Bilateral Weighted Relative Total Variation for Low-Dose CT Reconstruction.

Low-dose computed tomography (LDCT) has been widely used for various clinic applications to reduce the X-ray dose absorbed by patients. However, LDCT is usually degraded by severe noise over the image space. The image quality of LDCT has attracted aroused attentions of scholars. In this study, we propose the bilateral weighted relative total variation (BRTV) used for image restoration to simultaneously maintain edges and further reduce noise, then propose the BRTV-regularized projections onto convex sets (POCS-BRTV) model for LDCT reconstruction. Referring to the spacial closeness and the similarity of gray value between two pixels in a local rectangle, POCS-BRTV can adaptively extract sharp edges and minor details during the iterative reconstruction process. Evaluation indexes and visual effects are used to measure the performances among different algorithms. Experimental results indicate that the proposed POCS-BRTV model can achieve superior image quality than the compared algorithms in terms of the structure and texture preservation.

Structure-guided computed tomography reconstruction from limited-angle projections.

Limited-angle computed tomography (CT) imaging is one of the common imaging problems. The reconstructed images often encounter obvious artifacts and structure degradation. In recent years, the recoverability prior of image structure has been widely explored in limited-angle CT reconstruction, and the image quality has been greatly improved. However, the artifacts and structure degradation still exist. In this study, we establish a new reconstruction model based on weighted relative structure (wRS) determined by image gradients, which serves as weights to guide image reconstruction in order to reduce artifacts and preserve structures. Then, we develop an efficient algorithm using a surrogate function to solve this model. Moreover, this method is compared with some of other popular reconstruction methods, such as anisotropic total variation method and image gradient L0 norm minimization method and so on. Experiments on digital phantoms, real carved cheese and walnut projection are reported to demonstrate its superiority. Several quantitative indices including RMSE, PSNR, and SSIM of the reconstruction images from 90°-data of FORBILD head phantom are 0.0120, 43.52, and 0.9961. The experimental results indicate that the image obtained by our method is the closest to reference image. By comparing reconstruction images or their residual images, images reconstructed from real CT data, the experimental results of the residual images and the respective quantitative data analysis also demonstrate that the images reconstructed using our new method suffer from less artifacts and structure degradation.

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.

Exterior computed tomography image reconstruction based on anisotropic relative total variation in polar coordinates.

In computed tomography (CT) image reconstruction problems, exterior CT is an important application in industrial non-destructive testing (NDT). Different from the limited-angle problem that misses part of the rotation angle, the rotation angle of the exterior problem is complete, but for each rotation angle, the projection data through the central region of the object cannot be collected, so that the exterior CT problem is ill-posed inverse problem. The results of traditional reconstruction methods like filtered back-projection (FBP) and simultaneous algebra reconstruction technique (SART) have artifacts along the radial direction edges for exterior CT reconstruction. In this study, we propose and test an anisotropic relative total variation in polar coordinates (P-ARTV) model for addressing the exterior CT problem. Since relative total variation (RTV) can effectively distinguish edges from noises, and P-ARTV with different weights in radial and tangential directions can effectively enhance radial edges, a two-step iteration algorithm was developed to solve the P-ARTV model in this study. The fidelity term and the regularization term are solved in Cartesian and polar coordinate systems, respectively. Numerical experiments show that our new model yields better performance than the existing state-of-the-art algorithms.

Anisotropic structure property based image reconstruction method for limited-angle computed tomography.

Limited-angle computed tomography (CT) may appear in restricted CT scans. Since the available projection data is incomplete, the images reconstructed by filtered back-projection (FBP) or algebraic reconstruction technique (ART) often encounter shading artifacts. However, using the anisotropy property of the shading artifacts that coincide with the characteristic of limited-angle CT images can reduce the shading artifacts. Considering this concept, we combine the anisotropy property of the shading artifacts with the anisotropic structure property of an image to develop a new algorithm for image reconstruction. Specifically, we propose an image reconstruction method based on adaptive weighted anisotropic total variation (AwATV). This method, termed as AwATV method for short, is designed to preserve image structures and then remove the shading artifacts. It characterizes both of above properties. The anisotropy property of the shading artifacts accounts for reducing artifacts, and the anisotropic structure property of an image accounts for preserving structures. In order to evaluate the performance of AwATV, we use the simulation projection data of FORBILD head phantom and real CT data for image reconstruction. Experimental results show that AwATV can always reconstruct images with higher SSIM and PSNR, and smaller RMSE, which means that AwATV enables to reconstruct images with higher quality in term of artifact reduction and structure preservation.

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.

Geometric artifacts reduction for cone-beam CT via L0-norm minimization without dedicated phantoms.

For cone-beam computed tomography (CBCT), transversal shifts of the rotation center exist inevitably, which will result in geometric artifacts in CT images. In this work, we propose a novel geometric calibration method for CBCT, which can also be used in micro-CT. The symmetry property of the sinogram is used for the first calibration, and then L0-norm of the gradient image from the reconstructed image is used as the cost function to be minimized for the second calibration. An iterative search method is adopted to pursue the local minimum of the L0-norm minimization problem. The transversal shift value is updated with affirmatory step size within a search range determined by the first calibration. In addition, graphic processing unit (GPU)-based FDK algorithm and acceleration techniques are designed to accelerate the calibration process of the presented new method. In simulation experiments, the mean absolute difference (MAD) and the standard deviation (SD) of the transversal shift value were less than 0.2 pixels between the noise-free and noisy projection images, which indicated highly accurate calibration applying the new calibration method. In real data experiments, the smaller entropies of the corrected images also indicated that higher resolution image was acquired using the corrected projection data and the textures were well protected. Study results also support the feasibility of applying the proposed method to other imaging modalities.

Swinging multi-source industrial CT systems for aperiodic dynamic imaging.

The goal of this paper is to develop a new architecture for industrial computed tomography (ICT) aiming at dynamically imaging an aperiodic changing object. We propose a data acquisition approach with multiple x-ray source/detector pairs targeting a continuously changeable object with corresponding timeframes. In this named swinging multi-source CT (SMCT) structure, each source and its associated detector swing forth and back within a certain angle for CT scanning. In the SMCT system design, we utilize a circular journal bearing based setup to replace the normal CT slip ring by weakening the scanning speed requirement. Inspired by the prior image constrained compressed sensing (PICCS) algorithm, we apply a modified PICCS algorithm for the SMCT (SM-PICCS). Our numerical simulation and realistic specimen experiment studies demonstrate the feasibility of the proposed approach.

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.

Noise suppression-guided image filtering for low-SNR CT reconstruction.

In practical computed tomography (CT) applications, projections with low signal-to-noise ratio (SNR) are often encountered due to the reduction of radiation dose or device limitations. In these situations, classical reconstruction algorithms, like simultaneous algebraic reconstruction technique (SART), cannot reconstruct high-quality CT images. Block-matching and 3D filtering (BM3D)-based iterative reconstruction algorithm (POCS-BM3D) has remarkable effect in dealing with CT reconstruction from noisy projections. However, BM3D may restrain noise with excessive loss of details in the case of low-SNR CT reconstruction. In order to achieve a preferable trade-off between noise suppression and edge preservation, we introduce guided image filtering (GIF) into low-SNR CT reconstruction, and propose noise suppression-guided image filtering reconstruction (NSGIFR) algorithm. In each iteration of NSGIFR, the output image of SART reserves more details and is used as input image of GIF, while the image denoised by BM3D serves as guidance image of GIF. Experimental results indicate that the proposed algorithm displays outstanding performance on preserving structures and suppressing noise for low-SNR CT reconstruction. NSGIFR can achieve more superior image quality than SART, POCS-TV and POCS-BM3D in terms of visual effect and quantitative analysis. Graphical abstract Block-matching and 3D filtering (BM3D)-based iterative reconstruction algorithm (POCS-BM3D) has remarkable effect in dealing with CT reconstruction from noisy projections. However, BM3D may restrain noise with excessive loss of details in the case of low-SNR CT reconstruction. In order to achieve a preferable trade-off between noise suppression and edge preservation, we introduce guided image filtering (GIF) into low-SNR CT reconstruction, and propose noise suppression-guided image filtering reconstruction (NSGIFR) algorithm.

Design and Simulation Study of a CNT-Based Multisource Cubical CT System for Dynamic Objects.

The purpose of this paper is to design and simulate a new computed tomography (CT) system with a high temporal resolution for dynamic objects. We propose a multisource cubical CT (MCCT) system with X-ray tubes and detectors installed on a cube. Carbon nanotube- (CNT-) based X-ray focal spots are distributed on the twelve edges of the cube. The distribution of X-ray focal spots and detectors completely avoids mechanical movements to scan an object under inspection. CNTs are excellent electron field emitters because the use of a "cold" cathode makes it possible to fabricate a cathode with multiple electron emission points, and the CNT-based X-ray focal spots possess little response time and programmable emission. The proposed rotation-free MCCT system can acquire a high scanning speed when using a high frame rate detector. A three-dimensional (3D) reconstruction algorithm with tensor framelet-based L0-norm (TF-L0) minimization is developed for the simulation study of the MCCT. Simulation experiment results demonstrate the feasibility of the MCCT system.

Multiple limited-angles computed tomography reconstruction based on multi-direction total variation minimization.

Accurate computed tomography (CT) reconstruction from incomplete projections is an important research topic. Sparse sampling and limited-angle sampling are two effective ways to reduce the X-ray radiation dose or the scanning time. However, it is technically complicated to realize sparse sampling in medical CT since the tube power or the pre-patient collimator is difficult to be switched frequently. Limited-angle sampling makes it difficult to reconstruct an accurate image. The developed multiple limited-angles (MLA) sampling scheme could well balance the technical implementation complexity and the CT reconstruction difficulty. It does not require frequent switching of the tube power or the pre-patient collimator. The data correlation of the acquired projections is lower than that in limited-angle sampling. Using the projections acquired by MLA sampling, CT images reconstructed by the total variation minimization (TVM) method suffer from shading artifacts. Because the artifacts are distributed in several fixed directions, the artifact-suppression reconstruction model based on multi-direction total variation was designed for MLA CT reconstruction in this work. The multi-direction total variation minimization (MDTVM) was utilized to solve the optimization model. Experiments on digital phantoms and real projections indicated that MDTVM can better suppress the shading artifacts than TVM.

An electron beam linear scanning mode for industrial limited-angle nano-computed tomography.

Nano-computed tomography (nano-CT), which utilizes X-rays to research the inner structure of some small objects and has been widely utilized in biomedical research, electronic technology, geology, material sciences, etc., is a high spatial resolution and non-destructive research technique. A traditional nano-CT scanning model with a very high mechanical precision and stability of object manipulator, which is difficult to reach when the scanned object is continuously rotated, is required for high resolution imaging. To reduce the scanning time and attain a stable and high resolution imaging in industrial non-destructive testing, we study an electron beam linear scanning mode of nano-CT system that can avoid mechanical vibration and object movement caused by the continuously rotated object. Furthermore, to further save the scanning time and study how small the scanning range could be considered with acceptable spatial resolution, an alternating iterative algorithm based on ℓ0 minimization is utilized to limited-angle nano-CT reconstruction problem with the electron beam linear scanning mode. The experimental results confirm the feasibility of the electron beam linear scanning mode of nano-CT system.