Incomplete Projection Research Articles

Limited-Angle Computed Tomography Reconstruction using Combined FDK-Based Neural Network and U-Net.

The limited-angle cone-beam Computed Tomography (CT) is often used in C-arm for clinical diagnosis with the advantages of cheap cost and radiation dose reduction. However, due to incomplete projection data, the 3-dimensional CT images reconstructed by conventional methods, such as the Feldkamp, Davis and Kres (FDK) algorithm [1], suffer from heavy artifacts and missing features. In this paper, we propose a novel pipeline of neural networks jointly by a FDK-based neural network revisited from Würfl et al.'s work [2] and an image domain U-Net to enhance the 3-dimensional reconstruction quality for limited projection sinogram less than 180 degrees, i.e. 145 degrees in our work. Experimental results, on simulated projections of real-scan CTs, show that the proposed pipeline can reduce some of the major artifacts caused by the limited views while keep the key features, with a 16.60% improvement than Würfl et al.'s work on peak signal-to-noise ratio.

Incomplete angle reconstruction algorithm with the sparse optimization and the image optimal criterions

To solve the problem of artifact and image degradation caused by incomplete angle projection, this article presents an incomplete angle reconstruction algorithm based on sparse optimization and image optimization criterion (SO-IOC). Firstly, the joint objective function model is established based on the projection sparsity and the natural features of images. Secondly, by means of the idea of alternating direction method of multipliers, the augmented Lagrange method is used to decompose the reconstruction model into simple subproblems and the modified genetic algorithm is used for solving those subproblems. Finally, a multiobjective optimization operation is carried out to coordinate and select the candidate solutions to improve the quality of the reconstructed images. The algebraic reconstruction technique algorithm and the Split Bregman algorithm are compared with the SO-IOC algorithm. In the compared process, the mean relative error and the peak signal-to-noise ratio are used. The experimental results show the SO-IOC algorithm is best among the above three algorithms.

A deep learning reconstruction framework for X-ray computed tomography with incomplete data.

As a powerful imaging tool, X-ray computed tomography (CT) allows us to investigate the inner structures of specimens in a quantitative and nondestructive way. Limited by the implementation conditions, CT with incomplete projections happens quite often. Conventional reconstruction algorithms are not easy to deal with incomplete data. They are usually involved with complicated parameter selection operations, also sensitive to noise and time-consuming. In this paper, we reported a deep learning reconstruction framework for incomplete data CT. It is the tight coupling of the deep learning U-net and CT reconstruction algorithm in the domain of the projection sinograms. The U-net estimated results are not the artifacts caused by the incomplete data, but the complete projection sinograms. After training, this framework is determined and can reconstruct the final high quality CT image from a given incomplete projection sinogram. Taking the sparse-view and limited-angle CT as examples, this framework has been validated and demonstrated with synthetic and experimental data sets. Embedded with CT reconstruction, this framework naturally encapsulates the physical imaging model of CT systems and is easy to be extended to deal with other challenges. This work is helpful to push the application of the state-of-the-art deep learning techniques in the field of CT.

Partial-ring PET image restoration using a deep learning based method

PET scanners with partial-ring geometry have been proposed for various imaging purposes. The incomplete projection data obtained from this design cause undesirable artifacts in the reconstructed images. In this study, we investigated the performance of a deep learning (DL) based method for the recovery of partial-ring PET images. Twenty digital brain phantoms were used in the Monte Carlo simulation toolkit, SimSET, to simulate 15 min full-ring PET scans. Partial-ring PET data were generated from full-ring PET data by removing coincidence events that hit these specific detector blocks. A convolutional neural network based on the residual U-Net architecture was trained to predict full-ring data from partial-ring data in either the projection or image domain. The performance of the proposed DL-based method was evaluated by comparing with the PET images reconstructed using the full-ring projection data in terms of the mean squared error (MSE), structural similarity (SSIM) index and recovery coefficient (RC). The MSE results showed the superiority of the image-domain approach in reduction of 91.7% in contrast to 14.3% for the projection-domain approach. Therefore, the image-domain approach was used to study the influence of the number of detector block removal. The SSIM results were 0.998, 0.996 and 0.993 for 3, 5 and 7 detector block removals, respectively. The activity of gray and white matters could be fully recovered even with 7 detector block removal, while the RCs of two artificially inserted small lesions (3 pixels in diameter) in the testing data were 94%, 89% and 79% for 3, 5, and 7 detector block removals, respectively. Our simulation results suggest that DL has the potential to recover partial-ring PET images.

A Deep Learning Reconstruction Framework for Differential Phase-Contrast Computed Tomography With Incomplete Data.

Differential phase-contrast computed tomography (DPC-CT) is a powerful analysis tool for soft-tissue and low-atomic-number samples. Limited by the implementation conditions, DPC-CT with incomplete projections happens quite often. Conventional reconstruction algorithms face difficulty when given incomplete data. They usually involve complicated parameter selection operations, which are also sensitive to noise and are time-consuming. In this paper, we report a new deep learning reconstruction framework for incomplete data DPC-CT. It involves the tight coupling of the deep learning neural network and DPC-CT reconstruction algorithm in the domain of DPC projection sinograms. The estimated result is not an artifact caused by the incomplete data, but a complete phase-contrast projection sinogram. After training, this framework is determined and can be used to reconstruct the final DPC-CT images for a given incomplete projection sinogram. Taking the sparse-view, limited-view and missing-view DPC-CT as examples, this framework is validated and demonstrated with synthetic and experimental data sets. Compared with other methods, our framework can achieve the best imaging quality at a faster speed and with fewer parameters. This work supports the application of the state-of-the-art deep learning theory in the field of DPC-CT.

Sparse and limited-angle CT image reconstruction using dictionary learning constrained by L1 norm

Reconstructed images from computed tomography (CT) using the algebraic reconstruction technique (ART) and simultaneous ART (SART) algorithms often suffer from obvious artefacts when only sparse and limited-angle projection data are available. Using the ability of dictionary learning (DL) in image feature extraction and sparse signal representation, a new iterative reconstruction algorithm, ART-DL-L1, is proposed to overcome the aforementioned limitations. This new algorithm is based on DL and an L1 norm constraint, combined with ART. An alternate iterative solving strategy based on an approach of 'ART first, then adaptive dictionary learning' is suggested and is explicitly described in a flowchart depicting the ART-DL-L1 algorithm. For both a noisy projection of 360° sparse data and limitedangle data of 120°, simulation reconstruction results from the classic Shepp-Logan image obtained using ART-DL-L1 appear to be better than those obtained using SART and total variation (TV) algorithms and also better than the cutting-edge ART-DL-L2 algorithm. Five evaluation metrics corresponding to the root-mean-square error (RMSE), the mean absolute error (MAE), the peak signal-to-noise ratio (PSNR), the residuals and the structural similarity (SSIM) index are adopted to estimate the reconstruction effect. The results suggest that the five metrics obtained using ART-DL-L1 outperform those obtained using the other three algorithms. The impact of using patches of various sizes played by the DL part in ART-DL-L1 is considered in the simulations and the patch size achieving the best reconstructed image quality is identified in this case as 25 (5 × 5). Overall, the proposed ART-DL-L1 algorithm may reduce artefacts and suppress noise from incomplete noisy projection CT imaging to some degree.

Reduced iteration image reconstruction of incomplete projection CT using regularization strategy through Lp norm dictionary learning.

For sparse and limited angle projection Computed Tomography (CT), the reconstructed image usually suffers from considerable artifacts due to undersampled data. To improve image reconstruction quality of sparse and limited angle projection CT, this study tested a novel reconstruction algorithm based on Dictionary Learning (DL) from sparse and limited projections. The study used signal sparse representation and feature extraction to render the DL technology, which is constrained by L2 and Lp norms, respectively. A Lp Norm Dictionary Learning term is suitable for regular term of objective function for CT image reconstruction. This is helpful for solving the objective function by combining algorithm of ART. Based on these features, the new algorithm of ART-DL-Lp is proposed for CT image reconstruction. The alternate solving strategy of the algorithm of "ART first, then adaptive DL" is provided in sequence. The impact on reconstruction results of ART-DL-Lp at different p values (0 < p < 1) is also considered. For non-ideal projections with noise, the digital experiments show that ART-DL-Lp data were superior to those of ART, SART, and ART-DL-L2. Accordingly, the objective evaluation metrics for non-ideal situation of RMSE, MAE, PSNR, Residuals and SSIM are all better than those of contrasted three algorithms. The metrics curves of ART-DL-Lp algorithm are recorded as the best. In both incomplete projection situations, smaller p-value of ART-DL-Lp algorithm induces more close reconstructed images to the original form and better five objective evaluation metrics. Overall, the reconstruction efficiency of the proposed ART-DL-Lp for CT imaging using the noisy incomplete projections outperforms ART, SART and ART-DL-L2 algorithms. For ART-DL-Lp algorithm, lower p-values result in better reconstruction performance.

Application of an Adaptive Multi-Population Parallel Genetic Algorithm with Constraints in Electromagnetic Tomography with Incomplete Projections

Electromagnetic tomography technology (EMT) is widely used in underground energy exploration. Limited by objective conditions, the collected projection data of electromagnetic waves are sparse and incomplete. Therefore, a study of the tomographic inversion algorithm of EMT based on incomplete projection data has an important guiding significance for the exploitation of underground energy. As a global optimization probability search algorithm, the simple genetic algorithm (SGA) has been widely used in the process of tomographic inversion. However, SGA evolves through a single population, and the values of crossover and mutation probability are always fixed, so there are risks of premature convergence and poor local search ability. To improve the performance of the SGA, a new approach of adaptive multi-population parallel genetic algorithm (AMPGA) with constraints is proposed in this paper. First, the AMPGA makes full use of multi-group adaptive co-evolution to improve the local and global search ability of SGA and restrain the risk of premature convergence. Then, the introduction of prior information as a constraint makes the results clearer and more accurate. The proposed algorithm has been verified in a numerical experiment and field tests, and the results show that the proposed algorithm can well balance global and local search capabilities, which offers a more realistic and stable tomographic result.

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.

Recovery of missing data in partial geometry PET scanners: Compensation in projection space vs image space.

Robust and reliable reconstruction of images from noisy and incomplete projection data holds significant potential for proliferation of cost-effective medical imaging technologies. Since conventional reconstruction techniques can generate severe artifacts in the recovered images, a notable line of research constitutes development of appropriate algorithms to compensate for missing data and to reduce noise. In the present work, we investigate the effectiveness of state-of-the-art methodologies developed for image inpainting and noise reduction to preserve the quality of reconstructed images from undersampled PET data. We aimed to assess and ascertain whether missing data recovery is best performed in the projection space prior to reconstruction or adjoined with the reconstruction step in image space. Different strategies for data recovery were investigated using realistic patient derived phantoms (brain and abdomen) in PET scanners with partial geometry (small and large gap structures). Specifically, gap filling strategies in projection space were compared with reconstruction based compensation in image space. The methods used for filling the gap structure in sinogram PET data include partial differential equationbased techniques (PDE), total variation (TV) regularization, discrete cosine transform(DCT)-based penalized regression, and dictionary learning based inpainting (DLI). For compensation in image space, compressed sensing based image reconstruction methods were applied. These include the preconditioned alternating projection (PAPA) algorithm with first and higher order total variation (HOTV) regularization as well as dictionary learning based compressed sensing (DLCS). We additionally investigated the performance of the methods for recovery of missing data in the presence of simulated lesion. The impact of different noise levels in the undersampled sinograms on performance of the approaches were also evaluated. In our first study (brain imaging), DLI was shown to outperform other methods for small gap structure in terms of root mean square error (RMSE) and structural similarity (SSIM), though having relatively high computational cost. For large gap structure, HOTV-PAPA produces better results. In the second study (abdomen imaging), again the best performance belonged to DLI for small gap, and HOTV-PAPA for large gap. In our experiments for lesion simulation on patient brain phantom data, the best performance in term of contrast recovery coefficient (CRC) for small gap simulation belonged to DLI, while in the case of large gap simulation, HOTV-PAPA outperformed others. Our evaluation of the impact of noise on performance of approaches indicated that in case of low and medium noise levels, DLI still produces favorable results among inpainting approaches. However, for high noise levels, the performance of PDE4 (variant of PDE) and DLI are very competitive. Our results showed that estimation of missing data in projection space as a preprocessing step before reconstruction can improve the quality of recovered images especially for small gap structures. However, when large portions of data are missing, compressed sensing techniques adjoined with the reconstruction step in image space were the best strategy.

Edge information diffusion based reconstruction (EIDR) for cone beam computed laminography.

Computed laminography (CL) is a prospective nondestructive testing technique for flat object inspection in industrial applications. However, CL image reconstruction is a challenging task because incomplete projection data are acquired from the CL scan. When a conventional computed tomography (CT) reconstruction method is applied to cone beam CL data, the vertical edges (singularities in the z-direction) in the reconstructed image would be blurred. On the contrary, the horizontal edges (singularities within slices) can be quite accurately reconstructed. Based on this key observation, an edge information diffusion method is developed, which fixes the horizontal edges and propagates their values within the slices. An effective CL reconstruction method is then proposed for flat object inspection by combining the edge information diffusion procedure, which plays the role of regularization, with conventional CT image reconstruction algorithms. Experiments on both simulated data and real data are performed to verify the effectiveness of the proposed method. The results show that the proposed method can effectively suppress the inter-slice aliasing and blurring caused by incompleteness of the CL scan data, and that it outperforms other state-of-the-art methods.

A non-smooth and non-convex regularization method for limited-angle CT image reconstruction

Abstract Restricted by the practical applications and radiation exposure of computed tomography (CT), the obtained projection data is usually incomplete, which may lead to a limited-angle reconstruction problem. Whereas reconstructing an object from limited-angle projection views is a challenging and ill-posed inverse problem. Fortunately, the regularization methods offer an effective way to deal with that. Recently, several researchers are absorbed in ℓ 1 {\ell_{1}} regularization to address such problem, but it has some problems for suppressing the limited-angle slope artifacts around edges due to incomplete projection data. In this paper, in order to surmount the ill-posedness, a non-smooth and non-convex method that is based on ℓ 0 {\ell_{0}} and ℓ 1 {\ell_{1}} regularization is presented to better deal with the limited-angle problem. Firstly, the splitting technique is utilized to deal with the presented approach called LWPC-ST-IHT. Afterwards, some propositions and convergence analysis of the presented approach are established. Numerical implementations show that our approach is more capable of suppressing the slope artifacts compared with the classical and state of the art iterative reconstruction algorithms.

Exemplar-based inpainting as a solution to the missing wedge problem in electron tomography

A new method for dealing with incomplete projection sets in electron tomography is proposed. The approach is inspired by exemplar-based inpainting techniques in image processing and heuristically generates data for missing projection directions. The method has been extended to work on three dimensional data. In general, electron tomography reconstructions suffer from elongation artifacts along the beam direction. These artifacts can be seen in the corresponding Fourier domain as a missing wedge. The new method synthetically generates projections for these missing directions with the help of a dictionary based approach that is able to convey both structure and texture at the same time. It constitutes a preprocessing step that can be combined with any tomographic reconstruction algorithm. The new algorithm was applied to phantom data, to a real electron tomography data set taken from a catalyst, as well as to a real dataset containing solely colloidal gold particles. Visually, the synthetic projections, reconstructions, and corresponding Fourier power spectra showed a decrease of the typical missing wedge artifacts. Quantitatively, the inpainting method is capable to reduce missing wedge artifacts and improves tomogram quality with respect to full width half maximum measurements.

A novel CT reconstruction algorithm for incomplete projection based on information repairment

An incomplete projection reconstruction algorithm was proposed in this study. In synchrotron radiation computed tomography (SRCT) of mechanical loading process, shielded projection due to the loading device is the main problem of high-resolution CT reconstruction. Thus, the proposed algorithm was developed based on information repairment considering the continuity of sinogram and slice. The truncated sinogram was estimated using orientation total variation minimization (TVM), which was based on the continuity of projections at adjacent angles in sinogram. Slice rectification was conducted to restrain image distortion, which was based on the continuity of matter contribution. Then, the algorithm was validated by a series of numerical reconstruction experiments. Results showed that the new algorithm could repair the lost boundary and restrain the artifacts. Quantitative comparison of evaluation parameters indicated that the new algorithm worked well when the shielded angle was less than 60° and that satisfactory results could be obtained by approximately 200 times of iteration. Finally, the new algorithm was validated using actual SRCT data and demonstrated effective improvement of reconstruction quality. Therefore, the proposed algorithm may be a suitable method for the in situ SRCT studies of mechanical loading processes.

Hybrid reconstruction algorithm for computed tomography based on diagonal total variation

Inspired by total variation (TV), this paper represents a new iterative algorithm based on diagonal total variation (DTV) to address the computed tomography image reconstruction problem. To improve the quality of a reconstructed image, we used DTV to sparsely represent images when iterative convergence of the reconstructed algorithm with TV-constraint had no effect during the reconstruction process. To investigate our proposed algorithm, the numerical and experimental studies were performed, and root-mean-square error (RMSE) and structure similarity (SSIM) were used to evaluate the reconstructed image quality. The results demonstrated that the proposed method could effectively reduce noise, suppress artifacts, and reconstruct high-quality image from incomplete projection data.

Block matching sparsity regularization-based image reconstruction for incomplete projection data in computed tomography

In medical imaging many conventional regularization methods, such as total variation or total generalized variation, impose strong prior assumptions which can only account for very limited classes of images. A more reasonable sparse representation frame for images is still badly needed. Visually understandable images contain meaningful patterns, and combinations or collections of these patterns can be utilized to form some sparse and redundant representations which promise to facilitate image reconstructions. In this work, we propose and study block matching sparsity regularization (BMSR) and devise an optimization program using BMSR for computed tomography (CT) image reconstruction for an incomplete projection set. The program is built as a constrained optimization, minimizing the L1-norm of the coefficients of the image in the transformed domain subject to data observation and positivity of the image itself. To solve the program efficiently, a practical method based on the proximal point algorithm is developed and analyzed. In order to accelerate the convergence rate, a practical strategy for tuning the BMSR parameter is proposed and applied. The experimental results for various settings, including real CT scanning, have verified the proposed reconstruction method showing promising capabilities over conventional regularization.

Incomplete projection reconstruction of computed tomography based on the modified discrete algebraic reconstruction technique

Based on the discrete algebraic reconstruction technique (DART), this study aims to address and test a new improved algorithm applied to incomplete projection data to generate a high quality reconstruction image by reducing the artifacts and noise in computed tomography. For the incomplete projections, an augmented Lagrangian based on compressed sensing is first used in the initial reconstruction for segmentation of the DART to get higher contrast graphics for boundary and non-boundary pixels. Then, the block matching 3D filtering operator was used to suppress the noise and to improve the gray distribution of the reconstructed image. Finally, simulation studies on the polychromatic spectrum were performed to test the performance of the new algorithm. Study results show a significant improvement in the signal-to-noise ratios (SNRs) and average gradients (AGs) of the images reconstructed from incomplete data. The SNRs and AGs of the new images reconstructed by DART-ALBM were on average 30%–40% and 10% higher than the images reconstructed by DART algorithms. Since the improved DART-ALBM algorithm has a better robustness to limited-view reconstruction, which not only makes the edge of the image clear but also makes the gray distribution of non-boundary pixels better, it has the potential to improve image quality from incomplete projections or sparse projections.

GPU-Accelerated Dynamic Wavelet Thresholding Algorithm for X-Ray CT Metal Artifact Reduction

The computed tomography (CT) imaging technique has been used to diagnose widespread disease for many years; however, severe streaking artifacts have been observed to appear in the reconstructed images of examinate contains metal objects. In this paper, we propose a dynamic wavelet thresholding metal artifact reduction (MAR) algorithm based on a statistic iterative reconstruction (SIR) model for 2-D fan beam CT. Cubic spline interpolation is utilized to remove blocky black artifacts caused by incomplete projections, and it also makes the solution closer to the optimum. The dynamic wavelet thresholding method contains the benefits of both wavelet soft and hard thresholding methods and promotes the sparsity of the image, which is used to erase residual streaking artifacts and accelerate the convergence of the SIR. The algorithm is accelerated by graphics processing unit programming and costs 14.44s with 40 iterations, meeting the demand of clinical practice. The performance of the proposed algorithm is compared with two classical MAR algorithms: the total variation (TV) constraint SIR algorithm and the reweighted TV constraint SIR algorithm. The experimental datasets include nine artificial datasets. Both qualitative and quantitative evaluation results show the outstanding performance of the proposed algorithm in suppressing the metal artifacts and preserving the image details.

A Joint Reconstruction and Segmentation Method for Limited-Angle X-Ray Tomography

Limited-angle computed tomography (CT) is common in industrial applications, where incomplete projection data can cause artifacts. For objects made from homogeneous materials, we propose a joint reconstruction and segmentation method that performs joint image reconstruction and segmentation directly on the projection data. We describe an alternating minimization algorithm to solve the resulting optimization problem, and we modify the primal-dual hybrid gradient algorithm for the non-convex piecewise constant Mumford-Shah model, which is a popular approximation model in biomedical image segmentation. The effectiveness of the proposed approach is validated by simulation and by application to actual micro-CT data sets.

Impact of statistical reconstruction and compressed sensing algorithms on projection data elimination during X-ray CT image reconstruction.

To examine the effect of incomplete, or total elimination of, projection data on computed tomography (CT) images subjected to statistical reconstruction and/or compressed sensing algorithms. Multidetector row CT images were used. The algebraic reconstruction technique (ART) and the maximum likelihood-expectation maximization (ML-EM) method were compared with filtered back-projection (FBP). Effects on reconstructed images were studied when the projection data of 360° (360 projections) were decreased to 180 or 90 projections by reducing the collection angle or thinning the image data. The total variation (TV) regularization method using compressed sensing was applied to images processed by the ART. Image noise was subjectively evaluated using the root-mean-square error and signal-to-noise ratio. When projection data were reduced by one-half or three-quarters, ART and ML-EM produced better image quality than FBP. Both ART and ML-EM resulted in high quality at a spread of 90 projections over 180° rotation. Computational loading was high for statistical reconstruction, but not for ML-EM, compared with the ART. TV regularization made it possible to use only 36 projections while still achieving acceptable image quality. Incomplete projection data-accomplished by reducing the angle to collect image data or thinning the projection data without reducing the angle of rotation over which it is collected-made it possible to reduce the radiation dose while retaining image quality with statistical reconstruction algorithms and/or compressed sensing. Despite heavier computational calculation loading, these methods should be considered for reducing radiation doses.