Sparse-view X-ray Research Articles

Neighborhood transformer for sparse-view X-ray 3D foot reconstruction

In medical imaging, Sparse-View X-ray 3D reconstruction is crucial for analyzing and diagnosing foot bone structures. However, existing methods face limitations when handling sparse view data and complex bone structures. To enhance reconstruction accuracy and detail preservation, this paper proposes an innovative Sparse-View X-ray 3D foot reconstruction technique based on Neighborhood Transformer. A new Neighborhood Position Encoding strategy is introduced, which divides X-ray images into local regions using a window mechanism and precisely selects these regions through nearest neighbor methods, thereby capturing detailed features in the images. Building upon existing NeRF (Neural Radiance Fields) technology, the paper introduces the Neighborhood Transformer module. This module significantly improves the expression capability for complex foot bone structures through depthwise separable convolutions and a dual-branch local–global Transformer network. Additionally, an adaptive weight learning strategy is applied within the Transformer module, enabling the model to better capture long-distance dependencies, thereby improving its ability to handle sparse view data.

A non-local total generalized variation regularization reconstruction method for sparse-view x-ray CT

Sparse-view x-ray computed tomography (CT) reconstruction, employing total generalized variation (TGV), effectively mitigates the stepwise artifacts associated with total variation (TV) regularization while preserving structural features within transitional regions of the reconstructed image. Despite TGV surpassing TV in reconstruction quality, it neglects the non-local self-similarity prior, recognized for its efficacy in restoring details during CT reconstruction. This study introduces a non-local TGV (NLTGV) to address the limitation of TGV regularization method. Specifically, we propose an NLTGV-regularized method for sparse-view CT reconstruction, utilizing non-local high-order derivative information to maintain image features and non-local self-similarity for detail recovery. Owing to the non-differentiability of the NLTGV regularized, we employ an alternating direction method of multipliers optimization method, facilitating an efficient solution by decomposing the reconstruction model into sub-problems. The proposed method undergoes evaluation using both simulated and real-world projection data. Simulation and experimental results demonstrate the efficacy of the proposed approach in enhancing the quality of reconstructed images compared to other competitive variational reconstruction methods. In conclusion, the simultaneous incorporation of sparsity priors of high-order TV and non-local similarity proves advantageous for structural detail recovery in sparse-view CT reconstruction.

Sparse-view X-ray CT based on a box-constrained nonlinear weighted anisotropic TV regularization.

Sparse-view computed tomography (CT) is an important way to reduce the negative effect of radiation exposure in medical imaging by skipping some X-ray projections. However, due to violating the Nyquist/Shannon sampling criterion, there are severe streaking artifacts in the reconstructed CT images that could mislead diagnosis. Noting the ill-posedness nature of the corresponding inverse problem in a sparse-view CT, minimizing an energy functional composed by an image fidelity term together with properly chosen regularization terms is widely used to reconstruct a medical meaningful attenuation image. In this paper, we propose a regularization, called the box-constrained nonlinear weighted anisotropic total variation (box-constrained NWATV), and minimize the regularization term accompanying the least square fitting using an alternative direction method of multipliers (ADMM) type method. The proposed method is validated through the Shepp-Logan phantom model, alongisde the actual walnut X-ray projections provided by Finnish Inverse Problems Society and the human lung images. The experimental results show that the reconstruction speed of the proposed method is significantly accelerated compared to the existing $ L_1/L_2 $ regularization method. Precisely, the central processing unit (CPU) time is reduced more than 8 times.

Reconstruction of Sparse-View X-ray Computed Tomography Based on Adaptive Total Variation Minimization.

Sparse-view reconstruction has garnered significant interest in X-ray computed tomography (CT) imaging owing to its ability to lower radiation doses and enhance detection efficiency. Among current methods for sparse-view CT reconstruction, an algorithm utilizing iterative reconstruction based on full variational regularization demonstrates good performance. The optimized direction and number of computations for the gradient operator of the regularization term play a crucial role in determining not only the reconstructed image quality but also the convergence speed of the iteration process. The conventional TV approach solely accounts for the vertical and horizontal directions of the two-dimensional plane in the gradient direction. When projection data decrease, the edges of the reconstructed image become blurred. Exploring too many gradient directions for TV terms often comes at the expense of more computational costs. To enhance the balance of computational cost and reconstruction quality, this study suggests a novel TV computation model that is founded on a four-direction gradient operator. In addition, selecting appropriate iteration parameters significantly impacts the quality of the reconstructed image. We propose a nonparametric control method utilizing the improved TV approach as a solution to the tedious manual parameter optimization issue. The relaxation parameters of projection onto convex sets (POCS) are determined according to the scanning number and numerical proportion of the projection data; according to the image error before and after iterations, the gradient descent step of the TV item is adaptively adjusted. Compared with several representative iterative reconstruction algorithms, the experimental results show that the algorithm can effectively preserve edges and suppress noise in sparse-view CT reconstruction.

Image Quality Improvement in Sparse-View X-Ray Phase-Contrast Trimodal CBCT With Multifrequency Fringe Modulation and Iterative Methods

X-ray grating interferometer can simultaneously retrieve attenuation, refraction and scattering signals of the imaged sample, which shows its great potential in biomedical imaging. However, fast scan of gratings and high centrifugal forces during rotating in X-ray grating-based cone-beam computed tomography (CBCT) system may lead to phase-stepping errors and grating position fluctuations, which cause reconstruction failure with phase-stepping (PS) method. Whats more, the reconstructed slices usually suffer from severe artifacts under low dose conditions. Herein, we propose a multi-frequency model to simulate the mechanical instability of the system and put forward novel iterative image reconstruction methods named MFM-TLI and MLEM-FISTA-TV to improve image quality in sparse-view trimodal CBCT. Results reveal that the model and MFM-TLI is effective to retrieve high quality absorption, differential phase contrast (DPC) and dark-field (DF) signals under mechanical instability, significantly outperforming the PS method. Image quality reconstructed by MLEM-FISTA-TV is improved compared to other iterative and analytical algorithms with sparse-view data. To the best of our knowledge, this is the first time multi-frequency method is applied in X-ray grating interferometer and iterative MLEM-TV algorithm is evaluated on experimental sparse-view dark-field CBCT data. This work might provide support for future trimodal CBCT reconstruction.

Fast algorithms based on Empirical Interpolation Methods for selecting best projections in Sparse-View X-ray Computed Tomography using a priori information

To ensure the safety of critical parts in mass production, non-destructive techniques are increasingly considered. Industrial Computed Tomography (CT) is a unique tool to inspect a part integrity and dimensional conformity. However, it usually requires many radiographies (also called projections) to reconstruct a 3D CT image accurately. To reconstruct an object from a reduced number of projections has become one of the most crucial challenges in X-ray CT. Iterative reconstruction algorithms have relieved robotic CT systems from usual circular or helical trajectories, allowing them to focus on the most informative and relevant projections. In this paper, we propose an approach to select the best projections for X-ray tomographic reconstructions when a priori information on the inspected object is available. The presented algorithms are based on Empirical Interpolation Methods and show a good reconstruction quality from a dozen of projections. Those methods have been selected for their flexibility, speed, and the perspectives they open up for sinogram inpainting.

Sparse-View Cone-Beam X-Ray Luminescence Computed Tomography Imaging for Optimized Regional Prior Knowledge

Sparse-View Cone-Beam X-Ray Luminescence Computed Tomography Imaging for Optimized Regional Prior Knowledge

Fast Algorithms Based on Empirical Interpolation Methods for Selecting Best Projections in Sparse-View X-Ray Computed Tomography Using a Priori Information

Fast Algorithms Based on Empirical Interpolation Methods for Selecting Best Projections in Sparse-View X-Ray Computed Tomography Using a Priori Information

A nonconvex truncated regularization and box-constrained model for CT reconstruction

X-ray computed tomography has been a useful technology in cancer detection and radiation therapy. However, high radiation dose during CT scans may increase the underlying risk of healthy organs. Usually, sparse-view X-ray projection is an effective method to reduce radiation. In this paper, we propose a constrained nonconvex truncated regularization model for this low-dose CT reconstruction. It preserves sharp edges very well. Although this model is quite complicated to analyze, we establish two useful theoretical results for its minimizers. Motivated by them, an iterative support shrinking algorithm is introduced. To handle more nondifferentiable points of the regularization function except zero point, we use a general proximally linearization technique at them, which is helpful to implement our algorithm. For this algorithm, we prove the convergence of the objective function, and give a lower bound theory of the iterative sequence. Numerical experiments and comparisons demonstrate that our model with the proposed algorithm performs good for low-dose CT reconstruction.

Interpolation based Low Dose CT Image Reconstruction

Abstract Medical imaging has grown tremendously over years. The CT and MRI are used at most. MRI is less harmful, but one cannot underestimate the side effects of CT. Current study demonstrate the serious risk of cancer, due to repeated use of harmful X-rays. Consequently the plan of low dose imaging protocol is emerging as vital solution in the present scenario. Low dose imaging is achieved by sparse view scanning. The sparse-view x-ray computed tomography (CT) is appreciated in medical diagnosis and industrial non-destructive testing. However, when the sampling is insufficient due to sparse view, the reconstructed image usually suffers from complex artifacts and noise. In order to deal such issue, we present interpolation technique to fill the sinogram as promising method to address issues of low dose imaging. Reconstructed image quality parameters are recorded, and are compared to original image and the low dose image. The evidenced results convey substantial improved performance compared to conventional low does image.

Sparse-view statistical image reconstruction with improved total variation regularization for X-ray micro-CT imaging

Sparse-view x-ray micro computed tomography (micro-CT) reconstruction algorithms via total variation (TV) optimize the data without introducing notable noise and artifacts, resulting in significant scanning time reduction while maintaining image quality. However, due to the piecewise constant assumption for the image, a conventional TV minimization often suffers from patchy artifacts in reconstructed images. Moreover, for lack of directional gradient in TV some directional information are lost. To obviate these drawbacks, in this study we develop a penalized weighted least-square (PWLS) strategy for micro-CT sparse-view image reconstruction by incorporating an adaptive weighted total variation in combination with an adaptive weighted diagonal total variation (AwTV+AwDTV) penalty term. The AwTV considers the vertical and horizontal gradients while the AwDTV uses the diagonal gradients. The associated weights which are defined based on the anisotropic edge properties of an image, are expressed as an exponential function and can be adaptively adjusted by the amount of the difference between voxel intensities to preserve the edge details. To evaluate the presented (AwTV+AwDTV)-PWLS algorithm, both qualitative and quantitative studies were performed by computer simulations and micro-CT data experiments. The Shepp-Logan phantom for computer simulation and the micro-CT water phantom and a rat skull for micro-CT experiments are employed to perform image reconstruction. To evaluate the performance of AwTV+AwDTV algorithm, we compared it with TV and AwTV reconstruction algorithms. The simulation results show that the presented (AwTV+AwDTV)-PWLS algorithm can achieve the lowest RMSE and highest PSNR, SSIM and MTF for different number of projections as compared to the AwTV and conventional TV algorithms. The micro-CT data results confirmed the superiority of the proposed (AwTV+AwDTV) method to the AwTV and TV methods for different number of projections.

Resolution and noise performance of sparse view X-ray CT reconstruction via Lp-norm regularization

ObjectivesAdaptive steepest descent projection onto convex sets (ASD-POCS) algorithms with Lp-norm (0 < p ≤ 1) regularization have shown great promise in sparse-view X-ray CT reconstruction. However, the difference in p value selection can lead to varying algorithm performance of noise and resolution. Therefore, it is imperative to develop a reliable method to evaluate the resolution and noise properties of the ASD-POCS algorithms under different Lp-norm priors. MethodsA comparative performance evaluation of ASD-POCS algorithms under different Lp-norm (0 < p ≤ 2) priors were performed in terms of modulation transfer function (MTF), noise power spectrum (NPS) and noise equivalent quanta (NEQ). Simulation data sets from the EGSnrc/BEAMnrc Monte Carlo system and an actual mouse data set were used for algorithms comparison. ResultsA considerable MTF improvement can be achieved with the decrement of p. L1 regularization based algorithm obtains the best noise performance, and shows superiority in NEQ evaluation. The advantage of L1-norm prior is also confirmed by the reconstructions from the actual mouse data set through contrast to noise ratio (CNR) comparison. ConclusionAlthough the ASD-POCS algorithms using small Lp-norm (p ≤ 0.5) priors yield a higher MTF than do the high Lp-norms, the best noise-resolution performance is achieved when p is between 0.8 and 1. The results are expected to be a reference to the choice of p in Lp-norm (0 < p ≤ 2) regularization.

A new Mumford-Shah total variation minimization based model for sparse-view x-ray computed tomography image reconstruction.

Total variation (TV) minimization for the sparse-view x-ray computer tomography (CT) reconstruction has been widely explored to reduce radiation dose. However, due to the piecewise constant assumption for the TV model, the reconstructed images often suffer from over-smoothness on the image edges. To mitigate this drawback of TV minimization, we present a Mumford-Shah total variation (MSTV) minimization algorithm in this paper. The presented MSTV model is derived by integrating TV minimization and Mumford-Shah segmentation. Subsequently, a penalized weighted least-squares (PWLS) scheme with MSTV is developed for the sparse-view CT reconstruction. For simplicity, the proposed algorithm is named as 'PWLS-MSTV.' To evaluate the performance of the present PWLS-MSTV algorithm, both qualitative and quantitative studies were conducted by using a digital XCAT phantom and a physical phantom. Experimental results show that the present PWLS-MSTV algorithm has noticeable gains over the existing algorithms in terms of noise reduction, contrast-to-ratio measure and edge-preservation.

Iterative reconstruction for sparse-view x-ray CT using alpha-divergence constrained total generalized variation minimization.

Accurate statistical model of the measured projection data is essential for computed tomography (CT) image reconstruction. The transmission data can be described by a compound Poisson distribution upon an electronic noise background. However, such a statistical distribution is numerically intractable for image reconstruction. Although the sinogram data is easily manipulated, it lacks a statistical description for image reconstruction. To address this problem, we present an alpha-divergence constrained total generalized variation (AD-TGV) method for sparse-view x-ray CT image reconstruction. The AD-TGV method is formulated as an optimization problem, which balances the alpha-divergence (AD) fidelity and total generalized variation (TGV) regularization in one framework. The alpha-divergence is used to measure the discrepancy between the measured and estimated projection data. The TGV regularization can effectively eliminate the staircase and patchy artifacts which is often observed in total variation (TV) regularization. A modified proximal forward-backward splitting algorithm was proposed to minimize the associated objective function. Qualitative and quantitative evaluations were carried out on both phantom and patient data. Compared with the original TV-based method, the evaluations clearly demonstrate that the AD-TGV method achieves higher accuracy and lower noise, while preserving structural details. The experimental results show that the presented AD-TGV method can achieve more gains over the AD-TV method in preserving structural details and suppressing image noise and undesired patchy artifacts. The authors can draw the conclusion that the presented AD-TGV method is potential for radiation dose reduction by lowering the milliampere-seconds (mAs) and/or reducing the number of projection views.

Sparse-view X-ray CT reconstruction with Gamma regularization

By providing fast scanning with low radiation doses, sparse-view (or sparse-projection) reconstruction has attracted much research attention in X-ray computerized tomography (CT) imaging. Recent contributions have demonstrated that the total variation (TV) constraint can lead to improved solution by regularizing the underdetermined ill-posed problem of sparse-view reconstruction. However, when the projection views are reduced below certain numbers, the performance of TV regularization tends to deteriorate with severe artifacts. In this paper, we explore the applicability of Gamma regularization for the sparse-view CT reconstruction. Experiments on simulated data and clinical data demonstrate that the Gamma regularization can lead to good performance in sparse-view reconstruction.

A new linearized split Bregman iterative algorithm for image reconstruction in sparse-view X-ray computed tomography

In this paper, a new linearized split Bregman iterative algorithm is proposed for sparse-view X-ray computed tomography, which can avoid solving a large-scale and unstructured linear system in each iteration. Remarkably, our method can be generalized to efficiently resolve some other image processing and analysis models, for instance, the robust compressed sensing, the total variation-ℓ1, and the ℓ1–ℓ1. We also give rigorous proofs for the convergence of the proposed method under appropriate conditions for the aforementioned problems. Experimental results demonstrate that our algorithm has better performance in terms of reconstruction quality, effectiveness and robustness, compared with some other methods (e.g. gradient-flow-based semi-implicit finite element method, split Bregman, etc.) for the robust image reconstruction in sparse-view X-ray computed tomography.

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization**Projected supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603) and the National Natural Science Foundation of China (Grant No. 61372172).

Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform (NUFFT) is presented in this work along with advanced total variation (TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.

Reconstruction of sparse-view X-ray computed tomography using adaptive iterative algorithms

In this paper, we propose two reconstruction algorithms for sparse-view X-ray computed tomography (CT). Treating the reconstruction problems as data fidelity constrained total variation (TV) minimization, both algorithms adapt the alternate two-stage strategy: projection onto convex sets (POCS) for data fidelity and non-negativity constraints and steepest descent for TV minimization. The novelty of this work is to determine iterative parameters automatically from data, thus avoiding tedious manual parameter tuning. In TV minimization, the step sizes of steepest descent are adaptively adjusted according to the difference from POCS update in either the projection domain or the image domain, while the step size of algebraic reconstruction technique (ART) in POCS is determined based on the data noise level. In addition, projection errors are used to compare with the error bound to decide whether to perform ART so as to reduce computational costs. The performance of the proposed methods is studied and evaluated using both simulated and physical phantom data. Our methods with automatic parameter tuning achieve similar, if not better, reconstruction performance compared to a representative two-stage algorithm.

Sparse-view x-ray CT reconstruction via total generalized variation regularization

Sparse-view CT reconstruction algorithms via total variation (TV) optimize the data iteratively on the basis of a noise- and artifact-reducing model, resulting in significant radiation dose reduction while maintaining image quality. However, the piecewise constant assumption of TV minimization often leads to the appearance of noticeable patchy artifacts in reconstructed images. To obviate this drawback, we present a penalized weighted least-squares (PWLS) scheme to retain the image quality by incorporating the new concept of total generalized variation (TGV) regularization. We refer to the proposed scheme as ‘PWLS-TGV’ for simplicity. Specifically, TGV regularization utilizes higher order derivatives of the objective image, and the weighted least-squares term considers data-dependent variance estimation, which fully contribute to improving the image quality with sparse-view projection measurement. Subsequently, an alternating optimization algorithm was adopted to minimize the associative objective function. To evaluate the PWLS-TGV method, both qualitative and quantitative studies were conducted by using digital and physical phantoms. Experimental results show that the present PWLS-TGV method can achieve images with several noticeable gains over the original TV-based method in terms of accuracy and resolution properties.

Correction to “Total Variation-Stokes Strategy for Sparse-View X-ray CT Image Reconstruction” [Mar 14 749-763

In the above-named article [ibid., vol. 33, no. 3, pp. 749-763, Mar. 2014], Y. Liu was incorrectly listed as the corresponding author. Z. Liang should have been indicated as the corresponding author.