDEAS algorithm. Specifically, in the simulation experiments, the proposed IDEAS reconstructed high-quality images that are very close to the references. For example, the root mean square error (RMSE) of IDEAS image in energy bin 1 is as low as 0.0672, while the RMSE of other methods are higher than 0.0843. Besides, the structural similarity (SSIM) of IDEAS reconstructed image in energy bin 1 is greater than 0.98. For material decomposition, the RMSE of IDEAS bone component is as low as 0.0152, and other methods are higher than 0.0199. In addition, the computational cost of IDEAS is as low as 98.8 s for one iteration, and the competing tensor decomposition method is higher than 327 s.

Conclusions

To further improve the quality of the reconstructed multi-energy CT images, multiple prior regularizations are introduced to the multi-energy CT reconstructed model, leading to an IDEAS method. Both qualitative and quantitative evaluation of our results confirm the outstanding performance of the proposed algorithm compared to the state-of-the-arts.

Low-dose spectral reconstruction with global, local, and nonlocal priors based on subspace decomposition

Background

Multienergy computed tomography (MECT) is a promising imaging modality for material decomposition, lesion detection, and other clinical applications. However, there is an urgent need to design efficient and accurate algorithms to solve the inverse problems related to spectral reconstruction and improve image quality, especially under low-dose and incomplete datasets. The key issue for MECT reconstruction is how to efficiently describe the interchannel and intrachannel priors in multichannel images.

Methods

In this model, in order to correlate the similarities of interchannel images and regularize the multichannel images, the global, local, and nonlocal priors are jointly integrated into the low-dose MECT reconstruction model. First, the subspace decomposition method first employs the global low-rankness to map the original MECT images to the low-dimensional eigenimages. Then, nonlocal self-similarity of the eigenimages is cascaded into the optimization model. Additionally, the L0 quasi-norm on gradient images is incorporated into the proposed method to further enhance the local sparsity of intrachannel images. The alternating direction method is applied to solve the optimization model in an iterative scheme.

Results

Simulation, preclinical, and real datasets were applied to validate the effectiveness of the proposed method. From the simulation dataset, the new method was found to reduce the root-mean-square error (RMSE) by 42.31% compared with the latest research fourth-order nonlocal tensor decomposition MECT reconstruction (FONT-SIR) method under 160 projection views. The calculation time of an iteration for the proposed method was 23.07% of the FONT-SIR method. The results of material decomposition in real mouse data further confirmed the accuracy of the proposed method for different materials.

Conclusions

We developed a method in which the global, local, and nonlocal priors are jointly used to develop the reconstruction model for low-dose MECT, where the global low-rankness and nonlocal prior are cascaded by subspace decomposition and block-matching, and the L0 sparsity is applied to express the local prior. The results of the experiments demonstrate that the proposed method based on subspace improves computational efficiency and has advantages in noise suppression and structure preservation over competing algorithms.

Spectral CT reconstruction via Spectral-Image Tensor and Bidirectional Image-gradient minimization

It is challenging to obtain good image quality in spectral computed tomography (CT) as the photon-number for the photon-counting detectors is limited for each narrow energy bin. This results in a lower signal to noise ratio (SNR) for the projections. To handle this issue, we first formulate the weight bidirectional image gradient with L₀-norm constraint of spectral CT image. Then, as a new regularizer, bidirectional image gradient with L₀-norm constraint is introduced into the tensor decomposition model, generating the Spectral-Image Tensor and Bidirectional Image-gradient Minimization (SITBIM) algorithm. Finally, the split-Bregman method is employed to optimize the proposed SITBIM mathematical model. The experiments on the numerical mouse phantom and real mouse experiments are designed to validate and evaluate the SITBIM method. The results demonstrate that the SITBIM can outperform other state-of-the-art methods (including TVM, TV + LR, SSCMF and NLCTF). INDEX TERMS: -spectral CT, image reconstruction, tensor decomposition, unidirectional image gradient, image similarity.

DIOR: Deep Iterative Optimization-Based Residual-Learning for Limited-Angle CT Reconstruction

Limited-angle CT is a challenging problem in real applications. Incomplete projection data will lead to severe artifacts and distortions in reconstruction images. To tackle this problem, we propose a novel reconstruction framework termed Deep Iterative Optimization-based Residual-learning (DIOR) for limited-angle CT. Instead of directly deploying the regularization term on image space, the DIOR combines iterative optimization and deep learning based on the residual domain, significantly improving the convergence property and generalization ability. Specifically, the asymmetric convolutional modules are adopted to strengthen the feature extraction capacity in smooth regions for deep priors. Besides, in our DIOR method, the information contained in low-frequency and high-frequency components is also evaluated by perceptual loss to improve the performance in tissue preservation. Both simulated and clinical datasets are performed to validate the performance of DIOR. Compared with existing competitive algorithms, quantitative and qualitative results show that the proposed method brings a promising improvement in artifact removal, detail restoration and edge preservation.

Iterative dynamic dual-energy CT algorithm in reducing statistical noise in multi-energy CT imaging

Multi-energy spectral CT has a broader range of applications with the recent development of photon-counting detectors. However, the photons counted in each energy bin decrease when the number of energy bins increases, which causes a higher statistical noise level of the CT image. In this work, we propose a novel iterative dynamic dual-energy CT algorithm to reduce the statistical noise. In the proposed algorithm, the multi-energy projections are estimated from the dynamic dual-energy CT data during the iterative process. The proposed algorithm is verified on sufficient numerical simulations and a laboratory two-energy-threshold PCD system. By applying the same reconstruction algorithm, the dynamic dual-energy CT's final reconstruction results have a much lower statistical noise level than the conventional multi-energy CT. Moreover, based on the analysis of the simulation results, we explain why the dynamic dual-energy CT has a lower statistical noise level than the conventional multi-energy CT. The reason is that: the statistical noise level of multi-energy projection estimated with the proposed algorithm is much lower than that of the conventional multi-energy CT, which leads to less statistical noise of the dynamic dual-energy CT imaging.

DRONE: Dual-Domain Residual-based Optimization NEtwork for Sparse-View CT Reconstruction

Deep learning has attracted rapidly increasing attention in the field of tomographic image reconstruction, especially for CT, MRI, PET/SPECT, ultrasound and optical imaging. Among various topics, sparse-view CT remains a challenge which targets a decent image reconstruction from very few projections. To address this challenge, in this article we propose a Dual-domain Residual-based Optimization NEtwork (DRONE). DRONE consists of three modules respectively for embedding, refinement, and awareness. In the embedding module, a sparse sinogram is first extended. Then, sparse-view artifacts are effectively suppressed in the image domain. After that, the refinement module recovers image details in the residual data and image domains synergistically. Finally, the results from the embedding and refinement modules in the data and image domains are regularized for optimized image quality in the awareness module, which ensures the consistency between measurements and images with the kernel awareness of compressed sensing. The DRONE network is trained, validated, and tested on preclinical and clinical datasets, demonstrating its merits in edge preservation, feature recovery, and reconstruction accuracy.

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.

Image-domain Material Decomposition for Spectral CT using a Generalized Dictionary Learning

The spectral computed tomography (CT) has huge advantages by providing accurate material information. Unfortunately, due to the instability or overdetermination of material decomposition model, the accuracy of material decomposition can be compromised in practice. Very recently, the dictionary learning based image-domain material decomposition (DLIMD) can obtain high accuracy for material decompositions from reconstructed spectral CT images. This method can explore the correlation of material components to some extent by training a unified dictionary from all material images. In addition, the dictionary learning based prior as a penalty is applied on material components independently, and many parameters would be carefully elaborated in practice. Because the concentration of contrast agent in clinical applications is low, it can result in data inconsistency for dictionary based representation during the iteration process. To avoid the aforementioned limitations and further improve the accuracy of materials, we first construct a generalized dictionary learning based image-domain material decomposition (GDLIMD) model. Then, the material tensor image is unfolded along the mode-1 to enhance the correlation of different materials. Finally, to avoid the data inconsistency of low iodine contrast, a normalization strategy is employed. Both physical phantom and tissue-synthetic phantom experiments demonstrate the proposed GDLIMD method outperforms the DLIMD and direct inversion (DI) methods.

Refined Locally Linear Transform-Based Spectral-Domain Gradient Sparsity and Its Applications in Spectral CT Reconstruction

Spectral computed tomography (CT) is extension of the conventional single spectral CT (SSCT) along the energy dimension, which achieves superior energy resolution and material distinguishability. However, for the state-of-the-art photon counting detector (PCD) based spectral CT, because the emitted photons with a fixed total number for each X-ray beam are divided into several energy bins, the noise level is increased in each reconstructed channel image, and it further leads to an inaccurate material decomposition. To improve the reconstructed image quality and decomposition accuracy, in this work, we first employ a refined locally linear transform to convert the structural similarity among two-dimensional (2D) spectral CT images to a spectral-dimension gradient sparsity. By combining the gradient sparsity in the spatial domain, a global three-dimensional (3D) gradient sparsity is constructed, then measured with L 1-, L 0- and trace-norm, respectively. For each sparsity measurement, we propose the corresponding optimization model, develop the iterative algorithm, and verify the effectiveness and superiority with real datasets.

Whole Brain Myelin Water Mapping in One Minute Using Tensor Dictionary Learning With Low-Rank Plus Sparse Regularization

The quantification of myelin water content in the brain can be obtained by the multi-echo [Formula: see text] weighted images ( [Formula: see text]WIs). To accelerate the long acquisition, a novel tensor dictionary learning algorithm with low-rank and sparse regularization (TDLLS) is proposed to reconstruct the [Formula: see text]WIs from the undersampled data. The proposed algorithm explores the local and nonlocal similarity and the global temporal redundancy in the real and imaginary parts of the complex relaxation signals. The joint application of the low-rank constraints on the dictionaries and the sparse constraints on the core coefficient tensors improves the performance of the tensor-based recovery. Parallel imaging is incorporated into the TDLLS algorithm (pTDLLS) for further acceleration. A pulse sequence is proposed to prospectively undersample the Ky-t space to obtain the whole brain high-quality myelin water fraction (MWF) maps within 1 minute at an undersampling rate (R) of 6.

Tensor Gradient L₀-Norm Minimization-Based Low-Dose CT and Its Application to COVID-19

Methods to recover high-quality computed tomography (CT) images in low-dose cases will be of great benefit. To reach this goal, sparse-data subsampling is one of the common strategies to reduce radiation dose, which is attracting interest among the researchers in the CT community. Since analytic image reconstruction algorithms may lead to severe image artifacts, the iterative algorithms have been developed for reconstructing images from sparsely sampled projection data. In this study, we first develop a tensor gradient L₀-norm minimization (TGLM) for low-dose CT imaging. Then, the TGLM model is optimized by using the split-Bregman method. The Coronavirus Disease 2019 (COVID-19) has been sweeping the globe, and CT imaging has been deployed for detection and assessing the severity of the disease. Finally, we first apply our proposed TGLM method for COVID-19 to achieve low-dose scan by incorporating the 3-D spatial information. Two COVID-19 patients (64 years old female and 56 years old man) were scanned by the [Formula: see text]CT 528 system, and the acquired projections were retrieved to validate and evaluate the performance of the TGLM.

MD-NDNet: a multi-dimensional convolutional neural network for false-positive reduction in pulmonary nodule detection

Pulmonary nodule false-positive reduction is of great significance for automated nodule detection in clinical diagnosis of low-dose computed tomography (LDCT) lung cancer screening. Due to individual intra-nodule variations and visual similarities between true nodules and false positives as soft tissues in LDCT images, the current clinical practices remain subject to shortcomings of potential high-risk and time-consumption issues. In this paper, we propose a multi-dimensional nodule detection network (MD-NDNet) for automatic nodule false-positive reduction using deep convolutional neural network (DCNNs). The underlying method collaboratively integrates multi-dimensional nodule information to complementarily and comprehensively extract nodule inter-plane volumetric correlation features using three-dimensional CNNs (3D CNNs) and spatial nodule correlation features from sagittal, coronal, and axial planes using two-dimensional CNNs (2D CNNs) with attention module. To incorporate different sizes and shapes of nodule candidates, a multi-scale ensemble strategy is employed for probability aggregation with weights. The proposed method is evaluated on the LUNA16 challenge dataset in ISBI 2016 with ten-fold cross-validation. Experiment results show that the proposed framework achieves classification performance with a CPM score of 0.9008. All of these indicate that our method enables an efficient, accurate and reliable pulmonary nodule detection for clinical diagnosis.

Low-dose spectral CT reconstruction based on image-gradient L0-norm and adaptive spectral PICCS

The photon-counting detector based spectral computed tomography (CT) is promising for lesion detection, tissue characterization, and material decomposition. However, the lower signal-to-noise ratio within multi-energy projection dataset can result in poorly reconstructed image quality. Recently, as prior information, a high-quality spectral mean image was introduced into the prior image constrained compressed sensing (PICCS) framework to suppress noise, leading to spectral PICCS (SPICCS). In the original SPICCS model, the image gradient L₁-norm is employed, and it can cause blurred edge structures in the reconstructed images. Encouraged by the advantages in edge preservation and finer structure recovering, the image gradient L₀-norm was incorporated into the PICCS model. Furthermore, due to the difference of energy spectrum in different channels, a weighting factor is introduced and adaptively adjusted for different channel-wise images, leading to an L₀-norm based adaptive SPICCS (L₀-ASPICCS) algorithm for low-dose spectral CT reconstruction. The split-Bregman method is employed to minimize the objective function. Extensive numerical simulations and physical phantom experiments are performed to evaluate the proposed method. By comparing with the state-of-the-art algorithms, such as the simultaneous algebraic reconstruction technique, total variation minimization, and SPICCS, the advantages of our proposed method are demonstrated in terms of both qualitative and quantitative evaluation results.

Dictionary learning based image-domain material decomposition for spectral CT

The potential huge advantage of spectral computed tomography (CT) is that it can provide accurate material identification and quantitative tissue information by material decomposition. However, material decomposition is a typical inverse problem, where the noise can be magnified. To address this issue, we develop a dictionary learning based image-domain material decomposition (DLIMD) method for spectral CT to achieve accurate material components with better image quality. Specifically, a set of image patches are extracted from the mode-1 unfolding of normalized material images decomposed by direct inversion to train a unified dictionary using the K-SVD technique. Then, the DLIMD model is established to explore the redundant similarities of the material images, where the split-Bregman is employed to optimize the model. Finally, more constraints (i.e. volume conservation and the bounds of each pixel within material maps) are integrated into the DLIMD model. Numerical phantom, physical phantom and preclinical experiments are performed to evaluate the performance of the proposed DLIMD in material decomposition accuracy, material image edge preservation and feature recovery.

Multi-energy CT reconstruction using tensor nonlocal similarity and spatial sparsity regularization

Background

Multi-energy computed tomography (MECT) based on a photon-counting detector is an emerging imaging modality that collects projections at several energy bins with a single scan. However, the limited number of photons collected into the divided, narrow energy bins results in high quantum noise levels in reconstructed images. This study aims to improve MECT image quality by minimizing noise levels while retaining image details.

Methods

A novel MECT reconstruction method was proposed by exploiting the nonlocal tensor similarity among interchannel images and spatial sparsity in single-channel images. Similar patches were initially extracted from the interchannel images in spectral and spatial domains, then stacked into a new three-order tensor. Intrinsic tensor sparsity regularization that combined the Tuker and canonical polyadic (CP) low-rank decomposition techniques were applied to exploit the nonlocal similarity of the formulated tensor. Spatial sparsity in single-channel images was modeled by total variation (TV) regularization that utilizes the compressibility of gradient image. A new MECT reconstruction model was established by simultaneously incorporating the intrinsic tensor sparsity and TV regularizations. The iterative alternating minimization method was utilized to solve the reconstruction model based on a flexible framework.

Results

The proposed method was applied to the digital phantom and real mouse data to assess its feasibility and reliability. The reconstruction and decomposition results in the mouse data were encouraging and demonstrated the ability of the proposed method in noise suppression while preserving image details, not observed with other methods. Imaging data from the digital phantom illustrated this method as achieving the best intuitive reconstruction and decomposition results among all compared methods. They reduced the root mean square error (RMSE) by 89.75%, 50.75%, and 36.54% on the reconstructed images compared with analytic, TV-based, and tensor-based methods, respectively. This phenomenon was also observed with decomposition results, where the RMSE was also reduced by 97.96%, 67.74%, 72.05%, respectively.

Conclusions

In this study, we proposed a reconstruction method for photon counting detector-based MECT, using the intrinsic tensor sparsity and TV regularizations. Improvements in noise suppression and detail preservation in the digital phantom and real mouse data were validated by the qualitative and quantitative evaluations on the reconstruction and decomposition results, verifying the potential of the proposed method in MECT reconstruction.

Spectral CT Reconstruction via Low-Rank Representation and Region-Specific Texture Preserving Markov Random Field Regularization

Photon-counting spectral computed tomography (CT) is capable of material characterization and can improve diagnostic performance over traditional clinical CT. However, it suffers from photon count starving for each individual energy channel which may cause severe artifacts in the reconstructed images. Furthermore, since the images in different energy channels describe the same object, there are high correlations among different channels. To make full use of the inter-channel correlations and minimize the count starving effect while maintaining clinically meaningful texture information, this paper combines a region-specific texture model with a low-rank correlation descriptor as an a priori regularization to explore a superior texture preserving Bayesian reconstruction of spectral CT. Specifically, the inter-channel correlations are characterized by the low-rank representation, and the inner-channel regional textures are modeled by a texture preserving Markov random field. In other words, this paper integrates the spectral and spatial information into a unified Bayesian reconstruction framework. The widely-used Split-Bregman algorithm is employed to minimize the objective function because of the non-differentiable property of the low-rank representation. To evaluate the tissue texture preserving performance of the proposed method for each channel, three references are built for comparison: one is the traditional CT image from energy integration detection. The second one is spectral images from dual-energy CT. The third one is individual channels images from custom-made photon-counting spectral CT. As expected, the proposed method produced promising results in terms of not only preserving texture features but also suppressing image noise in each channel, comparing to existing methods of total variation (TV), low-rank TV and tensor dictionary learning, by both visual inspection and quantitative indexes of root mean square error, peak signal to noise ratio, structural similarity and feature similarity.

Full-Spectrum-Knowledge-Aware Tensor Model for Energy-Resolved CT Iterative Reconstruction

Energy-resolved computed tomography (ErCT) with a photon counting detector concurrently produces multiple CT images corresponding to different photon energy ranges. It has the potential to generate energy-dependent images with improved contrast-to-noise ratio and sufficient material-specific information. Since the number of detected photons in one energy bin in ErCT is smaller than that in conventional energy-integrating CT (EiCT), ErCT images are inherently more noisy than EiCT images, which leads to increased noise and bias in the subsequent material estimation. In this work, we first deeply analyze the intrinsic tensor properties of two-dimensional (2D) ErCT images acquired in different energy bins and then present a F ull- S pectrum-knowledge-aware Tensor analysis and processing (FSTensor) method for ErCT reconstruction to suppress noise-induced artifacts to obtain high-quality ErCT images and high-accuracy material images. The presented method is based on three considerations: (1) 2D ErCT images obtained in different energy bins can be treated as a 3-order tensor with three modes, i.e., width, height and energy bin, and a rich global correlation exists among the three modes, which can be characterized by tensor decomposition. (2) There is a locally piecewise smooth property in the 3-order ErCT images, and it can be captured by a tensor total variation regularization. (3) The images from the full spectrum are much better than the ErCT images with respect to noise variance and structural details and serve as external information to improve the reconstruction performance. We then develop an alternating direction method of multipliers algorithm to numerically solve the presented FSTensor method. We further utilize a genetic algorithm to tackle the parameter selection in ErCT reconstruction, instead of manually determining parameters. Simulation, preclinical and synthesized clinical ErCT results demonstrate that the presented FSTensor method leads to significant improvements over the filtered back-projection, robust principal component analysis, tensor-based dictionary learning and low-rank tensor decomposition with spatial-temporal total variation methods.

Computed tomography medical image reconstruction on affordable equipment by using Out-Of-Core techniques

BACKGROUND AND OBJECTIVE

As Computed Tomography scans are an essential medical test, many techniques have been proposed to reconstruct high-quality images using a smaller amount of radiation. One approach is to employ algebraic factorization methods to reconstruct the images, using fewer views than the traditional analytical methods. However, their main drawback is the high computational cost and hence the time needed to obtain the images, which is critical in the daily clinical practice. For this reason, faster methods for solving this problem are required.

METHODS

In this paper, we propose a new reconstruction method based on the QR factorization that is very efficient on affordable equipment (standard multicore processors and standard Solid-State Drives) by using Out-Of-Core techniques.

RESULTS

Combining both affordable hardware and the new software proposed in our work, the images can be reconstructed very quickly and with high quality. We analyze the reconstructions using real Computed Tomography images selected from a dataset, comparing the QR method to the LSQR and FBP. We measure the quality of the images using the metrics Peak Signal-To-Noise Ratio and Structural Similarity Index, obtaining very high values. We also compare the efficiency of using spinning disks versus Solid-State Drives, showing how the latter performs the Input/Output operations in a significantly lower amount of time.

CONCLUSIONS

The results indicate that our proposed me thod and software are valid to efficiently solve large-scale systems and can be applied to the Computed Tomography reconstruction problem to obtain high-quality images.

Microstructural Changes in Compressed Cervical Spinal Cord Are Consistent With Clinical Symptoms and Symptom Duration

STUDY DESIGN

A prospective study.

OBJECTIVE

To investigate the association between microstructural changes measured by diffusion tensor imaging (DTI) and clinical symptoms and their duration in patients with cervical spondylotic myelopathy (CSM) affected by single level.

SUMMARY OF BACKGROUND DATA

No report was reported regarding the association between the microstructural changes and the symptoms and their duration at single-level spinal cord compression.

METHODS

Twenty-nine consecutive patients with CSM and 29 normal subjects were enrolled in this study. DTI with tractography was performed on the cervical spinal cord. Clinical symptoms were evaluated using modified Japanese Orthopaedic Association (mJOA) scores for each patient, and the duration of clinical symptoms was noted based on the earliest instance of limb pain or numbness or weakness or bladder dysfunction. Mean fractional anisotropy (FA) and apparent diffusion coefficient (ADC) values were calculated from tractography images.

RESULTS

The mean FA value of the cervical compressed spinal cord was significantly lower than the FA of the normal population (P < 0.001). The mean ADC value in the cervical compressed spinal cord was obviously higher than those of normal cervical spinal cord (P < 0.001). In the CSM patients, a significant positive association was observed between FA values and mJOA scores (P < 0.001). However, there were a notable negative association between mJOA scores and ADC values (P < 0.001), and between mJOA scores and symptom duration (P < 0.001).

CONCLUSION

These results illustrate DTI can measure the micostructural changes of cervical spinal cord and DTI parameters are potential biomarkers for spinal cord dysfunction in patients with CSM.

LEVEL OF EVIDENCE

3.

A Robust Regularizer for Multiphase CT

Joint image reconstruction for multiphase CT can potentially improve image quality and reduce dose by leveraging the shared information among the phases. Multiphase CT scans are acquired sequentially. Inter-scan patient breathing causes small organ shifts and organ boundary misalignment among different phases. Existing multi-channel regularizers such as the joint total variation (TV) can introduce artifacts at misaligned organ boundaries. We propose a multi-channel regularizer using the infimal convolution (inf-conv) between a joint TV and a separable TV. It is robust against organ misalignment; it can work like a joint TV or a separable TV depending on a parameter setting. The effects of the parameter in the inf-conv regularizer are analyzed in detail. The properties of the inf-conv regularizer are then investigated numerically in a multi-channel image denoising setting. For algorithm implementation, the inf-conv regularizer is nonsmooth; inverse problems with the inf-conv regularizer can be solved using a number of primal-dual algorithms from nonsmooth convex minimization. Our numerical studies using synthesized 2-phase patient data and phantom data demonstrate that the inf-conv regularizer can largely maintain the advantages of the joint TV over the separable TV and reduce image artifacts of the joint TV due to organ misalignment.

Material decomposition for simulated dual-energy breast computed tomography via hybrid optimization method

BACKGROUND

Dual-energy breast CT reconstruction has a potential application that includes separation of microcalcification from healthy breast tissue for assisting early breast cancer detection.

OBJECTIVE

To investigate and validate the noise suppression algorithm applied in the decomposition of the simulated breast phantom into microcalcification and healthy breast.

METHODS

The proposed hybrid optimization method (HOM) uses a simultaneous algebraic reconstruction technique (SART) output as a prior image, which is then incorporated into the self-adaptive dictionary learning. This self-adaptive dictionary learning seeks each group of patches to faithfully represent the learned dictionary, and the sparsity and non-local similarity of group patches are used to enforce the image regularization term of the prior image. We simulate a numerical phantom by adding different levels of Gaussian noise to test performance of the proposed method.

RESULTS

The mean value of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and root mean square error (RMSE) for the proposed method are (49.043±1.571), (0.997±0.002), (0.003±0.001) and (51.329±1.998), (0.998±0.002), (0.003±0.001) for 35 kVp and 49 kVp, respectively. The PSNR of the proposed method shows greater improvement over TWIST (5.2%), SART (34.6%), FBP (40.4%) and TWIST (3.7%), SART (39.9%), FBP (50.3%) for 35 kVp and 49 kVp energy images, respectively. For the proposed method, the signal-to-noise ratio (SNR) of decomposed normal breast tissue (NBT) is (22.036±1.535), which exceeded that of TWIST, SART, and FBP by 7.5%, 49.6%, and 96.4%, respectively. The results reveal that the proposed algorithm achieves the best performance in both reconstructed and decomposed images under different levels of noise and the performance is due to the high sparsity and good denoising ability of minimization exploited to solve the convex optimization problem.

CONCLUSIONS

This study demonstrates the potential of applying dual-energy reconstruction in breast CT to detect and separate clustered MCs from healthy breast tissues without noise amplification. Compared to other competing methods, the proposed algorithm achieves the best noise suppression performance for both reconstructed and decomposed images.

Block matching frame based material reconstruction for spectral CT

Spectral computed tomography (CT) has a great potential in material identification and decomposition. To achieve high-quality material composition images and further suppress the x-ray beam hardening artifacts, we first propose a one-step material reconstruction model based on Taylor's first-order expansion. Then, we develop a basic material reconstruction method named material simultaneous algebraic reconstruction technique (MSART). Considering the local similarity of each material image, we incorporate a powerful block matching frame (BMF) into the material reconstruction (MR) model and generate a BMF based MR (BMFMR) method. Because the BMFMR model contains the L 0-norm problem, we adopt a split-Bregman method for optimization. The numerical simulation and physical phantom experiment results validate the correctness of the material reconstruction algorithms and demonstrate that the BMF regularization outperforms the total variation and no-local mean regularizations.

Image gradient L0-norm based PICCS for swinging multi-source CT reconstruction

Dynamic computed tomography (CT) is usually employed to image motion objects, such as beating heart, coronary artery and cerebral perfusion, etc. Recently, to further improve the temporal resolution for aperiodic industrial process imaging, the swinging multi-source CT (SMCT) systems and the corresponding swinging multi-source prior image constrained compressed sensing (SM-PICCS) method were developed. Since the SM-PICCS uses the L1-norm of image gradient, the edge structures in the reconstructed images are blurred and motion artifacts are still present. Inspired by the advantages in terms of image edge preservation and fine structure recovering, the L0-norm of image gradient is incorporated into the prior image constrained compressed sensing, leading to an L0-PICCS Algorithm 1Table 1The parameters of L0-PICCS (δ1,δ2,λ1*,λ2*) for numerical simulation.Sourceswδ1(10-2)δ2(10-2)λ1*(10-2)λ2*(10-8)Noise-free510522.001.525522.001.55035002.00471014.33332.00500025522.00500050222.005000Noise51062002.505002554502.501.55054502.901.571027.385.91.5810000258.285.91.5850050522.001.5. The experimental results confirm that the L0-PICCS outperforms the SM-PICCS in both visual inspection and quantitative analysis.