A dual-energy CT reconstruction method based on anchor network from dual quarter scans.

Compared with conventional single-energy computed tomography (CT), dual-energy CT (DECT) provides better material differentiation but most DECT imaging systems require dual full-angle projection data at different X-ray spectra. Relaxing the requirement of data acquisition is an attractive research to promote the applications of DECT in wide range areas and reduce the radiation dose as low as reasonably achievable. In this work, we design a novel DECT imaging scheme with dual quarter scans and propose an efficient method to reconstruct the desired DECT images from the dual limited-angle projection data. We first study the characteristics of limited-angle artifacts under dual quarter scans scheme, and find that the negative and positive artifacts of DECT images are complementarily distributed in image domain because the corresponding X-rays of high- and low-energy scans are symmetric. Inspired by this finding, a fusion CT image is generated by integrating the limited-angle DECT images of dual quarter scans. This strategy enhances the true image information and suppresses the limited-angle artifacts, thereby restoring the image edges and inner structures. Utilizing the capability of neural network in the modeling of nonlinear problem, a novel Anchor network with single-entry double-out architecture is designed in this work to yield the desired DECT images from the generated fusion CT image. Experimental results on the simulated and real data verify the effectiveness of the proposed method. This work enables DECT on imaging configurations with half-scan and largely reduces scanning angles and radiation doses.

Nitrogen-doped carbon dots as a fluorescent probe for the highly sensitive detection of bilirubin and cell imaging.

Nitrogen-doped carbon dots (NCDs) with bright blue fluorescence were constructed by a hydrothermal method using sucrose and l-proline as raw materials. The NCDs were characterized by transmitted electron microscopy, X-ray diffraction, Fourier-transform infrared spectrometry, X-ray photoelectron spectroscopy, and ultraviolet-visible absorption and fluorescence spectroscopy to investigate the morphology, elemental composition, and optical properties. The NCDs had good water solubility, high dispersibility with an average diameter of only 1.7 nm, and satisfactory optical properties with a fluorescence quantum yield of 23.4%. The NCDs were employed for the detection of bilirubin. A good linear response of the NCDs in the range 0.35-9.78 µM was obtained for bilirubin with a detection limit of 33 nM. The NCDs were also applied to the analysis of real samples, serum and urine, with a recovery of 95.34% to 104.66%. The low cytotoxicity and good biocompatibility of the NCDs were indicated by an MTT assay and cell imaging of HeLa cells. Compared with other detection systems, using NCDs for bilirubin detection was a facile and efficient method with good selectivity and sensitivity.

An effective sinogram inpainting for complementary limited-angle dual-energy computed tomography imaging using generative adversarial networks.

Dual-energy computed tomography (DECT) provides more anatomical and functional information for image diagnosis. Presently, the popular DECT imaging systems need to scan at least full angle (i.e., 360°). In this study, we propose a DECT using complementary limited-angle scan (DECT-CL) technology to reduce the radiation dose and compress the spatial distribution of the imaging system. The dual-energy total scan is 180°, where the low- and high-energy scan range is the first 90° and last 90°, respectively. We describe this dual limited-angle problem as a complementary limited-angle problem, which is challenging to obtain high-quality images using traditional reconstruction algorithms. Furthermore, a complementary-sinogram-inpainting generative adversarial networks (CSI-GAN) with a sinogram loss is proposed to inpainting sinogram to suppress the singularity of truncated sinogram. The sinogram loss focuses on the data distribution of the generated sinogram while approaching the target sinogram. We use the simultaneous algebraic reconstruction technique namely, a total variable (SART-TV) algorithms for image reconstruction. Then, taking reconstructed CT images of pleural and cranial cavity slices as examples, we evaluate the performance of our method and numerically compare different methods based on root mean square error (RMSE), peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). Compared with traditional algorithms, the proposed network shows advantages in numerical terms. Compared with Patch-GAN, the proposed network can also reduce the RMSE of the reconstruction results by an average of 40% and increase the PSNR by an average of 26%. In conclusion, both qualitative and quantitative comparison and analysis demonstrate that our proposed method achieves a good artifact suppression effect and can suitably solve the complementary limited-angle problem.

Promising Generative Adversarial Network Based Sinogram Inpainting Method for Ultra-Limited-Angle Computed Tomography Imaging.

Limited-angle computed tomography (CT) image reconstruction is a challenging problem in the field of CT imaging. In some special applications, limited by the geometric space and mechanical structure of the imaging system, projections can only be collected with a scanning range of less than 90°. We call this kind of serious limited-angle problem the ultra-limited-angle problem, which is difficult to effectively alleviate by traditional iterative reconstruction algorithms. With the development of deep learning, the generative adversarial network (GAN) performs well in image inpainting tasks and can add effective image information to restore missing parts of an image. In this study, given the characteristic of GAN to generate missing information, the sinogram-inpainting-GAN (SI-GAN) is proposed to restore missing sinogram data to suppress the singularity of the truncated sinogram for ultra-limited-angle reconstruction. We propose the U-Net generator and patch-design discriminator in SI-GAN to make the network suitable for standard medical CT images. Furthermore, we propose a joint projection domain and image domain loss function, in which the weighted image domain loss can be added by the back-projection operation. Then, by inputting a paired limited-angle/180° sinogram into the network for training, we can obtain the trained model, which has extracted the continuity feature of sinogram data. Finally, the classic CT reconstruction method is used to reconstruct the images after obtaining the estimated sinograms. The simulation studies and actual data experiments indicate that the proposed method performed well to reduce the serious artifacts caused by ultra-limited-angle scanning.

Efficient solving algorithm for determining the exact sampling condition of limited-angle computed tomography reconstruction.

Total variation (TV) regularization-based iterative reconstruction algorithms have an impressive potential to solve limited-angle computed tomography with insufficient sampling projections. The analysis of exact reconstruction sampling conditions for a TV-minimization reconstruction model can determine the minimum number of scanning angle and minimize the scanning range. However, the large-scale matrix operations caused by increased testing phantom size are the computation bottleneck in determining the exact reconstruction sampling conditions in practice. When the size of the testing phantom increases to a certain scale, it is very difficult to analyze quantitatively the exact reconstruction sampling condition using existing methods. In this paper, we propose a fast and efficient algorithm to determine the exact reconstruction sampling condition for large phantoms. Specifically, the sampling condition of a TV minimization model is modeled as a convex optimization problem, which is derived from the sufficient and necessary condition of solution uniqueness for the L1 minimization model. An effective alternating direction minimization algorithm is developed to optimize the objective function by alternatively solving two sub-problems split from the convex problem. The Cholesky decomposition method is used in solving the first sub-problem to reduce computational complexity. Experimental results show that the proposed method can efficiently solve the verification problem of the accurate reconstruction sampling condition. Furthermore, we obtain the lower bounds of scanning angle range for the exact reconstruction of a specific phantom with the larger size.

Joint regularization-based image reconstruction by combining data-driven tight frame and total variation for low-dose computed tomography.

Since the excessive radiation dose may induce potential body lesion, the low-dose computed tomography (LDCT) is widely applied for clinical diagnosis and treatment. However, the dose reduction will inevitably cause severe noise and degrade image quality. Most state-of-the-art methods utilize a pre-determined regularizer to account for the prior images, which may be insufficient for the most images acquired in the clinical practice. This study proposed and investigated a joint regularization method combining a data-driven tight frame and total variation (DDTF-TV) to solve this problem. Unlike the existing methods that designed pre-determined sparse transform for image domain, data-driven regularizer introduced a learning strategy to adaptively and iteratively update the framelets of DDTF, which can preferably recover the detailed image structures. The other regularizer, TV term can reconstruct strong edges and suppress noise. The joint term, DDTF-TV, collaboratively affect detail preservation and noise suppression. The proposed new model was efficiently solved by alternating the direction method of the multipliers. Qualitative and quantitative evaluations were carried out in simulation and real data experiments to demonstrate superiority of the proposed DDTF-TV method. Both visual inspection and numerical accuracy analysis show the potential of the proposed method for improving image quality of the LDCT.

Optimization-based image reconstruction in computed tomography by alternating direction method with ordered subsets.

Nowadays, diversities of task-specific applications for computed tomography (CT) have already proposed multiple challenges for algorithm design of image reconstructions. Consequently, efficient algorithm design tool is necessary to be established. A fast and efficient algorithm design framework for CT image reconstruction, which is based on alternating direction method (ADM) with ordered subsets (OS), is proposed, termed as OS-ADM. The general ideas of ADM and OS have been abstractly introduced and then they are combined for solving convex optimizations in CT image reconstruction. Standard procedures are concluded for algorithm design which contain 1) model mapping, 2) sub-problem dividing and 3) solving, 4) OS level setting and 5) algorithm evaluation. Typical reconstruction problems are modeled as convex optimizations, including (non-negative) least-square, constrained L1 minimization, constrained total variation (TV) minimization and TV minimizations with different data fidelity terms. Efficient working algorithms for these problems are derived with detailed derivations by the proposed framework. In addition, both simulations and real CT projections are tested to verify the performances of two TV-based algorithms. Experimental investigations indicate that these algorithms are of the state-of-the-art performances. The algorithm instances show that the proposed OS-ADM framework is promising for practical applications.

A multifunctional chitosan composite aerogel for PPCPs adsorption.

Pharmaceuticals and personal care products (PPCPs) are gaining attention due to their persistence in the environment. Therefore, the development of novel adsorbents to remove them is strongly anticipated. In this study, an improved dual ice-template assembly method had been used for the preparation of ZIF-67/QGO/SB-CS aerogel through ZIF-67, benzoquinone-modified graphene oxide (QGO), and sulfobetaine-modified chitosan (SB-CS) for the adsorption and removal of PPCPs in water. We reported for the first time that the chitosan composite aerogel has antifouling, bacterial filtration and oil-water separation abilities with excellent PPCPs adsorption performance and reusable, which would be a viable option for long-lasting adsorbents for PPCPs in water.

Preparation of chitosan crosslinked with metal-organic framework (MOF-199)@aminated graphene oxide aerogel for the adsorption of formaldehyde gas and methyl orange.

Chitosan crosslinked with metal-organic framework (MOF-199)@aminated graphene oxide aerogel (MOF-199@AFGO/CS) were prepared to adsorb formaldehyde and methyl orange. The prepared MOF-199@AFGO/CS aerogel was well characterized via SEM, EDX, FT-IR, XRD and XPS to reveal the microstructure and composition. Besides, the mechanical property and the stability of MOF-199@AFGO/CS aerogel were investigated. The results showed that MOF-199@AFGO/CS aerogel had good stability in water, compression resilience and thermostability. The study on the ability to adsorb formaldehyde gas and methyl orange showed that the adsorption capacity of MOF-199@AFGO/CS aerogel was related to the pore size and the surface functional groups of MOF-199@AFGO/CS aerogel. When the pore size is moderate, as the amino group and MOF-199 on the aerogel increased, the adsorption capacity of formaldehyde gas (197.89 mg/g) and methyl orange (412 mg/g) can reach the maximum. Furthermore, the adsorption process at equilibrium followed the Freundlich isotherm model. The kinetic behavior was well fitted by the pseudo-second-order model, indicating chemisorption as the rate-determining step. This work can provide a reliable basis for the adsorbent to remove pollutants in different forms at the same time, and has potential application in simultaneously adsorbing liquid pollutants and gas pollutants.

Multi-segment spectral reconstruction via zero-value set prior.

Most scanning schemes of multi-energy computed tomography (MECT) require multiple sets of full-scan measurements under different x-ray spectra, which limits the application of MECT with incomplete scan. To handle this problem, a flexible MECT scanning strategy is proposed in this paper, which divides one half scan into three curves. Also, a novel MECT reconstruction algorithm is developed to relax the requirement of data acquisition of MECT. For MECT, gradient images of CT images at different energies ideally share the same position of zero-value set (Pos-OS) for the same object. Based on this observation, the characteristics of limited-angle artifacts is first explored, and it is found that the limited-angle artifacts in the image domain are closely related to the angle trajectory of the scan. Inspired by this discovery, the Pos-OS of the gradient image from the fusion CT image is extracted, and it is incorporated as prior knowledge into the TV minimization model in the form of equality constraints. The alternating direction method is exploited to solve the improved optimization model iteratively. Based on this, the proposed algorithm is derived to eliminate the limited angle artifacts in the image domain.The experimental results show that the proposed method achieves higher reconstruction quality under the designed scanning configuration than other methods in the literature.

Generative adversarial network-based sinogram super-resolution for computed tomography imaging.

Compared with the conventional 1×1 acquisition mode of projection in computed tomography (CT) image reconstruction, the 2×2 acquisition mode improves the collection efficiency of the projection and reduces the x-ray exposure time. However, the collected projection based on the 2×2 acquisition mode has low resolution (LR) and the reconstructed image quality is poor, thus limiting the use of this mode in CT imaging systems. In this study, a novel sinogram-super-resolution (SR) generative adversarial network model is proposed to obtain high-resolution (HR) sinograms from LR sinograms, thereby improving the reconstruction image quality under the 2×2 acquisition mode. The proposed generator is based on the residual network for LR sinogram feature extraction and SR sinogram generation. A relativistic discriminator is designed to render the network capable of obtaining more realistic SR sinograms. Moreover, we combine the cycle consistency loss, sinogram domain loss, and reconstruction image domain loss in the total loss function to supervise SR sinogram generation. Then, a trained model can be obtained by inputting the paired LR/HR sinograms into the network. Finally, the classic filtered-back-projection reconstruction algorithm is used for CT image reconstruction based on the generated SR sinogram. The qualitative and quantitative results of evaluations on digital and real data illustrate that the proposed model not only obtains clean SR sinograms from noisy LR sinograms but also outperforms its counterparts.

Reconstruction method for DECT with one half-scan plus a second limited-angle scan using prior knowledge of complementary support set (Pri-CSS).

Dual-energy computed tomography (DECT) has capability to improve material differentiation, but most scanning schemes require two sets of full-scan measurements at different x-ray spectra, limiting its application to imaging system with incomplete scan. In this study, using one half-scan and a second limited-angle scan, we propose a DECT reconstruction method by exploiting the consistent information of gradient images at high- and low-energy spectra, which relaxes the requirement of data acquisition of DECT. Based on the theory of sampling condition analysis, the complementary support set of gradient images plays an important role in image reconstruction because it constitutes the sufficient and necessary condition for accurate CT reconstruction. For DECT, the gradient images of high- and low-energy CT images ideally share the same complementary support set for the same object. Inspired by this idea, we extract the prior knowledge of complementary support set (Pri-CSS) from the gradient image of the first half-scan CT image to promote the second limited-angle CT reconstruction. Pri-CSS will be incorporated into total variation regularization model in the form of constrains. Alternative direction method is applied to iteratively solve the modified optimization model, thereby deriving the proposed algorithm to recover low-energy CT image from limited-angle measurements. The qualitative and quantitative experiments on digital and real data are performed to validate the proposed method. The results show that the proposed method outperforms its counterparts and achieve high reconstruction quality for the designed scanning configuration.

Fabrication of green poly(vinyl alcohol) nanofibers using natural deep eutectic solvent for fast-dissolving drug delivery.

Fast-dissolving drug delivery systems are essential to drug delivery owing to the enhanced drug solubility, controlled drug concentration, target and rapid drug delivery. In this study, we developed fast-dissolving drug delivery systems using honey and acetylsalicylic acid-embedded poly(vinyl alcohol) (PVA) nanofibers based on natural deep eutectic solvent (DES). The efficacy of our fast-dissolving drug delivery system was tested by incorporating honey and acetylsalicylic acid in the PVA nanofibers. Firstly, the morphology and structure of the functional PVA-DES nanofibers (PVA-DES-honey and PVA-DES-ASA) were observed and analyzed, which proved the successful preparation of functional PVA-DES nanofibers. NIH/3T3 and HepG2 cells incubated on the nanofiber had more than 90% of cell viability, suggesting our materials were biocompatible and non-toxic. The nanofiber materials dissolved rapidly in artificial saliva solutions, suggesting potential use of our materials for fast dissolving drug delivery in oral cavities. The honey incorporated PVA nanofiber (PVA-DES-honey) showed a total bacterial reduction of 37.0% and 37.9% against E. coli and S. aureus, respectively, after 6 hour incubation in bacterial cultures. Furthermore, in vivo study proved that the PVA-DES-honey nanofibers accelerated the wound healing process, and they improved the wound healing rate on rat skin to 85.2% after 6 days of surgery, when compared to the control PVA (68.2%) and PVA-DES (76.3%) nanofibers. Overall, the nanofiber materials reported in our study showed potential as a green and biocompatible fast-dissolving drug delivery system and can be used for pharmaceutical fields, such as antibacterial wound dressing and oral ulcer stickers.

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

BACKGROUND: Multi-energy computed tomography (MECT) based on a photon-counting detector is an emerging imaging modality that collects projections at several energy bins with a single scan. However, the limited number of photons collected into the divided, narrow energy bins results in high quantum noise levels in reconstructed images. This study aims to improve MECT image quality by minimizing noise levels while retaining image details. METHODS: A novel MECT reconstruction method was proposed by exploiting the nonlocal tensor similarity among interchannel images and spatial sparsity in single-channel images. Similar patches were initially extracted from the interchannel images in spectral and spatial domains, then stacked into a new three-order tensor. Intrinsic tensor sparsity regularization that combined the Tuker and canonical polyadic (CP) low-rank decomposition techniques were applied to exploit the nonlocal similarity of the formulated tensor. Spatial sparsity in single-channel images was modeled by total variation (TV) regularization that utilizes the compressibility of gradient image. A new MECT reconstruction model was established by simultaneously incorporating the intrinsic tensor sparsity and TV regularizations. The iterative alternating minimization method was utilized to solve the reconstruction model based on a flexible framework. RESULTS: The proposed method was applied to the digital phantom and real mouse data to assess its feasibility and reliability. The reconstruction and decomposition results in the mouse data were encouraging and demonstrated the ability of the proposed method in noise suppression while preserving image details, not observed with other methods. Imaging data from the digital phantom illustrated this method as achieving the best intuitive reconstruction and decomposition results among all compared methods. They reduced the root mean square error (RMSE) by 89.75%, 50.75%, and 36.54% on the reconstructed images compared with analytic, TV-based, and tensor-based methods, respectively. This phenomenon was also observed with decomposition results, where the RMSE was also reduced by 97.96%, 67.74%, 72.05%, respectively. CONCLUSIONS: In this study, we proposed a reconstruction method for photon counting detector-based MECT, using the intrinsic tensor sparsity and TV regularizations. Improvements in noise suppression and detail preservation in the digital phantom and real mouse data were validated by the qualitative and quantitative evaluations on the reconstruction and decomposition results, verifying the potential of the proposed method in MECT reconstruction.

Image domain dual material decomposition for dual-energy CT using butterfly network.

PURPOSE: Dual-energy CT (DECT) has been increasingly used in imaging applications because of its capability for material differentiation. However, material decomposition suffers from magnified noise from two CT images of independent scans, leading to severe degradation of image quality. Existing algorithms exhibit suboptimal decomposition performance because they fail to fully depict the mapping relationship between DECT images and basis materials under noisy conditions. Convolutional neural network exhibits great promise in the modeling of data coupling and has recently become an important technique in medical imaging application. Inspired by its impressive potential, we developed a new Butterfly network to perform the image domain dual material decomposition. METHODS: The Butterfly network is derived from the model of image domain DECT decomposition by exploring the geometric relationship between the mapping functions of the data model and network components. The network is designed as the double-entry double-out crossover architecture based on the decomposition formulation. It enters a pair of dual-energy images as inputs and defines the ground true decomposed images as each label. The crossover architecture, which plays an important role in material decomposition, is designed to implement the information exchange between the two material generation pathways in the network. The proposed network is further applied on the digital phantom and clinical data to evaluate its performance. RESULTS: The qualitative and quantitative evaluations of the material decomposition of digital phantoms and clinical data indicate that the proposed network outperforms its counterparts. For the digital phantom, the proposed network reduces the standard deviation (SD) of noise in tissue, bone, and mixture regions by an average of 95.75% and 86.58% compared with the direct matrix inversion and the conventional iterative method, respectively. The line profiles and image biases of the decomposition results of digital phantom indicate that the proposed network provides the decomposition results closest to the ground truth. The proposed network reduces the SD of the noise in decomposed images of clinical head data by over 90% and 80% compared with the direct matrix inversion and conventional iterative method, respectively. As the modulation transfer function decreases to 50%, the proposed network increases the spatial resolution by average factors of 1.34 and 1.17 compared with the direct matrix inversion and conventional iterative methods, respectively. The proposed network is further applied to the clinical abdomen data. Among the three methods, the proposed method received the highest score from six radiologists in the visual inspection of noise suppression in the clinical data. CONCLUSIONS: We develop a model-based Butterfly network to perform image domain material decomposition for DECT. The decomposition results of digital phantom validate its capability of decomposing two basis materials from DECT images. The proposed approach also leads to higher decomposition quality in noise suppression on clinical datasets as compared with those using conventional schemes.

Unpaired Low-Dose CT Denoising Network Based on Cycle-Consistent Generative Adversarial Network with Prior Image Information.

The widespread application of X-ray computed tomography (CT) in clinical diagnosis has led to increasing public concern regarding excessive radiation dose administered to patients. However, reducing the radiation dose will inevitably cause server noise and affect radiologists' judgment and confidence. Hence, progressive low-dose CT (LDCT) image reconstruction methods must be developed to improve image quality. Over the past two years, deep learning-based approaches have shown impressive performance in noise reduction for LDCT images. Most existing deep learning-based approaches usually require the paired training dataset which the LDCT images correspond to the normal-dose CT (NDCT) images one-to-one, but the acquisition of well-paired datasets requires multiple scans, resulting the increase of radiation dose. Therefore, well-paired datasets are not readily available. To resolve this problem, this paper proposes an unpaired LDCT image denoising network based on cycle generative adversarial networks (CycleGAN) with prior image information which does not require a one-to-one training dataset. In this method, cyclic loss, an important trick in unpaired image-to-image translation, promises to map the distribution from LDCT to NDCT by using unpaired training data. Furthermore, to guarantee the accurate correspondence of the image content between the output and NDCT, the prior information obtained from the result preprocessed using the LDCT image is integrated into the network to supervise the generation of content. Given the map of distribution through the cyclic loss and the supervision of content through the prior image loss, our proposed method can not only reduce the image noise but also retain critical information. Real-data experiments were carried out to test the performance of the proposed method. The peak signal-to-noise ratio (PSNR) improves by more than 3 dB, and the structural similarity (SSIM) increases when compared with the original CycleGAN without prior information. The real LDCT data experiment demonstrates the superiority of the proposed method according to both visual inspection and quantitative evaluation.

In situ assembly of well-dispersed Ag nanoparticles on the surface of polylactic acid-Au@polydopamine nanofibers for antimicrobial applications.

Nanofibrous membranes which exhibit bacteriostatic functions are a good strategy to prevent microorganisms from adhering to the surface of biomaterials. Here, we report the synthesis of such a nanofibrous membrane which can be applied to biological coatings to reduce bacteriostatic functionality. Ascorbic acid was utilized to reduced chloroauric acid to gold nanoparticles (AuNPs). Dopamine was then polymerized upon AuNP surfaces by ultrasound-assistance, to synthesize core-shell structured polydopamine-coated AuNPs (Au@PDA NPs). The Au@PDA NPs were then mixed with polylactic acid (PLA) for electrospinning into cylindrical nanofibers (136.6 nm diameter). PLA-Au@PDA nanofibrous membranes were finally immersed in silver nitrate for in situ reduction into a silver nanoparticle (AgNP) coating to yield PLA-Au@PDA@Ag nanofibers. The PLA-Au@PDA@Ag nanofibers were characterized based on field emission scanning electron microscopy, Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy, and contact angle analyses. The antibacterial properties of the PLA-Au@PDA@Ag nanofibers were examined based on the optical density absorbance of bacterial cell suspensions, traditional colony plate counts, zone inhibition analyses, and field-emission scanning electron microscopy. Escherichia coli and Staphylococcus aureaus respectively served as Gram negative and positive bacterial models of industrial relevance. The data conclusively illustrates the antimicrobial and biomedical applications of PLA-Au@PDA@Ag nanofibers.

Quantitative study on exact reconstruction sampling condition by verifying solution uniqueness in limited-view CT.

In limited-view computed tomography reconstruction, iterative image reconstruction with sparsity-exploiting methods, such as total variation (TV) minimization, inspired by compressive sensing, potentially claims large reductions in sampling requirements. However, a quantitative notion of this claim is non-trivial because of the ill-defined reduction in sampling achieved by the sparsity-exploiting method. In this paper, exact reconstruction sampling condition for limited-view problem is studied by verifying the uniqueness of solution in TV minimization model. Uniqueness is tested by solving a convex optimization problem derived from the sufficient and necessary condition of solution uniqueness. Through this method, the sufficient sampling number of exact reconstruction is quantified for any fixed phantom and settled geometrical parameter in the limited-view problem. This paper provides a reference to quantify the sampling condition. Three phantoms are tested to study the sampling condition of limited view exact reconstruction in this paper. The experiment results show the quantified sampling number and indicate that an object would be accurately reconstructed as the scanning range becomes narrower by increasing sampling number. The increased samplings compensate for the deficiency of the projection angle. However, the lower bound of the scanning range corresponding to three different phantoms are presented, in which an exact reconstruction cannot be obtained once the projection angular is narrowed to this extent no matter how to increase sampling.

A promising limited angular computed tomography reconstruction via segmentation based regional enhancement and total variation minimization.

X-ray computed tomography (CT) is a powerful and common inspection technique used for the industrial non-destructive testing. However, large-sized and heavily absorbing objects cause the formation of artifacts because of either the lack of specimen penetration in specific directions or the acquisition of data from only a limited angular range of views. Although the sparse optimization-based methods, such as the total variation (TV) minimization method, can suppress artifacts to some extent, reconstructing the images such that they converge to accurate values remains difficult because of the deficiency in continuous angular data and inconsistency in the projections. To address this problem, we use the idea of regional enhancement of the true values and suppression of the illusory artifacts outside the region to develop an efficient iterative algorithm. This algorithm is based on the combination of regional enhancement of the true values and TV minimization for the limited angular reconstruction. In this algorithm, the segmentation approach is introduced to distinguish the regions of different image knowledge and generate the support mask of the image. A new regularization term, which contains the support knowledge to enhance the true values of the image, is incorporated into the objective function. Then, the proposed optimization model is solved by variable splitting and the alternating direction method efficiently. A compensation approach is also designed to extract useful information from the initial projections and thus reduce false segmentation result and correct the segmentation support and the segmented image. The results obtained from comparing both simulation studies and real CT data set reconstructions indicate that the proposed algorithm generates a more accurate image than do the other reconstruction methods. The experimental results show that this algorithm can produce high-quality reconstructed images for the limited angular reconstruction and suppress the illusory artifacts caused by the deficiency in valid data.