Incomplete Projection Research Articles

Multiobjective optimization guided by image quality index for limited-angle CT image reconstruction.

Due to the incomplete projection data collected by limited-angle computed tomography (CT), severe artifacts are present in the reconstructed image. Classical regularization methods such as total variation (TV) minimization, ℓ0 minimization, are unable to suppress artifacts at the edges perfectly. Most existing regularization methods are single-objective optimization approaches, stemming from scalarization methods for multiobjective optimization problems (MOP). To further suppress the artifacts and effectively preserve the edge structures of the reconstructed image. This study presents a multiobjective optimization model incorporates both data fidelity term and ℓ0-norm of the image gradient as objective functions. It employs an iterative approach different from traditional scalarization methods, using the maximization of structural similarity (SSIM) values to guide optimization rather than minimizing the objective function.The iterative method involves two steps, firstly, simultaneous algebraic reconstruction technique (SART) optimizes the data fidelity term using SSIM and the Simulated Annealing (SA) algorithm for guidance. The degradation solution is accepted in the form of probability, and guided image filtering (GIF) is introduced to further preserve the image edge when the degradation solution is rejected. Secondly, the result from the first step is integrated into the second objective function as a constraint, we use ℓ0 minimization to optimize ℓ0-norm of the image gradient, and the SSIM, SA algorithm and GIF are introduced to guide optimization process by improving SSIM value like the first step. With visual inspection, the peak signal-to-noise ratio (PSNR), root mean square error (RMSE), and SSIM values indicate that our approach outperforms other traditional methods. The experiments demonstrate the effectiveness of our method and its superiority over other classical methods in artifact suppression and edge detail restoration.

Learning Scatter Artifact Correction in Cone-Beam X-Ray CT Using Incomplete Projections with Beam Hole Array

X-ray cone-beam computed tomography (CBCT) is a powerful tool for nondestructive testing and evaluation, yet the CT image quality can be compromised by artifact due to X-ray scattering within dense materials such as metals. This problem leads to the need for hardware- and software-based scatter artifact correction to enhance the image quality. Recently, deep learning techniques have merged as a promising approach to obtain scatter-free images efficiently. However, these deep learning techniques rely heavily on training data, often gathered through simulation. Simulated CT images, unfortunately, do not accurately reproduce the real properties of objects, and physically accurate X-ray simulation still requires significant computation time, hindering the collection of a large number of CT images. To address these problems, we propose a deep learning framework for scatter artifact correction using projections obtained solely by real CT scanning. To this end, we utilize a beam-hole array (BHA) to block the X-rays deviating from the primary beam path, thereby capturing scatter-free X-ray intensity at certain detector pixels. As the BHA shadows a large portion of detector pixels, we incorporate several regularization losses to enhance the training process. Furthermore, we introduce radiographic data augmentation to mitigate the need for long scanning time, which is a concern as CT devices equipped with BHA require two series of CT scans. Experimental validation showed that the proposed framework outperforms a baseline method that learns simulated projections where the entire image is visible and does not contain scattering artifacts.

An interactive method based on multi-objective optimization for limited-angle CT reconstruction

Objective. Limited-angle x-ray computed tomography (CT) is a typical ill-posed inverse problem, leading to artifacts in the reconstructed image due to the incomplete projection data. Most iteration CT reconstruction methods involve optimization for a single object. This paper explores a multi-objective optimization model and an interactive method based on multi-objective optimization to suppress the artifacts of limited-angle CT. Approach. The model includes two objective functions on the dual domain within the data consistency constraint. In the interactive method, the structural similarity index measure (SSIM) is regarded as the value function of the decision maker (DM) firstly. Secondly, the DM arranges the objective functions of the multi-objective optimization model to be optimized according to their absolute importance. Finally, the SSIM and the simulated annealing (SA) method help the DM choose the desirable reconstruction image by improving the SSIM value during the iteration process. Main results. Simulation and real data experiments demonstrate that the artifacts can be suppressed by the proposed method, and the results were superior to those reconstructed by the other three reconstruction methods in preserving the edge structure of the image. Significance. The proposed interactive method based on multi-objective optimization shows some potential advantages over classical single object optimization methods.

Image reconstruction method for incomplete CT projection based on self-guided image filtering.

In some fields of medical diagnosis or industrial nondestructive testing, it is difficult to obtain complete computed tomography (CT) data due to the limitation of radiation dose or other factors. Therefore, image reconstruction of incomplete projection data is the focus of this paper. In this paper, a new image reconstruction model based on self-guided image filtering (SGIF) term is proposed for few-view and segmental limited-angle (SLA) CT reconstruction. Then the alternating direction method (ADM) is used to solve this model. For simplicity, we call it ADM-SGIF method. The key idea of ADM-SGIF method is to use the reconstructed image itself as a reference and utilize its structural features to guide CT reconstruction. This method can effectively preserve image structures and remove shading artifacts. To validate the effectiveness of the proposed reconstruction method, we conduct digital phantom and real CT data experiments. The results indicate that ADM-SGIF method outperforms competing methods, including total variation (TV), relative total variation (RTV), and L0-norm minimization solved by ADM (ADM-L0) methods, in both subjective and objective evaluations.

A Review of Deep Learning CT Reconstruction From Incomplete Projection Data

A Review of Deep Learning CT Reconstruction From Incomplete Projection Data

The Block Landweber Iterative Method for Light Field Reconstruction from a Focal Stack

Light field imaging involves reconstructing a 4D light field from a 3D focal stack, which makes it challenging to reconstruct the light field from incomplete projection data. To address this problem, a linear projection system is established to model the focal stack imaging process using discrete refocusing equations. Based on this system, we propose the block Landweber iterative method to find the least-squares solution. This method computes the sparse matrix while iterating, which overcomes the problem of data storage. The 2-norm of the block matrix is utilized as the weighted matrix to normalize every block matrix on an identical scale, delivering an effective relaxation strategy under the convergence condition in the inconsistent case, which yields better reconstruction results and accelerates the convergence speed. The experimental results based on the image quality assessments of reference and non-reference images show that our method achieved better reconstruction results compared to other relevant common methods, even with fewer focal stacks and higher angle resolution.

Monocular eye patching modulates ipsilesional reactive saccades and smooth pursuit in patients with left hemispatial neglect

Patients with hemispatial neglect show multiple oculomotor deficits like delayed contralesional saccade latencies, hypometric saccade amplitudes, and impaired smooth pursuit. We aimed to investigate whether modulation of superior colliculus (SC) activity via monocular eye patching improves neglect patients’ eye movements to the contralesional side of space. Thirteen neglect patients with left-hemispheric (LH) stroke, 22 neglect patients with right-hemispheric (RH) stroke, and 24 healthy controls completed a video-oculographic examination of horizontal smooth pursuit and reactive saccades twice, while the left or right eye was covered with an eye patch. Independent of the eye patch position, LH and RH patients showed enlarged saccade latencies toward contralesional stimuli. In addition, both during smooth pursuit and reactive saccades, RH patients made significantly fewer rightward saccades when the right than when the left eye was patched. Moreover, during reactive saccades, RH patients made significantly fewer right than left saccades, but only when the right eye was patched. These findings suggest that the ipsilesional eye patch modulated ipsilesional ocular performance in the RH group, presumably resulting from differences in SC activity. Yet, ipsilesional eye patching did not improve eye movements to the contralesional side of space, possibly due to the incomplete contralateral retinocollicular projection in humans.

The multi-scale fusion reconstruction algorithm of CT and CL

Computed tomography (CT) is a widely used nondestructive testing (NDT) technique for material research, paleontology research and other fields. However, it is difficult for CT to reconstruct flat objects at high magnification ratios. Computed laminography (CL) enables high-resolution imaging for flat objects due to its unique scanning geometry. A challenging task for CL image reconstruction is to deal with the cross-section artifacts resulting from the incomplete projection data acquired from the CL scan. An effective multi-scale fusion reconstruction algorithm of CT and CL was proposed in this paper. The algorithm combining the advantages of the two scanning geometries, low-resolution CT data was used to compensate for the data missing in CL projection domain, and the cross-section artifacts were reduced. Experiments on paleontological fossils and multilayer printed circuit boards (PCB) were performed, where CT and CL data from different systems and scanning conditions. The results showed that the method can effectively suppress the cross-section artifacts of CL and obtain high-resolution reconstructed images.

HTSE: hierarchical time-surface model for temporal knowledge graph embedding

Representation learning based on temporal knowledge graphs (TKGs) has attracted widespread interest, and temporal knowledge graph embedding (TKGE) expresses time entity and relation tokens and exhibit strong dynamics. Despite the significance of the dynamics and the persistent updates in TKGs, most studies have been devoted to static knowledge graphs. Moreover, previous temporal works ignored the semantic hierarchies observed in knowledge modelling cases, which are common in real-world applications. Inaccurate semantic expressions caused by incomplete projections might not capture complex topological structures very well. To solve this problem, a novel hierarchical time-surface embedding (HTSE) model is proposed for the representation learning of entities, relations and time. Specifically, a unified relation-oriented hierarchical space aims to distinguish relations at different semantic levels of a hierarchy, and entities can naturally reflect the corresponding hierarchy. Then, a time surface aims to enhance the temporal characteristics, and quadruples are learned through exponential mapping and tangent planes in the time surface. According to extensive experiments, HTSE can achieve remarkable performance on five benchmark datasets, outperforming baseline models for time scope prediction, temporal link prediction and hierarchical relation embedding tasks.Furthermore, the qualitative analysis is used to demonstrate the explainable strategy for hierarchical embeddings and their significance in TKGs.

A Mathematical Interpretation of Autoregressive Generative Pre-Trained Transformer and Self-Supervised Learning

In this paper, we present a rigorous mathematical examination of generative pre-trained transformer (GPT) models and their autoregressive self-supervised learning mechanisms. We begin by defining natural language space and knowledge space, which are two key concepts for understanding the dimensionality reduction process in GPT-based large language models (LLMs). By exploring projection functions and their inverses, we establish a framework for analyzing the language generation capabilities of these models. We then investigate the GPT representation space, examining its implications for the models’ approximation properties. Finally, we discuss the limitations and challenges of GPT models and their learning mechanisms, considering trade-offs between complexity and generalization, as well as the implications of incomplete inverse projection functions. Our findings demonstrate that GPT models possess the capability to encode knowledge into low-dimensional vectors through their autoregressive self-supervised learning mechanism. This comprehensive analysis provides a solid mathematical foundation for future advancements in GPT-based LLMs, promising advancements in natural language processing tasks such as language translation, text summarization, and question answering due to improved understanding and optimization of model training and performance.

Learning from Projection to Reconstruction: A Deep Learning Reconstruction Framework for Sparse-View Phase Contrast Computed Tomography via Dual-Domain Enhancement

Phase contrast computed tomography (PCCT) provides an effective non-destructive testing tool for weak absorption objects. Limited by the phase stepping principle and radiation dose requirement, sparse-view sampling is usually performed in PCCT, introducing severe artifacts in reconstruction. In this paper, we report a dual-domain (i.e., the projection sinogram domain and image domain) enhancement framework based on deep learning (DL) for PCCT with sparse-view projections. It consists of two convolutional neural networks (CNN) in dual domains and the phase contrast Radon inversion layer (PCRIL) to connect them. PCRIL can achieve PCCT reconstruction, and it allows the gradients to backpropagate from the image domain to the projection sinogram domain while training. Therefore, parameters of CNNs in dual domains are updated simultaneously. It could overcome the limitations that the enhancement in the image domain causes blurred images and the enhancement in the projection sinogram domain introduces unpredictable artifacts. Considering the grating-based PCCT as an example, the proposed framework is validated and demonstrated with experiments of the simulated datasets and experimental datasets. This work can generate high-quality PCCT images with given incomplete projections and has the potential to push the applications of PCCT techniques in the field of composite imaging and biomedical imaging.

CROSS: Cross-Domain Residual-Optimization-Based Structure Strengthening Reconstruction for Limited-Angle CT

Limited-angle CT is an effective way for practical scenario due to its flexibility in various complex scanning conditions. However, incomplete projection data will lead to severe wedge artifacts and degraded images, which significantly lower the diagnostic values. To overcome this problem, we propose a novel method termed Cross-domain Residual-Optimization Based Structure Strengthening (CROSS) Reconstruction for limited-angle CT. The proposed CROSS framework consists of three steps, which are conducted on the image domain and measurement domain alternatively. Differing from traditional dual-domain-based algorithms, our CROSS method not only regularizes the reconstruction results on the image space but also the residual-error space, which boosts organ recovery where the area has a larger attenuation coefficient. Besides, the structure-strengthening network is adopted to enhance tissue preservation. Simulated and preclinical datasets are conducted to evaluate the proposed CROSS method. Experiments show that the proposed framework could produce a better performance in artifact removal and edge preservation.

Multi-scale dilated dense reconstruction network for limited-angle computed tomography

Objective. Due to the incomplete projection data, the image reconstructed by limited-angle computed tomography (CT) usually suffers from significant artifacts, by which the structural details are heavily blurred. In this study, we aim to develop a novel approach to improve the limited-angle CT reconstruction performance, especially for the narrow scanning angular range. Approach. A deep learning based iterative framework for limited-angle tomography is proposed, which is named multi-scale dilated dense reconstruction network (MSDDRNet). The MSDDRNet utilizes a multi-scale dilated dense convolution neural network (MSDD-CNN) with conventional reconstruction algorithm for predicting image from incomplete projection data. The MSDD-CNN enhances the image features in the network by merging the DenseNet-Like structure, which serves to restore invisible singularities and reduce artifacts, as well as introducing constraints on the projection domain data into the iterative process to achieve better image detail recovery. Additionally, to improve the training speed of the network, we use a strategy of pre-training and model migration. Main results. Numerical experiments demonstrate that the proposed MSDDRNet performs well in terms of artifact correction, noise reduction and structure recovery compared to existing methods with limited scan angles, and we also extend the proposed method to more general scanning condition and other application such as dental CT data. Significance. The proposed method is a general framework, which can be applied to other CT problems, such as low dose CT, sparse-data CT and spectral CT.

Cone beam computed laminography based on adaptive-weighted dynamic-adjusted relative total variation

X-ray computed laminography (CL) is an advanced non-destructive testing technique. It allows 3D imaging of the interior of a plate–shell object using projections at a tilted angle, making up for the shortcomings of traditional computed tomography (CT) in imaging plate–shell objects. Nevertheless, the incomplete projections of the cone beam CL result in inter-slice aliasing and cone angle artifacts in the reconstructed image. To address this issue, we present an adaptive-weighted dynamic-adjusted relative total variation (AwDaRTV) minimization algorithm. Based on relative total variation (RTV), the proposed AwDaRTV considers the edge property among adjacent image voxels and introduces weights that are adaptively adjusted with local image gradients. In addition, a dynamically adjusted weight is designed for the regularization term in the hierarchical direction of the reconstructed image. And the weight updates with the number of iterations. To demonstrate the superiority of the proposed algorithm, experiments are carried out on the PCB phantom and the workpiece phantom. Qualitative and quantitative analyzes show that the proposed algorithm works well in reconstructing critical structural features and is effective at suppressing noise, as well as inter-slice aliasing and blurring.

Lidar Reflective Tomography of the Target Under Incomplete View State

The lidar reflective tomography (LRT) system transmits a laser signal and obtains laser reflection projections of the target, which shows great potential for further long-distance noncooperative target detection. However, the received projections are normally in an incomplete view state. Hence, in this article, an improved algebraic reconstruction technique (ART) utilizing the sparse regularization model and nonlocal means (NLMs) algorithm is introduced and proposed for LRT reconstruction to restore incomplete signals or projections. By using the designed LRT outfield system, the comparative experiments are carried out to validate the effectiveness of the proposed method. By considering different investigation states, the improved NLM-ART sparse method shows great capability for LRT of noncooperative targets in long distance.

Sherlock Holmes and the Adventure of Lucid Dreaming: The Place of Oneirogenesis in the Science of Deduction

ABSTRACT This article examines a much-underrated aspect in the Holmesian canon: dreams and the potential for dream-rehearsals by virtue of the brain’s “dream drugstore” faculty. Frequently described as “dreamy-eyed” or the “dreamer” of Baker Street, Holmes possesses powers of visiting scenes of crime “in spirit,” exhibiting powers of oneirogenesis. This unorthodox criminological strategy marks him as a critic of Western rationality, placing him in a genealogy dating back to Thomas De Quincey (who recorded vivid hallucinogenic dreams) and The Moonstone’s character Ezra Jennings (practically the first sleuth in Victorian English literature). In the Holmesian canon, (lucid) dreaming plays a subliminal role, which calls to question what this repressed unorthodoxy in Holmesian investigations implies for the detective’s preeminent science of deduction. Representations and adaptations that do not account for Holmesian oneirogenesis, are incomplete projections of the, ultimately and absolutely, human and oneirically harnessed faculties of the Victorian detective.

Nonconvex [formula omitted]- regularized nonlocal self-similarity denoiser for compressive sensing based CT reconstruction

Compressive sensing (CS) based computed tomography (CT) image reconstruction aims at reducing the radiation risk through sparse-view projection data. However, it is challenging to achieve satisfying image quality from incomplete projections. Recent works demonstrate the promising potential of nonconvex L1/2-norm in CS problem, while the applications on medical imaging are constrained by its nonconvexity. In this paper, we develop an L1/2-regularized nonlocal self-similarity (NSS) denoiser based CT reconstruction model, which combines with low-rank approximation and group sparse coding (GSC) framework. Concretely, we firstly split the CT reconstruction problem into two subproblems, then improve CT image quality furtherly using our proposed denoiser. Instead of optimizing the nonconvex problem under the perspective of GSC, we particularly reconstruct CT image via low-rank minimization based on two simple yet essential schemes, which build the equivalent relationship between GSC based denoiser and low-rank minimization. Furtherly, the weighted singular value thresholding (WSVT) operator is utilized to optimize the resulting nonconvex L1/2 minimization problem. Following this, our proposed denoiser is integrated with the CT reconstruction problem by alternating direction method of multipliers (ADMM) framework. Extensive experimental results on typical clinical CT images have demonstrated that our approach can further achieve better performance than popular approaches.

LRIP-Net: Low-Resolution Image Prior-Based Network for Limited-Angle CT Reconstruction

In the practical applications of computed tomography (CT) imaging, the projection data may be acquired within a limited-angle range and corrupted by noises due to the limitation of scanning conditions. The noisy incomplete projection data results in the ill-posedness of the inverse problems. Based on the observation that the low-resolution reconstruction problem has better numerical stability, we propose a novel low-resolution image prior-based CT reconstruction model for limited-angle reconstruction. More specifically, we build up a low-resolution reconstruction problem on the down-sampled projection data, and use the reconstructed low-resolution image as prior knowledge for the high-resolution limited-angle CT problem. The constrained minimization problem is then solved by the alternating direction method with all subminimization problems approximated by the convolutional neural networks. Numerical experiments demonstrate that our double-resolution network outperforms both the variational method and popular learning-based reconstruction methods on noisy limited-angle reconstruction problems.

Segmental limited-angle CT reconstruction based on image structural prior.

CT reconstruction from incomplete projection data is one of the key researches of X-ray CT imaging. The projection data acquired by few-view and limited-angle sampling are incomplete. In addition, few-view sampling often requires turning on and off the tube voltage, but rapid switching of tube voltage demands for high technical requirements. Limited-angle sampling is easy to realize. However, reconstructed images may encounter obvious artifacts. In this study we investigate a new segmental limited-angle (SLA) sampling strategy, which avoids rapid switching of tube voltage. Thus, the projection data has lower data correlation than limited-angle CT, which is conducive to reconstructing high-quality images. To suppress potential artifacts, we incorporate image structural prior into reconstruction model to present a reconstruction method. The limited-angle CT reconstruction experiments on digital phantoms, real carved cheese and walnut projections are used to test and verify the effectiveness of the proposed method. Several image quality evaluation indices including RMSE, PSNR, and SSIM of the reconstructions in simulation experiments are calculated and listed to show the superiority of our method. The experimental results indicate that the CT image reconstructed using the proposed new method is closer to the reference image. Images from real CT data and their residual images also show that applying the proposed new method can more effectively reduce artifacts and image structures are well preserved.

Sam's Net: A Self-Augmented Multistage Deep-Learning Network for End-to-End Reconstruction of Limited Angle CT.

Limited angle reconstruction is a typical ill-posed problem in computed tomography (CT). Given incomplete projection data, images reconstructed by conventional analytical algorithms and iterative methods suffer from severe structural distortions and artifacts. In this paper, we proposed a self-augmented multi-stage deep-learning network (Sam's Net) for end-to-end reconstruction of limited angle CT. With the merit of the alternating minimization technique, Sam's Net integrates multi-stage self-constraints into cross-domain optimization to provide additional constraints on the manifold of neural networks. In practice, a sinogram completion network (SCNet) and artifact suppression network (ASNet), together with domain transformation layers constitute the backbone for cross-domain optimization. An online self-augmentation module was designed following the manner defined by alternating minimization, which enables a self-augmented learning procedure and multi-stage inference manner. Besides, a substitution operation was applied as a hard constraint for the solution space based on the data fidelity and a learnable weighting layer was constructed for data consistency refinement. Sam's Net forms a new framework for ill-posed reconstruction problems. In the training phase, the self-augmented procedure guides the optimization into a tightened solution space with enriched diverse data distribution and enhanced data consistency. In the inference phase, multi-stage prediction can improve performance progressively. Extensive experiments with both simulated and practical projections under 90-degree and 120-degree fan-beam configurations validate that Sam's Net can significantly improve the reconstruction quality with high stability and robustness.