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We propose an algorithm for limited angle CT which extends the LEARN algorithm of Chen et al. [IEEE TMI, 2018]. The algorithm is based on a superiorized [Herman et al., Med Phys, 2012] version of the simultaneous algebraic reconstruction technique (SART), in which a convolutional neural network (CNN) is used to perturb the solution between SART iterations. Specifically, by assuming a fixed number of iterations and unrolling the iteration, it can be trained in end-to-end fashion as a neural network with untrained layers (representing forward and back projection) in addition to trained convolutional layers. Additionally, we replace the three-layer CNN used in LEARN with a U-net-based architecture to achieve multilevel decomposition and precise localization during the iterative training. The algorithm is implemented in Python using the Pyro-NN library [Syben et al., Med Phys, 2019] and trained on simulated limited angle data generated from lung CT images. Our numerical experiments indicate that the superiorized SART algorithm with U-net-based CNN significantly reduces artifacts arising in limited angle scenarios. In particular, it is able to recover internal features that similar methods using the three-layer CNN are unable to recover, such as edges of ribs and soft tissue.

Computed Tomography (CT) Imaging is a widely used technique for medical and industrial applications. Iterative reconstruction algorithms are desired for improved reconstructed image quality and lower dose, but its computational requirements limit its practical usage. Reconstruction toolkit (RTK) is a package of open source GPU accelerated algorithms for CBCT (cone beam computed tomography). GPU based iterative algorithms gives immense acceleration, but it may not be optimized to use the GPU resources efficiently. Nvidia has released several profilers (Nsight-systems, Nsight-compute) to analyze the GPU implementation of an algorithm from compute utilization and memory efficiency perspective. This paper profiles and analyzes the GPU implementation of iterative FDK algorithm in RTK and optimizes it for computation and memory usage on a Quadro GV100 GPU with 32 GB of memory and over 5000 cuda cores. RTK based GPU accelerated iterative FDK when applied on a 4 byte per pixel input projection dataset of size 1.1 GB (512×512×1024) for 20 iterations, to reconstruct a volume of size 440 MB (512×512×441) with 4 byte per pixel, resulted in total runtime of ~11.2 seconds per iteration. Optimized RTK based iterative FDK presented in this paper took ~1.3 seconds per iteration.

Compressed sensing (CS) reconstruction methods employing sparsity regularization and prior constraints are successfully applied in sparse-view computed tomography (CT) reconstruction and yield high-quality images compared with other low-dose imaging methods. In this paper, we proposed an adaptive prior patch size (APPS) strategy in sparse-view CT reconstruction. The method adopts sparse representation (SR) using adaptive patch size instead of a constant one to synthesize prior image of higher quality, because the optimal patch size should vary from each distribution range of local feature. The simulation experiments show that the proposed strategy has the better performance than the method with fixed patch size in terms of artifact reduction and edge preservation.

Model-Based Iterative Reconstruction (MBIR) methods for X-ray CT provide improved image quality compared to conventional techniques like filtered backprojection (FBP), but their computational burden is undesirably high. Distributed algorithms have the potential to significantly reduce reconstruction time, but the communication overhead of existing methods has been a considerable bottleneck. This paper proposes a distributed algorithm called Block-Axial Checkerboarding (BAC) that utilizes the special structure found in helical CT geometry to reduce inter-node communication. Preliminary results using a simulated 3D helical CT scan suggest that the proposed algorithm has the potential to reduce reconstruction time in multi-node systems, depending on the balance between compute speed and communication bandwidth.

Using a small number of sampling views during a CT (computed tomography) exam is a widely accepted technique for low-dose CT reconstruction, which reduces the risk of inducing cancer or other diseases in patients. In this scenario, total variation (TV) based compressed sensing (CS) methods, which uses a regularization term that penalizes the $\ell_{1}$ norm of the reconstructed image's gradient, outperform the traditional FBP (filtered back-projection) based algorithms in CT reconstruction. Furthermore, in order to reduce well-known artifacts (smoothed edges and texture details) favored by TV-based CS methods, several variants have been proposed, which, in a general context, can be understood as using a regularization term that approximates the $\ell_{0}$ norm of the reconstructed image's gradient. These type of methods yield state-of-the-art reconstruction results. In this paper we exploit a variant of the $\ell_{0}$ gradient minimization problem, which directly penalizes the number of non-zero gradients in the reconstructed image, and propose to solve the low-dose CT reconstruction problem. Extended experiments, based on the ASTRA toolbox, show that the propose method is faster (almost twice as fast) and delivers higher quality reconstructions than TV-based CS methods and alternatives that reduce smooth artifacts.

Computed tomography (CT) plays an increasingly important role in clinical diagnosis. However, in practical applications of CT, physical limitations on acquisition lead to some blind regions where data cannot be sampled. CT image reconstruction from limited-angle would enable a rapid scanning with a reduced x-ray dose delivered to the patient. As it is known, Generative Adversarial Networks (GAN) can keep the original information and details of the sample very well. In this paper, we propose an end-to-end Generative Adversarial Networks model used for removing artifacts from limited-angle CT reconstruction images. The proposed GAN is based on the conditional GAN with the joint loss function, which .can remove the artifacts while retaining the complete details and sharp edges. The intensity of reconstruction using the proposed method is very close to the full-view projective reconstructed image. Compared to several other classic methods, our GAN model shows better consequent, in terms of artifact reduction, feature preservation, and computational efficiency for limited-angle CT reconstruction.

Weighting methods have been widely used and achieved great success in filtered-backprojection (FBP) based CT reconstruction. However, the same weighting methods cooperated with derivative backprojection filtration (DBF) reconstruction usually produce unexpected streaking artifacts, leading in severe unevenness of images. This paper aims to suppress the streaking artifacts in weighted DBF reconstructions. From the analysis on the decomposition of the general form of weighted DBF reconstruction formula, we consider the streaking artifacts as an effect of the combination of the signum function and the derivative of weightings, based on which we extract the streaking artifacts from the raw images in three specific scan modes, i.e., half fan scan, short scan and multi-source scan. Mode-specific correction methods are then proposed to suppress streaking artifacts according to the different characteristics of each scan mode. Evaluation via simulation and phantom studies demonstrates that proposed methods effectively suppress streaking artifacts and smooth the unevenness of images without reducing the spatial resolution.

There is an increasing need to reconstruct objects in four or more dimensions corresponding to space, time and other independent parameters. The best 4D reconstruction algorithms use regularized iterative reconstruction approaches such as model based iterative reconstruction (MBIR), which depends critically on the quality of the prior modeling. Recently, Plug-and-Play methods have been shown to be an effective way to incorporate advanced prior models using state-of-the-art denoising algorithms designed to remove additive white Gaussian noise (AWGN). However, state-of-the-art denoising algorithms such as BM4D and deep convolutional neural networks (CNNs) are primarily available for 2D and sometimes 3D images. In particular, CNNs are difficult and computationally expensive to implement in four or more dimensions, and training may be impossible if there is no associated high-dimensional training data. In this paper, we present Multi-Slice Fusion, a novel algorithm for 4D and higher-dimensional reconstruction, based on the fusion of multiple low-dimensional denoisers. Our approach uses multi-agent consensus equilibrium (MACE), an extension of Plug-and-Play, as a framework for integrating the multiple lower-dimensional prior models. We apply our method to the problem of 4D cone-beam X-ray CT reconstruction for Non Destructive Evaluation (NDE) of moving parts. This is done by solving the MACE equations using lower-dimensional CNN denoisers implemented in parallel on a heterogeneous cluster. Results on experimental CT data demonstrate that Multi-Slice Fusion can substantially improve the quality of reconstructions relative to traditional 4D priors, while also being practical to implement and train., Comment: 8 pages, 8 figures, IEEE International Conference on Computational Photography 2019, Tokyo

Sparse-view computed tomography (CT) has attracted much attention to reduce the potential radiation risk. However, image reconstruction from insufficient data suffers from distortion. As a discrete form of Radon transform, Mojette transform is exactly invertible even with few samples based on discrete projection and reconstruction lattice. The goal of this paper is to apply Mojette transform to reconstruct images from few views in practice. Due to the fact that its acquisition is incompatible with physical X-ray properties, this paper resorts to deep learning technique to map Radon projection into Mojette domain. Experimental results confirm the effectiveness of the proposed reconstruction scheme based on Mojette transform.

This paper analyzes the principle of general CT reconstruction. By comparing and combining the FBP and ART reconstruction algorithms, an improved algorithm of direct solution for CT reconstruction is studied. It is on the base of back projection method and the result satisfies the ART algebraic equations. The method should be used to obtain accurate CT reconstruction results without any iteration. It is a direct solution method.

Low dose and sparse view CT are effective approaches to reduce the radiation dose and accelerate scan speed. Images reconstructed from insufficient data acquired from low dose and sparse view CT are associated with severe streaking artifacts. Therefore, reducing the radiation dose will further degrade the imaging quality. Several attempts have been made to remove these artifacts using deep learning methods such as CNN. Although the deep learning methods for low dose and sparse view CT reconstruction have gained impressive successes, the reconstruction results are still over-smooth. In this work, we propose an artifacts reduction method for low dose and sparse-view CT via a single model trained by generative adversarial networks (GAN). Several numerical simulation experiments are implemented to test the performance of our network. The results show that our GAN can significantly reduce the streaking atrifacts campared with FBP mehtod, and carries more detailed information than CNN.

Computer tomography (CT) has been widely used in medical industry for non-invasive reconstruction of the internal structure of human body. Despite the many benefits reaped from it, patients undergoing CT scans also receive large amount of hazardous x-ray radiations. However, lowering the radiation dose reduces the quality of CT image. The presented work focus on reducing the radiation dose through under-sampled CT reconstruction. This research work investigates the use of interpolation for mitigating the deficiency caused by angularly under-sampled projections. Different interpolation techniques were investigated and implemented using computer simulations.

Iterative image reconstruction algorithms have the potential to reduce the radiation dose in computed tomography (CT), but they are computationally intensive and their performance usually depends on careful parameter tuning. In this paper, we propose an iterative CT reconstruction algorithm based on the new class of variance-reduced stochastic gradient descent (VR-SGD) algorithms. Our experiments show that the proposed algorithm has a very fast convergence, while also eliminating the need for step size tuning. This study shows that VR-SGD can be used to devise very efficient iterative CT reconstruction algorithms.

The ℓ1 regularization problem has been widely used to solve the sparsity constrained problems. To enhance the sparsity constraint for better imaging performance, a promising direction is to use the ℓp norm (0 p minimization problem. Very recently, Xu et al. developed an analytic solution for the ℓ1/2 regularization via an iterative thresholding operation, which is also referred to as half-threshold filtering. In this paper, we design a simultaneous algebraic reconstruction technique (SART)-type half-threshold filtering framework to solve the computed tomography (CT) reconstruction problem. In the medical imaging filed, the discrete gradient transform (DGT) is widely used to define the sparsity. However, the DGT is noninvertible and it cannot be applied to half-threshold filtering for CT reconstruction. To demonstrate the utility of the proposed SART-type half-threshold filtering framework, an emphasis of this paper is to construct a pseudoinverse transforms for DGT. The proposed algorithms are evaluated with numerical and physical phantom data sets. Our results show that the SART-type half-threshold filtering algorithms have great potential to improve the reconstructed image quality from few and noisy projections. They are complementary to the counterparts of the state-of-the-art soft-threshold filtering and hard-threshold filtering.

Since exposure to ionizing radiation brought by X-rays is harmful to the human's health, the dose of X-rays in CT devices should be reduced as low as possible. However, that would degrade the reconstructed CT images greatly, especially when the number of projections is limited. Although some moment-based methods can improve the images reconstructed from limited-view projections, they resort to continuous image moments which can introduce numerical errors when they are applied to 2-D digital images. To reduce the effect of the numerical errors, this paper proposes a new limited-view CT reconstruction method based on discrete Krawtchouk moments which do not require the discrete approximation. By establishing relationship between discrete Krawtchouk projection moments and discrete Krawtchouk moments, it can estimate the unknown projections from the known ones. In this manner, the CT images reconstructed from limited-view projections can be improved further. The experimental results show that our method has good performance in limited-view CT reconstruction.

With computed tomography (CT) technology more and more widely used in clinical applications, low-dose CT arouses people's attention gradually. In this paper, we propose an adaptive low-dose CT reconstruction framework. This framework is based on the iterative algorithm, and tries to find the fewest projection angles adaptively insuring the image quality, achieves the goal of reducing the radiation dose at last. The simulation results show that this adaptive low-dose CT reconstruction framework can find the fewest projection angles adaptively according to the requirement of image quality.

This paper describes the use of Differential Cone-Beam algorithm to improve CT reconstruction resolution for enhanced visualization of semiconductor flip chip package defects. Results demonstrated improvements in CT reconstruction resolution and time.

The results of computer simulation of CT reconstruction for a system of point source - receiver plane and comparisons with existing methods of reconstruction used in third-generation scanners system have been provided. Obtained data show that the level of SNR in such a system is similar as for the third generation of scanners. Also, it is possible to reconstruct distributions not only in the plane perpendicular to the axis of rotation, but other planes without having to increase the dose for patient.

We systematically evaluate the performance of smoothing on several state-of-the-art sparsity prior CT reconstruction algorithms. State-of-the-art algorithms have been implemented and their performance analyzed with and without applying different smoothing filters. Aiming for successful reconstruction from less number of projections, sparsity prior reconstruction algorithms are found to be useful in CT, provided that the signal reconstruction is performed in a compressed domain (i.e. gradient or wavelet domain). The subject matter of this work is the investigation of the reconstruction performance variation with the application of a smoothing filter prior sparsifying transform. Experiments on simulated and real medical images show that the performance of the reconstruction algorithms vary, and smoothing before the sparsifying transform ensures better reconstruction.

Computed tomography (CT) reconstruction methods are often unaware of the requirements of the subsequent 3D volume visualization stage. In this stage, a delicate and often-studied component is the interpolation of off-grid samples, where aliasing can lead to misleading artifacts and blurring, potentially hiding fine details of critical importance. The visualization-aware CT reconstruction framework we describe aims to account for these errors directly in the volume generation stage. Our framework informs the CT reconstruction process of the specific filter intended for interpolation in the subsequent visualization process, and this in turn ensures an accurate interpolation there at a set tolerance. Here, we focus on fast trilinear interpolation in conjunction with an octree-type mixed resolution volume representation without T-junctions. Efficient rendering is achieved by a space-efficient and locality-optimized representation, which can straightforwardly exploit fast fixed-function pipelines on GPUs.

The model-based iterative reconstruction methods have recently found its popularity in X-ray CT reconstruction due to its ability in providing improved image quality (than analytical methods) especially in low-dose condition where it requires less radiation dose delivering through the patient body. However, the application of iterative methods in practice is still limited due to its expensive computation time. In particular, the iterative methods require time-consuming calculations for repeated projection and backprojection operations. This requirement is more severe in reconstruction from low-dose scan where more iterations are required to regularize the high noise due to low detected counts. While the computational speed of projection and backprojection has been dramatically increased by using GPUs (graphics processing units), efforts to improve the accuracy of modeling a projector-backprojector pair have been hindered by the needs for approximations to maximize the efficiency of the GPU. The unmatched projector-backprojector pairs often used for GPU-accelerated methods also cause additional errors in iterative reconstruction. For low-dose CT reconstruction, the degradation due to these errors becomes more significant as the number of iterations is increased. Despite the appearance of many recent advanced methods to perform projection and backprojection, the ray-tracing method (RTM) is still popular due to its accurate representation of the physics of the Beer's law as well as the ease of use. In this work, we propose a GPU-accelerated RTM. Unlike the previous works that used the RTM in forward projection and the pixel-driven method in backprojection, this work develops a new GPU-accelerated method for a RTM projector-backprojector pair which does not use any approximations for parallelizing the projection and backprojection. Since our method is exact, the results are as accurate as those obtained from the non-accelerated method.

We propose a method to improve spatial resolution in CT reconstruction. We show that the proposed method improves spatial resolution with both numerical simulations and real CT data, without side-effects of aliasing artifacts.

Computed tomography (CT) has evolved into an indispensable imaging method in clinical routine for a long time. It gives us high resolution, high contrast and non-invasive tomographic images in a brief scan time. However, their high radiation dose is an important issue to be solved in CT system development.

This paper introduces the Cph CT Toolbox - an open source collection of the most commonly used filtered back-projection algorithms for CT image reconstruction. The toolbox targets teaching, research and production environments providing simple codes for teaching and highly optimized codes for research and industrial applications. The toolbox has a flexible plugin infrastructure making it applicable to all existing CT systems using filtered back-projection reconstruction. The package is available online for download and modification under the GPLv2 license.

Inter- and intra-rater agreement in assessing Interstitial Pulmonary Fibrosis (IPF) on CT scans is poor. Lack of approaches to understand the nuances of CT reconstruction parameters and their effect on patient scans hampers objective IPF quantification. In this paper, we propose an image analytic methodology to characterize the relationship between CT reconstruction parameters and IPF manifestation in scans. The raw data acquired from a patient was reconstructed with a combination of image thickness, interval and reconstruction kernels to derive 104 datasets. Quantitative and qualitative analyses were performed on the regional statistics computed in the neighborhood of each parenchymal voxel and for expert-chosen regions of interest (ROIs). The proposed approach could facilitate the selection of optimal CT reconstruction parameters to more robustly quantify IPF.

In this paper we propose two novel image reconstruction methods for low-dose X-ray CT data. Both approaches are based on anisotropic sinogram smoothing coupled with sparse local image representation with respect to a learned overcomplete dictionary. The redundant dictionary is learned from normal-dose CT training images and encodes artifact-free image behavior. The methods differ in the details of how the redundant dictionary information is included. Efficient solution approaches to the new formulations are provided. Comparative results on simulated low-dose imagery are given. Our approach is new in how it applies learning-based dictionary techniques to low-dose CT reconstruction, in its use of high quality training data in dictionary generation, and in its incorporation of anisotropic sinogram constraints together with the dictionary-based representation.

Surgery planning often requires a precise evaluation of rigid-objects collisions and movements recently. A 3D CT reconstruction can be used to precisely and efficiently detect the virtual rigid objects for assurance and reliability analysis. The common methods of collision detection in computer graphics are developed only for general-purpose applications. The employment of such methods cannot handle the thighbone, which is commonly seen. In this paper, we present an efficiency collision detection scheme that takes advantage of the relative proximity. In order to optimize the collision detection among very-elongated rigid objects, a novel nearest-neighbor list method is proposed. This method is based on a bounding-oriented box. The Efficiency of our proposed algorithm is extensively tested before experimented various scenarios for method vilification.

In dental Cone-Beam CT reconstruction images, the metallic implants will cause apparent streak artifacts, which may seriously increase the difficulty of diagnosis. Here we present a new metal artifacts reducing method designed for our dental CBCT with a half-size detector. In our method, we first locate the positions of all the metallic implants in the three-dimensional space, and then the projection points of the metal positions will greatly simplify the segmentation and modification of the metal area in each projection image. This method is proved to be efficient and accurate by experimental results.

Reconstruction from only a limited number of projections is an important problem in medical imaging. In this paper, a novel kernel-based limited-view CT reconstruction method is proposed. First based on the classical FDK algorithm, we derive the reconstruction kernel. Then the FDK kernel is truncated to reduce the noises aroused by the oscillations of the kernel. And a novel anisotropic diffusion model is introduced to suppress the artifacts and noise. Finally, several reconstruction experiments are presented to verify the efficiency and accuracy of proposed method.

Reconstruction algorithm based on total variation (TV) minimization has become a hot topic in CT field. In order to make a better balance between suppressing noise and preserving edge, an improved variation is proposed in this paper. An anisotropic strategy is developed to effectively preserve the edges of imaging objects. Simultaneously, the unity weight in the original variation is substituted by an amplitude dependent weight to suppress the smaller variations, which arise from noise effect with a higher possibility. Numerical simulations validated that the CT reconstruction based on the improved variation has a better reconstruction performance as compared to its original counterpart.

We propose an algorithm to solve the problem of Time-Resolved Cardiac Computed Tomography (CT). The goal of the algorithm is to reconstruct a snapshot of the moving heart at any time instant from CT projection data acquired over a single heart-cycle. The object is modeled by a spatio-temporal state-space model which requires a nonlinear version of the Kalman Filter to assimilate the sequentially acquired projection data. Simulation results show that the nonlinear model overcomes shortcomings of the previously used linear model.

In this paper we present a new efficient framework that implements volumetric object detection for dual energy CT. First, we improve the original H-L curve table method with 28 elements, to get accurate material information by reconstruction. Then, we use the material information to localize suspicious regions and apply our volumetric object detection function. We reduce the dimension of the detection from 3D to 2D by using central slices, and use boosting 2d Haar features to achieve the 2D detection. Finally, we succeed in locating the target in our real world circumstance simulated baggage.

We constructed a preliminary tomographic imaging system using CW THz-source based on the concept of CT reconstruction with the projection angles limited. We demonstrate the feasibility using the paper phantom.

We propose an algorithm to solve the problem of Time-Resolved Cardiac Computed Tomography (CT). The algorithm reconstructs a snapshot of the moving heart at any time instant from CT projection data acquired over a single heart-cycle. The object is modeled by a spatio-temporal state-space model, and an ensemble Kalman Filter (a Monte-Carlo approximation to the Kalman filter) is used to assimilate the sequentially acquired projection data. Simulation results of the dynamic NCAT cardiac phantom, under the fan-beam geometry and a two-source CT system, show reconstructions that are free of the motion artifacts that mar conventional methods.

The aim of present work is application of novel single photon counting system for detection of gamma-rays in CT using semiconductor radiation detector based on semi-insulating (SI) GaAs compound. A simple positioning test system consisting of two stepper motors with 241 Am gamma source of 60 keV photons and single SI GaAs radiation detector operated in single photon counting mode is used for taking CT projections. First, rather preliminary results of CT reconstruction applied to imaging of inner structure of a small phantom using developed reconstruction algorithms is demonstrated

The geometrical properties of saddle-trajectories are studied based on the requirements of possible CT reconstruction algorithms. Besides the standard saddle we introduce the so-called high-frequency saddle. The study focuses on Pi-lines. First, we illustrate the volume, which is covered by Pi-lines. Furthermore, we discuss, how the number of Pi-lines varies over the volume of object-points, and we analyze the detector utilization of a saddle-scan.

We examined the impact of several CT reconstruction approaches on image noise and spatial resolution. Reconstructions were performed using filtered backprojection (FBP) with ramp and low pass filters, weighted least squares (WLS) iterative reconstruction (IR) with ordered subsets and post-smoothing, and penalized weighted least squares (PWLS) IR with ordered subsets using a generalized Geman prior, varying the exponent and the strength of the prior. The results show that WLS could have a significant noise-resolution benefit relative to FBP, depending on the object and the corresponding statistics of the measurements. The use of priors (PWLS) can further reduce the image noise compared to non-penalized WLS. The spatial resolution is very well preserved for larger contrasts/edges and for larger values of n, but the performance is more comparable to FBP for smaller contrasts/edges and for smaller values of n. Penalized IR has the potential of improving spatial resolution and reducing image noise when compared to post-smoothed non-penalized IR and FBP.

An X-ray MicroCT system with high spatial resolution for imaging of small animals has been developed and characterized. In the future, this system will be combined with a high resolution SPECT system under development and will also serve as a source of data for the evaluation and development of 3D volume CT reconstruction algorithms. This system is comprised of an X-ray source, phosphor-CCD detector and motor-driven positioning stages. The major components of this system, the geometric calibration, the time response of the X-ray power supply and the measured contrast resolution are discussed. Finally, we present images of a mouse.

Reprojection is the process by which projections are produced from an image such that, if these projections are reconstructed, they yield the original image. Because of the computational expense of reprojection, algorithms that employ this process have never been widely used. We present three techniques to speed up reprojection. The methods either exploit hardware already present in commercial CT scanners or the fact that reprojections can be of lower bandwidth than the original projections. We will also show how the reprojections can be used to correct for the presence of metal and for beam hardening artifacts.

Several approaches have been proposed to speed-up the back-projection part of CT image reconstruction. In this paper, two methods of simplifying respectively the data pre-processing and filtering steps are introduced. Both methods rely on the projection data redundancy that is shown to exist from view-to-view in X-ray CT. For the pre-processing step, and for a given view, the input of pre-processing is divided into the output to form a linearization vector. Such linearization vectors for views i and k are applied (with regularization) to estimate intermediate pre-processed views j, i