A content-adaptive unstructured grid based regularized CT reconstruction method with a SART-type preconditioned fixed-point proximity algorithm

2022 ◽  
Author(s):  
Yun Chen ◽  
Yao Lu ◽  
Xiangyuan Ma ◽  
Yuesheng Xu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Optimization Problem ◽  
Unstructured Grid ◽  
Reconstruction Technique ◽  
Reconstruction Method ◽  
Ct Reconstruction ◽  
Image Domain ◽  
Computational Costs ◽  
Content Adaptive

Abstract The goal of this study is to develop a new computed tomography (CT) image reconstruction method, aiming at improving the quality of the reconstructed images of existing methods while reducing computational costs. Existing CT reconstruction is modeled by pixel-based piecewise constant approximations of the integral equation that describes the CT projection data acquisition process. Using these approximations imposes a bottleneck model error and results in a discrete system of a large size. We propose to develop a content-adaptive unstructured grid (CAUG) based regularized CT reconstruction method to address these issues. Specifically, we design a CAUG of the image domain to sparsely represent the underlying image, and introduce a CAUG-based piecewise linear approximation of the integral equation by employing a collocation method. We further apply a regularization defined on the CAUG for the resulting illposed linear system, which may lead to a sparse linear representation for the underlying solution. The regularized CT reconstruction is formulated as a convex optimization problem, whose objective function consists of a weighted least square norm based fidelity term, a regularization term and a constraint term. Here, the corresponding weighted matrix is derived from the simultaneous algebraic reconstruction technique (SART). We then develop a SART-type preconditioned fixed-point proximity algorithm to solve the optimization problem. Convergence analysis is provided for the resulting iterative algorithm. Numerical experiments demonstrate the outperformance of the proposed method over several existing methods in terms of both suppressing noise and reducing computational costs. These methods include the SART without regularization and with quadratic regularization on the CAUG, the traditional total variation (TV) regularized reconstruction method and the TV superiorized conjugate gradient method on the pixel grid.

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

Sensors ◽  
2019 ◽  
Vol 19 (18) ◽  
pp. 3941 ◽  
Author(s):  
Li ◽  
Cai ◽  
Wang ◽  
Zhang ◽  
Tang ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Imaging System ◽  
Reconstruction Method ◽  
Ct Reconstruction ◽  
Reconstruction Algorithms ◽  
Generative Adversarial Network ◽  
Image Domain ◽  
Adversarial Network ◽  
Domain Loss ◽  
Limited Angle

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.

scholarly journals A CT Reconstruction Algorithm Based on Non-Aliasing Contourlet Transform and Compressive Sensing

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Lu-zhen Deng ◽  
Peng Feng ◽  
Mian-yi Chen ◽  
Peng He ◽  
Quang-sang Vo ◽  
...  
Keyword(s):  
Compressive Sensing ◽  
Iteration Process ◽  
Reconstruction Algorithm ◽  
Ct Images ◽  
Contourlet Transform ◽  
Projection Data ◽  
Reconstruction Technique ◽  
Reconstruction Method ◽  
Ct Reconstruction ◽  
Split Bregman

Compressive sensing (CS) theory has great potential for reconstructing CT images from sparse-views projection data. Currently, total variation (TV-) based CT reconstruction method is a hot research point in medical CT field, which uses the gradient operator as the sparse representation approach during the iteration process. However, the images reconstructed by this method often suffer the smoothing problem; to improve the quality of reconstructed images, this paper proposed a hybrid reconstruction method combining TV and non-aliasing Contourlet transform (NACT) and using the Split-Bregman method to solve the optimization problem. Finally, the simulation results show that the proposed algorithm can reconstruct high-quality CT images from few-views projection using less iteration numbers, which is more effective in suppressing noise and artefacts than algebraic reconstruction technique (ART) and TV-based reconstruction method.

Study on Improved Computed Tomography Algorithm in Concrete Structure

2012 ◽  
Vol 189 ◽  
pp. 401-405
Author(s):  
Qiu Feng Li ◽  
Hong Guang Liu ◽  
Hui Cong Ma ◽  
Zhen Hua Chen
Keyword(s):  
Concrete Structure ◽  
Engineering Application ◽  
Reconstruction Technique ◽  
Reconstruction Method ◽  
Ct Reconstruction ◽  
Inversion Algorithm ◽  
Weighting Matrix ◽  
Engineering Requirement ◽  
Ultrasonic Propagation ◽  
Ultrasonic Ct

In ultrasonic CT of concrete structure, ray tracing technology based on SNELL principle is far more meet the characteristics of ultrasonic propagation. Inversion algorithm of tomography imaging is to solve large sparse equations. Simultaneous iterative reconstruction technique (SIRT) algorithm solves the problem from the mathematical view. According to engineering application, A improved imaging reconstruction method is proposed in the basis. During the data processing of simulation, the data weighting matrix is introduced to increase the proportion of effective information firstly; And then the units without ray passing through is merged with its adjacent units so that the slow-wave in reconstruction section could be changed smoothly by using unit merger method and ensure high resolution in middle section; And finally the image of CT reconstruction is obtained. Simulation results show that the improved algorithm is effective and could meet engineering requirement.

scholarly journals A Total Fractional-Order Variation Regularized Reconstruction Method for CT

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yun Chen ◽  
Baoyu Guo ◽  
Yao Lu
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Numerical Experiments ◽  
Iterative Scheme ◽  
Reconstruction Method ◽  
Ct Reconstruction ◽  
Reconstruction Methods ◽  
Tv Regularization ◽  
Order Variation ◽  
Fidelity Term

The total variation (TV) regularized reconstruction methods for computed tomography (CT) may lead to staircase effects in the reconstructed images because of using the TV regularization. This paper develops a total fractional-order variation regularized CT reconstruction method, aiming at overcoming the weakness of the reconstruction methods based on the TV. Specifically, we propose an optimization model for CT reconstruction, including a fidelity term, a regularization term, and a constraint term. Here, the regularization is a total fractional-order variation arising from the fractional derivative of the underlying solution. To address the nondifferentiability of the resulting model, we introduce a fixed-point characterization for its solution through the proximity operators of the nondifferentiable functions. Based on the characterization, we further develop a fixed-point iterative scheme to solve the resulting model and provide convergence analysis of the developed scheme. Numerical experiments are presented to demonstrate that the developed method outperforms the TV regularized reconstruction method in terms of suppressing noise for CT reconstruction.

On existence result of a class of nonlinear integral equation

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuous Functions ◽  
Concave Functions ◽  
Real Numbers ◽  
Fixed Point Techniques ◽  
Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

Alternative pulmonary artery reconstruction technique in the arterial switch operation

2021 ◽  
Author(s):  
Hisayuki Hongu ◽  
Masaaki Yamagishi ◽  
Yoshinobu Maeda ◽  
Keiichi Itatani ◽  
Masatoshi Shimada ◽  
...  
Keyword(s):  
Pulmonary Artery ◽  
Arterial Switch Operation ◽  
Late Complication ◽  
Late Complications ◽  
Reconstruction Technique ◽  
Reconstruction Method ◽  
Arterial Switch ◽  
Switch Operation ◽  
Longitudinal Extension

Abstract OBJECTIVES Late complications of arterial switch operations (ASO) for transposition of the great arteries, such as neo-pulmonary artery (PA) stenosis and/or neoaortic regurgitation, have been reported. We developed an alternative reconstruction method called the longitudinal extension (LE) method to prevent PA bifurcation stenosis (PABS). METHODS We identified 48 patients diagnosed with transposition of the great arteries and performed ASO using the Lecompte manoeuvre for neo-PA reconstruction. In 9 consecutive patients (from 2014), the LE method was performed (LE). Before 2014, conventional techniques were performed in 39 patients (C). The median body weight and age in the LE and C groups were 3.0 and 3.1 kg and 12 and 26 days, respectively. In the LE group, 1 patient underwent bilateral PA banding before ASO. In C, PA banding and arch repair were performed in 1 patient each. Patients who received concomitant procedures were included. RESULTS The median follow-up in LE and C groups was 1.9 and 10.1 years, respectively. Early mortality/late death was not found in group LE and in 1 patient in group C. Only 1 case required ascending aorta sliding plasty in LE, and 8 patients needed PA augmentation for PABS in C. The median velocity of right/left PA was measured as 1.6/1.9 m/s in LE and 2.1/2.3 m/s in C, so it showed a lower value in LE. CONCLUSIONS Excellent mid-term results were obtained with the LE method. It was considered a useful procedure in preventing PABS, which is a primary late complication of ASO. Further follow-up and investigations are needed.

Guided image filtering based ℓ0 gradient minimization for limited-angle CT image reconstruction

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tianyi Wang ◽  
Chengxiang Wang ◽  
Kequan Zhao ◽  
Wei Yu ◽  
Min Huang
Keyword(s):  
Iteration Process ◽  
Real Data ◽  
Image Filtering ◽  
Reconstruction Technique ◽  
Ct Reconstruction ◽  
Imaging Device ◽  
Practical Applications ◽  
Guided Image Filtering ◽  
Simultaneous Algebraic Reconstruction Technique ◽  
Limited Angle

Abstract Limited-angle computed tomography (CT) reconstruction problem arises in some practical applications due to restrictions in the scanning environment or CT imaging device. Some artifacts will be presented in image reconstructed by conventional analytical algorithms. Although some regularization strategies have been proposed to suppress the artifacts, such as total variation (TV) minimization, there is still distortion in some edge portions of image. Guided image filtering (GIF) has the advantage of smoothing the image as well as preserving the edge. To further improve the image quality and protect the edge of image, we propose a coupling method, that combines ℓ 0 {\ell_{0}} gradient minimization and GIF. An intermediate result obtained by ℓ 0 {\ell_{0}} gradient minimization is regarded as a guidance image of GIF, then GIF is used to filter the result reconstructed by simultaneous algebraic reconstruction technique (SART) with nonnegative constraint. It should be stressed that the guidance image is dynamically updated as the iteration process, which can transfer the edge to the filtered image. Some simulation and real data experiments are used to evaluate the proposed method. Experimental results show that our method owns some advantages in suppressing the artifacts of limited angle CT and in preserving the edge of image.

scholarly journals Evaluating a calcium-aware kernel for CT CAC scoring with varying surrounding materials and heart rates: a dynamic phantom study

2021 ◽  
Author(s):  
Niels R. van der Werf ◽  
Ronald Booij ◽  
Bernhard Schmidt ◽  
Thomas G. Flohr ◽  
Tim Leiner ◽  
...  
Keyword(s):  
Coronary Artery ◽  
Soft Tissue ◽  
Patient Specific ◽  
Reconstruction Technique ◽  
Ct Reconstruction ◽  
Raw Data ◽  
Heart Rates ◽  
Tissue Equivalent ◽  
Tin Filtration ◽  
Reconstruction Kernel

Abstract Objectives The purpose of this study was twofold. First, the influence of a novel calcium-aware (Ca-aware) computed tomography (CT) reconstruction technique on coronary artery calcium (CAC) scores surrounded by a variety of tissues was assessed. Second, the performance of the Ca-aware reconstruction technique on moving CAC was evaluated with a dynamic phantom. Methods An artificial coronary artery, containing two CAC of equal size and different densities (196 ± 3, 380 ± 2 mg hydroxyapatite cm−3), was moved in the center compartment of an anthropomorphic thorax phantom at different heart rates. The center compartment was filled with mixtures, which resembled fat, water, and soft tissue equivalent CT numbers. Raw data was acquired with a routine clinical CAC protocol, at 120 peak kilovolt (kVp). Subsequently, reduced tube voltage (100 kVp) and tin-filtration (150Sn kVp) acquisitions were performed. Raw data was reconstructed with a standard and a novel Ca-aware reconstruction technique. Agatston scores of all reconstructions were compared with the reference (120 kVp) and standard reconstruction technique, with relevant deviations defined as > 10%. Results For all heart rates, Agatston scores for CAC submerged in fat were comparable to the reference, for the reduced-kVp acquisition with Ca-aware reconstruction kernel. For water and soft tissue, medium-density Agatston scores were again comparable to the reference for all heart rates. Low-density Agatston scores showed relevant deviations, up to 15% and 23% for water and soft tissue, respectively. Conclusion CT CAC scoring with varying surrounding materials and heart rates is feasible at patient-specific tube voltages with the novel Ca-aware reconstruction technique. Key Points • A dedicated calcium-aware reconstruction kernel results in similar Agatston scores for CAC surrounded by fatty materials regardless of CAC density and heart rate. • Application of a dedicated calcium-aware reconstruction kernel allows for radiation dose reduction. • Mass scores determined with CT underestimated physical mass.

scholarly journals Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mahmoud Bousselsal ◽  
Sidi Hamidou Jah
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Measure Of Weak Noncompactness ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Noncompactness Measure

We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.

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