Fused analytical and iterative reconstruction (AIR) via modified proximal forward–backward splitting: a FDK-based iterative image reconstruction example for CBCT

DECT sparse reconstruction based on hybrid spectrum data generative diffusion model

PURPOSE

Dual-energy computed tomography (DECT) enables the differentiation of different materials. Additionally, DECT images consist of multiple scans of the same sample, revealing information similarity within the energy domain. To leverage this information similarity and address safety concerns related to excessive radiation exposure in DECT imaging, sparse view DECT imaging is proposed as a solution. However, this imaging method can impact image quality. Therefore, this paper presents a hybrid spectrum data generative diffusion reconstruction model (HSGDM) to improve imaging quality.

METHOD

To exploit the spectral similarity of DECT, we use interleaved angles for sparse scanning to obtain low- and high-energy CT images with complementary incomplete views. Furthermore, we organize low- and high-energy CT image views into multichannel forms for training and inference and promote information exchange between low-energy features and high-energy features, thus improving the reconstruction quality while reducing the radiation dose. In the HSGDM, we build two types of diffusion model constraint terms trained by the image space and wavelet space. The wavelet space diffusion model exploits mainly the orientation and scale features of artifacts. By integrating the image space diffusion model, we establish a hybrid constraint for the iterative reconstruction framework. Ultimately, we transform the iterative approach into a cohesive sampling process guided by the measurement data, which collaboratively produces high-quality and consistent reconstructions of sparse view DECT.

RESULTS

Compared with the comparison methods, this approach is competitive in terms of the precision of the CT values, the preservation of details, and the elimination of artifacts. In the reconstruction of 30 sparse views, with increases of 3.51 dB for the peak signal-to-noise ratio (PSNR), 0.03 for the structural similarity index measure (SSIM), and a reduction of 74.47 for the Fréchet inception distance (FID) score on the test dataset. In the ablation study, we determined the effectiveness of our proposed hybrid prior, consisting of the wavelet prior module and the image prior module, by comparing the visual effects and quantitative results of the methods using an image space model, a wavelet space model, and our hybrid model approach. Both qualitative and quantitative analyses of the results indicate that the proposed method performs well in sparse DECT reconstruction tasks.

CONCLUSION

We have developed a unified optimized mathematical model that integrates the image space and wavelet space prior knowledge into an iterative model. This model is more practical and interpretable than existing approaches are. The experimental results demonstrate the competitive performance of the proposed model.

An efficient deep unrolling network for sparse-view CT reconstruction via alternating optimization of dense-view sinograms and images

Objective. Recently, there have been many advancements in deep unrolling methods for sparse-view computed tomography (SVCT) reconstruction. These methods combine model-based and deep learning-based reconstruction techniques, improving the interpretability and achieving significant results. However, they are often computationally expensive, particularly for clinical raw projection data with large sizes. This study aims to address this issue while maintaining the quality of the reconstructed image.Approach. The SVCT reconstruction task is decomposed into two subproblems using the proximal gradient method: optimizing dense-view sinograms and optimizing images. Then dense-view sinogram inpainting, image-residual learning, and image-refinement modules are performed at each iteration stage using deep neural networks. Unlike previous unrolling methods, the proposed method focuses on optimizing dense-view sinograms instead of full-view sinograms. This approach not only reduces computational resources and runtime but also minimizes the challenge for the network to perform sinogram inpainting when the sparse ratio is extremely small, thereby decreasing the propagation of estimation error from the sinogram domain to the image domain.Main results. The proposed method successfully reconstructs an image (512 × 512 pixels) from real-size (2304 × 736) projection data, with 3.39 M training parameters and an inference time of 0.09 s per slice on a GPU. The proposed method also achieves superior quantitative and qualitative results compared with state-of-the-art deep unrolling methods on datasets with sparse ratios of 1/12 and 1/18, especially in suppressing artifacts and preserving structural details. Additionally, results show that using dense-view sinogram inpainting not only accelerates the computational speed but also leads to faster network convergence and further improvements in reconstruction results.Significance. This research presents an efficient dual-domain deep unrolling technique that produces excellent results in SVCT reconstruction while requiring small computational resources. These findings have important implications for speeding up deep unrolling CT reconstruction methods and making them more practical for processing clinical CT projection data.

2V-CBCT: Two-Orthogonal-Projection Based CBCT Reconstruction and Dose Calculation for Radiation Therapy Using Real Projection Data

This work demonstrates the feasibility of two-orthogonal-projection-based CBCT (2V-CBCT) reconstruction and dose calculation for radiation therapy (RT) using real projection data, which is the first 2V-CBCT feasibility study with real projection data, to the best of our knowledge. RT treatments are often delivered in multiple fractions, for which on-board CBCT is desirable to calculate the delivered dose per fraction for the purpose of RT delivery quality assurance and adaptive RT. However, not all RT treatments/fractions have CBCT acquired, but two orthogonal projections are always available. The question to be addressed in this work is the feasibility of 2V-CBCT for the purpose of RT dose calculation. 2V-CBCT is a severely ill-posed inverse problem for which we propose a coarse-to-fine learning strategy. First, a 3D deep neural network that can extract and exploit the inter-slice and intra-slice information is adopted to predict the initial 3D volumes. Then, a 2D deep neural network is utilized to fine-tune the initial 3D volumes slice-by-slice. During the fine-tuning stage, a perceptual loss based on multi-frequency features is employed to enhance the image reconstruction. Dose calculation results from both photon and proton RT demonstrate that 2V-CBCT provides comparable accuracy with full-view CBCT based on real projection data.

Sparse-view cone-beam computed tomography iterative reconstruction based on new multi-gradient direction total variation

AIM

The accurate reconstruction of cone-beam computed tomography (CBCT) from sparse projections is one of the most important areas for study. The compressed sensing theory has been widely employed in the sparse reconstruction of CBCT. However, the total variation (TV) approach solely uses information from the i-coordinate, j-coordinate, and k-coordinate gradients to reconstruct the CBCT image.

MATERIALS AND METHODS

It is well recognized that the CBCT image can be reconstructed more accurately with more gradient information from different directions. Thus, this study introduces a novel approach, named the new multi-gradient direction total variation minimization method. The method uses gradient information from the ij-coordinate, ik-coordinate, and jk-coordinate directions to reconstruct CBCT images, which incorporates nine different types of gradient information from nine directions.

RESULTS

This study assessed the efficacy of the proposed methodology using under-sampled projections from four different experiments, including two digital phantoms, one patient's head dataset, and one physical phantom dataset. The results indicated that the proposed method achieved the lowest RMSE index and the highest SSIM index. Meanwhile, we compared the voxel intensity curves of the reconstructed images to assess the edge structure preservation. Among the various methods compared, the curves generated by the proposed method exhibited the highest level of consistency with the gold standard image curves.

CONCLUSION

In summary, the proposed method showed significant potential in enhancing the quality and accuracy of CBCT image reconstruction.

Deep convolutional dictionary learning network for sparse view CT reconstruction with a group sparse prior

Purpose Numerous techniques based on deep learning have been utilized in sparse view computed tomography (CT) imaging. Nevertheless, the majority of techniques are instinctively constructed utilizing state-of-the-art opaque convolutional neural networks (CNNs) and lack interpretability. Moreover, CNNs tend to focus on local receptive fields and neglect nonlocal self-similarity prior information. Obtaining diagnostically valuable images from sparsely sampled projections is a challenging and ill-posed task. Method To address this issue, we propose a unique and understandable model named DCDL-GS for sparse view CT imaging. This model relies on a network comprised of convolutional dictionary learning and a nonlocal group sparse prior. To enhance the quality of image reconstruction, we utilize a neural network in conjunction with a statistical iterative reconstruction framework and perform a set number of iterations. Inspired by group sparsity priors, we adopt a novel group thresholding operation to improve the feature representation and constraint ability and obtain a theoretical interpretation. Furthermore, our DCDL-GS model incorporates filtered backprojection (FBP) reconstruction, fast sliding window nonlocal self-similarity operations, and a lightweight and interpretable convolutional dictionary learning network to enhance the applicability of the model. Results The efficiency of our proposed DCDL-GS model in preserving edges and recovering features is demonstrated by the visual results obtained on the LDCT-P and UIH datasets. Compared to the results of the most advanced techniques, the quantitative results are enhanced, with increases of 0.6-0.8 dB for the peak signal-to-noise ratio (PSNR), 0.005-0.01 for the structural similarity index measure (SSIM), and 1-1.3 for the regulated Fréchet inception distance (rFID) on the test dataset. The quantitative results also show the effectiveness of our proposed deep convolution iterative reconstruction module and nonlocal group sparse prior. Conclusion In this paper, we create a consolidated and enhanced mathematical model by integrating projection data and prior knowledge of images into a deep iterative model. The model is more practical and interpretable than existing approaches. The results from the experiment show that the proposed model performs well in comparison to the others.

CT image denoising methods for image quality improvement and radiation dose reduction

With the ever-increasing use of computed tomography (CT), concerns about its radiation dose have become a significant public issue. To address the need for radiation dose reduction, CT denoising methods have been widely investigated and applied in low-dose CT images. Numerous noise reduction algorithms have emerged, such as iterative reconstruction and most recently, deep learning (DL)-based approaches. Given the rapid advancements in Artificial Intelligence techniques, we recognize the need for a comprehensive review that emphasizes the most recently developed methods. Hence, we have performed a thorough analysis of existing literature to provide such a review. Beyond directly comparing the performance, we focus on pivotal aspects, including model training, validation, testing, generalizability, vulnerability, and evaluation methods. This review is expected to raise awareness of the various facets involved in CT image denoising and the specific challenges in developing DL-based models.

SEA-Net: Structure-Enhanced Attention Network for Limited-Angle CBCT Reconstruction of Clinical Projection Data

This work aims to improve limited-angle (LA) cone beam computed tomography (CBCT) by developing deep learning (DL) methods for real clinical CBCT projection data, which is the first feasibility study of clinical-projection-data-based LA-CBCT, to the best of our knowledge. In radiation therapy (RT), CBCT is routinely used as the on-board imaging modality for patient setup. Compared to diagnostic CT, CBCT has a long acquisition time, e.g., 60 seconds for a full 360° rotation, which is subject to the motion artifact. Therefore, the LA-CBCT, if achievable, is of the great interest for the purpose of RT, for its proportionally reduced scanning time in addition to the radiation dose. However, LA-CBCT suffers from severe wedge artifacts and image distortions. Targeting at real clinical projection data, we have explored various DL methods such as image/data/hybrid-domain methods and finally developed a so-called Structure-Enhanced Attention Network (SEA-Net) method that has the best image quality from clinical projection data among the DL methods we have implemented. Specifically, the proposed SEA-Net employs a specialized structure enhancement sub-network to promote texture preservation. Based on the observation that the distribution of wedge artifacts in reconstruction images is non-uniform, the spatial attention module is utilized to emphasize the relevant regions while ignores the irrelevant ones, which leads to more accurate texture restoration.

An orthogonal matching pursuit optimization method for solving minimum-monitor-unit problems: Applications to proton IMPT, ARC and FLASH

BACKGROUND

The intensities (i.e., number of protons in monitor unit [MU]) of deliverable proton spots need to be either zero or meet a minimum-MU (MMU) threshold, which is a nonconvex problem. Since the dose rate is proportionally associated with the MMU threshold, higher-dose-rate proton radiation therapy (RT) (e.g., efficient intensity modulated proton therapy (IMPT) and ARC proton therapy, and high-dose-rate-induced FLASH effect needs to solve the MMU problem with larger MMU threshold, which however makes the nonconvex problem more difficult to solve.

PURPOSE

This work will develop a more effective optimization method based on orthogonal matching pursuit (OMP) for solving the MMU problem with large MMU thresholds, compared to state-of-the-art methods, such as alternating direction method of multipliers (ADMM), proximal gradient descent method (PGD), or stochastic coordinate descent method (SCD).

METHODS

The new method consists of two essential components. First, the iterative convex relaxation (ICR) method is used to determine the active sets for dose-volume planning constraints and decouple the MMU constraint from the rest. Second, a modified OMP optimization algorithm is used to handle the MMU constraint: the non-zero spots are greedily selected via OMP to form the solution set to be optimized, and then a convex constrained subproblem is formed and can be conveniently solved to optimize the spot weights restricted to this solution set via OMP. During this iterative process, the new non-zero spots localized via OMP will be adaptively added to or removed from the optimization objective.

RESULTS

The new method via OMP is validated in comparison with ADMM, PGD and SCD for high-dose-rate IMPT, ARC, and FLASH problems of large MMU thresholds, and the results suggest that OMP substantially improved the plan quality from PGD, ADMM and SCD in terms of both target dose conformality (e.g., quantified by max target dose and conformity index) and normal tissue sparing (e.g., mean and max dose). For example, in the brain case, the max target dose for IMPT/ARC/FLASH was 368.0%/358.3%/283.4% respectively for PGD, 154.4%/179.8%/150.0% for ADMM, 134.5%/130.4%/123.0% for SCD, while it was <120% in all scenarios for OMP; compared to PGD/ADMM/SCD, OMP improved the conformity index from 0.42/0.52/0.33 to 0.65 for IMPT and 0.46/0.60/0.61 to 0.83 for ARC.

CONCLUSIONS

A new OMP-based optimization algorithm is developed to solve the MMU problems with large MMU thresholds, and validated using examples of IMPT, ARC, and FLASH with substantially improved plan quality from ADMM, PGD, and SCD.

A treatment plan optimization method with direct minimization of number of energy jumps for proton arc therapy

Objective. The optimization of energy layer distributions is crucial to proton arc therapy: on one hand, a sufficient number of energy layers is needed to ensure the plan quality; on the other hand, an excess number of energy jumps (NEJ) can substantially slow down the treatment delivery. This work will develop a new treatment plan optimization method with direct minimization of (NEJ), which will be shown to outperform state-of-the-art methods in both plan quality and delivery efficiency.Approach. The proposed method jointly optimizes the plan quality and minimizes the NEJ. To minimize NEJ, (1) the proton spotsxis summed per energy layer to form the energy vectory; (2)yis binarized via sigmoid transform intoy1; (3)y1is multiplied with a predefined energy order vector via dot product intoy2; (4)y2is filtered through the finite-differencing kernel intoy3in order to identify NEJ; (5) only the NEJ ofy3is penalized, whilexis optimized for plan quality. The solution algorithm to this new method is based on iterative convex relaxation.Main results. The new method is validated in comparison with state-of-the-art methods called energy sequencing (ES) method and energy matrix (EM) method. In terms of delivery efficiency, the new method had fewer NEJ, less energy switching time, and generally less total delivery time. In terms of plan quality, the new method had smaller optimization objective values, lower normal tissue dose, and generally better target coverage.Significance. We have developed a new treatment plan optimization method with direct minimization of NEJ, and demonstrated that this new method outperformed state-of-the-art methods (ES and EM) in both plan quality and delivery efficiency.

Low-dose CT with deep learning regularization via proximal forward-backward splitting

Low-dose x-ray computed tomography (LDCT) is desirable for reduced patient dose. This work develops new image reconstruction methods with deep learning (DL) regularization for LDCT. Our methods are based on the unrolling of a proximal forward-backward splitting (PFBS) framework with data-driven image regularization via deep neural networks. In contrast to PFBS-IR, which utilizes standard data fidelity updates via an iterative reconstruction (IR) method, PFBS-AIR involves preconditioned data fidelity updates that fuse the analytical reconstruction (AR) and IR methods in a synergistic way, i.e. fused analytical and iterative reconstruction (AIR). The results suggest that the DL-regularized methods (PFBS-IR and PFBS-AIR) provide better reconstruction quality compared to conventional methods (AR or IR). In addition, owing to the AIR, PFBS-AIR noticeably outperformed PFBS-IR and another DL-based postprocessing method, FBPConvNet.

Multi-Scale Learned Iterative Reconstruction

Model-based learned iterative reconstruction methods have recently been shown to outperform classical reconstruction algorithms. Applicability of these methods to large scale inverse problems is however limited by the available memory for training and extensive training times, the latter due to computationally expensive forward models. As a possible solution to these restrictions we propose a multi-scale learned iterative reconstruction scheme that computes iterates on discretisations of increasing resolution. This procedure does not only reduce memory requirements, it also considerably speeds up reconstruction and training times, but most importantly is scalable to large scale inverse problems with non-trivial forward operators, such as those that arise in many 3D tomographic applications. In particular, we propose a hybrid network that combines the multiscale iterative approach with a particularly expressive network architecture which in combination exhibits excellent scalability in 3D. Applicability of the algorithm is demonstrated for 3D cone beam computed tomography from real measurement data of an organic phantom. Additionally, we examine scalability and reconstruction quality in comparison to established learned reconstruction methods in two dimensions for low dose computed tomography on human phantoms.

A fast regularized iterative algorithm for fan-beam CT reconstruction

We propose a fast iterative image reconstruction algorithm for normal, short-scan, and super-short-scan fan-beam computed tomography (CT), which aims at iterative reconstruction for low-dose and few-view CT by minimizing a data-fidelity term regularized with a total variation (TV) penalty. The derivation of the algorithm can be outlined as follows. First, the original minimization problem is formulated into a saddle-point (primal-dual) problem by using the Lagrangian duality, to which we apply the alternating projection proximal (APP) algorithm, which belongs to a class of first-order primal-dual methods. Second, we precondition the iterative formula using the modified ramp filter of the filtered back-projection (FBP) reconstruction algorithm in such a way that the solution to this preconditioned iteration perfectly coincides with the solution to the original problem. The resulting algorithm converges quickly to the minimizer of the cost function. To demonstrate the advantages of our method, we perform reconstruction experiments using projection data from both numerical phantoms and real CT data. Both qualitative and quantitative results are presented.

A new in-line X-ray phase-contrast computed tomography reconstruction algorithm based on adaptive-weighted anisotropic TpV regularization for insufficient data

In-line X-ray phase-contrast computed tomography (IL-PCCT) is a valuable tool for revealing the internal detailed structures in weakly absorbing objects (e.g. biological soft tissues), and has a great potential to become clinically applicable. However, the long scanning time for IL-PCCT will result in a high radiation dose to biological samples, and thus impede the wider use of IL-PCCT in clinical and biomedical imaging. To alleviate this problem, a new iterative CT reconstruction algorithm is presented that aims to decrease the radiation dose by reducing the projection views, while maintaining the high quality of reconstructed images. The proposed algorithm combines the adaptive-weighted anisotropic total p-variation (AwaTpV, 0 < p < 1) regularization technique with projection onto convex sets (POCS) strategy. Noteworthy, the AwaTpV regularization term not only contains the horizontal and vertical image gradients but also adds the diagonal image gradients in order to enforce the directional continuity in the gradient domain. To evaluate the effectiveness and ability of the proposed algorithm, experiments with a numerical phantom and synchrotron IL-PCCT were performed, respectively. The results demonstrated that the proposed algorithm had the ability to significantly reduce the artefacts caused by insufficient data and effectively preserved the edge details under noise-free and noisy conditions, and thus could be used as an effective approach to decrease the radiation dose for IL-PCCT.

Evaluation and Clinical Application of a Commercially Available Iterative Reconstruction Algorithm for CBCT-Based IGRT

PURPOSE

We have quantitatively evaluated the image quality of a new commercially available iterative cone-beam computed tomography reconstruction algorithm over standard cone-beam computed tomography image reconstruction results.

METHODS

This iterative cone-beam computed tomography reconstruction pipeline uses a finite element solver (AcurosCTS)-based scatter correction and a statistical (iterative) reconstruction in addition to a standard kernel-based correction followed by filtered back-projection-based Feldkamp-Davis-Kress cone-beam computed tomography reconstruction. Standard full-fan half-rotation Head, half-fan full-rotation Head, and standard Pelvis cone-beam computed tomography protocols have been investigated to scan a quality assurance phantom via the following image quality metrics: uniformity, HU constancy, spatial resolution, low contrast detection, noise level, and contrast-to-noise ratio. An anthropomorphic head phantom was scanned for verification of noise reduction. Clinical patient image data sets for 5 head/neck patients and 5 prostate patients were qualitatively evaluated.

RESULTS

Quality assurance phantom study results showed that relative to filtered back-projection-based cone-beam computed tomography, noise was reduced from 28.8 ± 0.3 HU to a range between 18.3 ± 0.2 and 5.9 ± 0.2 HU for Full-Fan Head scans, from 14.4 ± 0.2 HU to a range between 12.8 ± 0.3 and 5.2 ± 0.3 HU for Half-Fan Head scans, and from 6.2 ± 0.1 HU to a range between 3.8 ± 0.1 and 2.0 ± 0.2 HU for Pelvis scans, with the iterative cone-beam computed tomography algorithm. Spatial resolution was marginally improved while results for uniformity and HU constancy were similar. For the head phantom study, noise was reduced from 43.6 HU to a range between 24.8 and 13.0 HU for a Full-Fan Head and from 35.1 HU to a range between 22.9 and 14.0 HU for a Half-Fan Head scan. The patient data study showed that artifacts due to photon starvation and streak artifacts were all reduced, and image noise in specified target regions were reduced to 62% ± 15% for 10 patients.

CONCLUSION

Noise and contrast-to-noise ratio image quality characteristics were significantly improved using the iterative cone-beam computed tomography reconstruction algorithm relative to the filtered back-projection-based cone-beam computed tomography method. These improvements will enhance the accuracy of cone-beam computed tomography-based image-guided applications.

Low-Dose CBCT Reconstruction Using Hessian Schatten Penalties

Cone-beam computed tomography (CBCT) has been widely used in radiation therapy. For accurate patient setup and treatment target localization, it is important to obtain high-quality reconstruction images. The total variation (TV) penalty has shown the state-of-the-art performance in suppressing noise and preserving edges for statistical iterative image reconstruction, but it sometimes leads to the so-called staircase effect. In this paper, we proposed to use a new family of penalties-the Hessian Schatten (HS) penalties-for the CBCT reconstruction. Consisting of the second-order derivatives, the HS penalties are able to reflect the smooth intensity transitions of the underlying image without introducing the staircase effect. We discussed and compared the behaviors of several convex HS penalties with orders 1, 2, and for CBCT reconstruction. We used the majorization-minimization approach with a primal-dual formulation for the corresponding optimization problem. Experiments on two digital phantoms and two physical phantoms demonstrated the proposed penalty family's outstanding performance over TV in suppressing the staircase effect, and the HS penalty with order 1 had the best performance among the HS penalties tested.