Split Bregman Method Research Articles

Blind image deblurring with a difference of the mixed anisotropic and mixed isotropic total variation regularization

This paper proposes a simple model for image deblurring with a new total variation regularization. Classically, the L1-21 regularizer represents a difference of anisotropic (i.e. L1) and isotropic (i.e. L21) total variation, so we define a new regularization as Le-2e, which is the weighted difference of the mixed anisotropic (i.e. L0 + L1 = Le) and mixed isotropic (i.e. L0 + L21 = L2e), and it is characterized by sparsity-promotingand robustness in image deblurring. Then, we merge the L0-gradient into the model for edge-preserving and detail-removing. The union of the Le-2e regularization and L0-gradient improves the performance of image deblurring and yields high-quality blur kernel estimates. Finally, we design a new solution format that alternately iterates the difference of convex algorithm, the split Bregman method, and the approach of half-quadratic splitting to optimize the proposed model. Experimental results on quantitative datasets and real-world images show that the proposed method can obtain results comparable to state-of-the-art works.

Sparse-view neutron CT 3D image reconstruction algorithm based on split Bregman method

Sparse-view neutron CT 3D image reconstruction algorithm based on split Bregman method

Improved weighted nuclear norm with total variation for removing multiplicative noise

This paper introduces an improved weighted nuclear norm with a total variation model tailored for removing multiplicative noise. The model incorporates a weight matrix to regularize the residual matrix, effectively leveraging image redundancy to differentiate various statistical properties of the noise. Since there is no guarantee of a unique solution, the model is reformulated as a linear equality constraint problem and decomposed into two subproblems. These are addressed by using the alternating direction method of multipliers and the split Bregman method, respectively. In addition, each alternative update step has a closed-form and convergent solution. After obtaining the denoised image in the log-domain, the recovered image is given by using the exponential function and bias correction. Experimental evaluations demonstrate the efficacy of our algorithms in enhancing image restoration quality.

Data and measurement mechanism integrated imaging method for electrical capacitance tomography

This study presents a new imaging paradigm for overcoming the challenges limiting the improvement of the imaging quality in the electrical capacitance technique. The new imaging model enables the integration of measurement physics, sparsity-induced prior and physics-informed multi-fidelity learning prior (PIMFLP), as well as the synergy between data-driven and measurement physics modeling paradigms. The transformed L1 norm is used to model the PIMFLP, and the maximum correntropy criterion is used as a data misfit term to restrict the adverse impact of noises or outliers. The PIMFLP is learned from data and characterizes the structural details of imaging targets. The half-quadratic optimization method is developed to overcome computational challenges in solving the novel imaging model. A new physics-informed multi-fidelity learning method is developed to predict PIMFLP by synergizing deep convolutional neural network with measurement physics, and a new bilevel optimization model solved by a new nested algorithm that merges the genetic algorithm and the split Bregman method is proposed for training. Comparisons with other popular reconstruction algorithms confirm that the new imaging method leads to the improved reconstruction accuracy and noise immunity, and opens up new possibilities for unlocking the potential of the measurement technology.

Denoising on Textured Image Using Total Generalized Variation With Overlapping Group Sparsity Based on Fast Split Bregman Method

Denoising on Textured Image Using Total Generalized Variation With Overlapping Group Sparsity Based on Fast Split Bregman Method

On a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain and its computation

We introduce a capillary Chambolle-type scheme for mean curvature flow with prescribed contact angle. Our scheme includes a capillary functional instead of just the total variation. We show that the scheme is well-defined and has consistency with the energy minimizing scheme of Almgren–Taylor–Wang type. Moreover, for a planar motion in a strip, we give several examples of numerical computation of this scheme based on the split Bregman method instead of a duality method.

Sparse reconstruction of EMT based on compressed sensing and Lp regularization with the split Bregman method

Electromagnetic tomography (EMT) is a promising tomographic method used to reconstruct the conductivity and permeability material owing to its contactless nature. However, the EMT inverse problem is ill-posed due to the soft-field characteristic and limited prior information, which will severely affect the imaging quality. To address the challenge, a novel sparse reconstruction algorithm is proposed in this article on the basis of compressed sensing (CS) and Lp regularization. The EMT inverse problem is converted into the L1 norm regularization problem using the advantages of the compressed sensing theory. To combine the merits of L1 and L2 regularization, Lp regularization is deployed as the regularizer taking the place of L1 norm, which can overcome the over-smoothing and over-sparsity of the reconstruction objects. A modified split Bregman (SB) method is exploited to effectively cope with the Lp regularization problem. An accelerating method is further applied to improve the reconstruction speed. The sensitivity matrix calculation is performed by the perturbation method. Simulation studies are implemented to show the superiority of the presented method in comparison with the classical methods. The effectiveness of the proposed method is further validated by the developed EMT system. Experimental results confirm that the proposed method has better imaging capability, which provides a great candidate for the practical application of EMT.

Sparse-View Computed Tomography Reconstruction Based on a Novel Improved Prior Image Constrained Compressed Sensing Algorithm

The problem of sparse-view computed tomography (SVCT) reconstruction has become a popular research issue because of its significant capacity for radiation dose reduction. However, the reconstructed images often contain serious artifacts and noise from under-sampled projection data. Although the good results achieved by the prior image constrained compressed sensing (PICCS) method, there may be some unsatisfactory results in the reconstructed images because of the image gradient L1-norm used in the original PICCS model, which leads to the image suffering from step artifacts and over-smoothing of the edge as a result. To address the above-mentioned problem, this paper proposes a novel improved PICCS algorithm (NPICCS) for SVCT reconstruction. The proposed algorithm utilizes the advantages of PICCS, which could recover more details. Moreover, the algorithm introduces the L0-norm of image gradient regularization into the framework, which overcomes the disadvantage of conventional PICCS, and enhances the capability to retain edge and fine image detail. The split Bregman method has been used to resolve the proposed mathematical model. To verify the effectiveness of the proposed method, a large number of experiments with different angles are conducted. Final experimental results show that the proposed algorithm has advantages in edge preservation, noise suppression, and image detail recovery.

A novel method for increasing wind power output considering wind turbine failure

This work develops a complete process for power capture and power distribution. In our proposed approach, a power allocation model that considers wind turbine (WT) failure is presented using a new maximum power capture structure for wind farms (WFs). Specifically, the proposed approach adopts a hierarchical control strategy to maximize the wind power output from the WF. In the first level, a control strategy is employed between a centralized controller located in the substation and local controllers installed on each WT to maximize wind energy capture. Apart from this, we exploit a new competitive swarm optimizer with a local search (LSCSO) to implement the optimization process of maximum power capture at this level. In the second level, a new power allocation model that considers WT failure is presented, and the power distribution is optimized using a distributed split Bregman method (SBM). Finally, the proposed approach integrates the LSCSO-SBM method and yields improved wind-farm power optimization compared to traditional methods. Furthermore, this scheme has been applied to the Roy Billinton Test System to evaluate the reliability of the generating system, and the results demonstrate that the proposed approach can effectively reduce the impact of the wake effect and total electrical losses in WFs, especially the significant benefit of increasing the energy production of WFs and generating system reliability.

Using Legendre Spectral Element Method with Split Bregman Method for Solving Optimal Control Problem with Elliptic Partial Differential Equation Constraint

Using Legendre Spectral Element Method with Split Bregman Method for Solving Optimal Control Problem with Elliptic Partial Differential Equation Constraint

Retinex-qDPC: Automatic background-rectified quantitative differential phase contrast imaging

Background and objectiveThe quality of quantitative differential phase contrast reconstruction (qDPC) can be severely degenerated by the mismatch of the background of two oblique illuminated images, yielding problematic phase recovery results. These background mismatches may result from illumination patterns, inhomogeneous media distribution, or other defocusing layers. In previous reports, the background is manually calibrated which is time-consuming, and unstable, since new calibrations are needed if any modification to the optical system was made. It is also impossible to calibrate the background from the defocusing layers, or for high dynamic observation as the background changes over time. The background mismatch reduces the experimental robustness of qDPC and largely limits its applications. To tackle the mismatch of background and increases the experimental robustness, we propose the Retinex-qDPC. MethodsIn Retinex-qDPC, we replace the data fidelity term of the previous cost function for qDPC inverse problem, by the images’ edge features yielding L2-Retinex-qDPC and L1-Retinex-qDPC for high background-robustness qDPC reconstruction. The split Bregman method is used to solve the L1-Retinex DPC. We compare both Retinex-qDPC models against state-of-the-art DPC reconstruction algorithms including total-variation regularized qDPC, and isotropic-qDPC using both simulated and experimental data. ResultsRetinex qDPC can significantly improve the phase recovery quality by suppressing the impact of mismatch background. Within, the L1-Retinex-qDPC is better than L2-Retinex and other state-of-the-art qDPC algorithms. ConclusionsThe Retinex-qDPC increases the experimental robustness against background illumination without any modification of the optical system, which will benefit all qDPC applications.

A mixed finite element discretisation of linear and nonlinear multivariate splines using the Laplacian penalty based on biorthogonal systems

We consider a mixed finite element method for a linear multivariate spline using the Laplacian penalty. Our discretisation is based on biorthogonal systems leading to a very simple and efficient finite element scheme. We also extend our approach to a nonlinear case and describe a split Bregman iteration scheme for the resulting nonlinear equations. We apply our numerical schemes to remove the mixture of Gaussian and impulsive noise for some test images.•This paper presents a method of discretising a multivariate spline using a finite element method.•The method uses a biorthogonal system to achieve an efficient finite element method.•The method is extended to cover a discretisation scheme for a nonlinear case, including an adaptation of the split Bregman method for the nonlinear case.

A split Bregman method solving optimal reactive power dispatch for a doubly-fed induction generator-based wind farm

This paper proposes an optimal reactive power control method to maximize wind farm revenue and minimize the total electrical losses of a doubly-fed induction generator (DFIG)-based wind farm. Specifically, the split Bregman method is used to solve the optimal control problem in a distributed manner. That is, the optimization problem is decomposed into sub-problems by the optimal distributed control strategy, and each sub-problem is solved independently in each local controller through the parallel method, which reduces the calculating burden and improves the information privacy. Thus, when a fault occurs, the proposed distributed control strategy can overcome the system fault and improve the reliability and security of the system. Furthermore, an economic financial model of annual revenue is contributed to examine the income impact with or without certified emission reduction (CER) by the clean development mechanism (CDM). Compared with the dual ascent (DA) method, sequential quadratic programming (SQP) method and the proportional dispatch method (PDM), the annual revenue (AR) of the wind farm using the proposed split Bregman method is the highest. Simulation results demonstrate that this method has promising performance in both optimization quality and computational efficiency.

Physics-informed multi-fidelity learning-driven imaging method for electrical capacitance tomography

The electrical capacitance tomography is considered to be a promising non-invasive visualization method for the measurement of multiphase flow parameters, but low-quality tomograms limit the reliability and accuracy of measurements. In order to overcome this limitation and bottleneck, the physics-informed data-dependent prior learned from the given samples is introduced and coupled with the measurement mechanism and the domain knowledge modeled by a new L1/L2 norm-based regularizer into a new optimization imaging model in this study. To improve the convergence and reduce the computational load, the built imaging model is solved by a new numerical scheme driven by the split Bregman method and the forward–backward splitting method. A new physics-informed robust sparse extreme learning machine method that not only obeys the measurement mechanism in training but also promotes the robustness and performance of the model is proposed and used to build a novel multi-fidelity learning method to infer the physics-informed data-dependent prior. The new imaging method achieves multi-source data fusion, leads to new changes in reconstruction algorithms, increases the complementarity and diversity of image priors, unifies the image reconstruction and multi-fidelity learning method, and improves robustness, numerical stability and flexibility of the model. The reconstruction results show that the new imaging method achieves more accurate reconstruction with reduced sensitivity to noise compared to important and popular imaging methods. This study leads to new changes in imaging algorithms and mining and use of image priors, and serves as a catalyst for the paradigm shift in image reconstruction.

Spectral CT reconstruction via Spectral-Image Tensor and Bidirectional Image-gradient minimization

It is challenging to obtain good image quality in spectral computed tomography (CT) as the photon-number for the photon-counting detectors is limited for each narrow energy bin. This results in a lower signal to noise ratio (SNR) for the projections. To handle this issue, we first formulate the weight bidirectional image gradient with L0-norm constraint of spectral CT image. Then, as a new regularizer, bidirectional image gradient with L0-norm constraint is introduced into the tensor decomposition model, generating the Spectral-Image Tensor and Bidirectional Image-gradient Minimization (SITBIM) algorithm. Finally, the split-Bregman method is employed to optimize the proposed SITBIM mathematical model. The experiments on the numerical mouse phantom and real mouse experiments are designed to validate and evaluate the SITBIM method. The results demonstrate that the SITBIM can outperform other state-of-the-art methods (including TVM, TV + LR, SSCMF and NLCTF). Index terms—spectral CT, image reconstruction, tensor decomposition, unidirectional image gradient, image similarity.

Computer-Assisted Quantitative Analysis of Skeletal Muscles of Snowboarding Parallel Giant Slalom Athletes after Exercise Based on Artificial Intelligence and Complex Networks.

The snowboarding project has the characteristics of high risk and high technical level. The current publicity level is not high, and the number of participants is also very limited. Another potential advantage medal breakthrough project that is expected to be achieved in the Winter Olympics has received a lot of attention, creating favorable opportunities for the promotion and development of this project in China. The event requires good special physical support, skeletal muscle contraction is the body to produce motor function, and special physical training and recovery are key factors for athletes to obtain excellent results in the competition. This article is aimed at performing ultrasonic quantitative analysis on the skeletal muscles of skiers after exercise based on artificial intelligence and complex networks and at studying the skeletal muscle conditions of snowboarders after exercise, so as to provide a certain theoretical basis for coaches in future scientific training. Based on a large amount of literature, this paper uses variational optical flow calculation and split Bregman method to solve the typical HS model, L1-L2 model, and L1-high-order model, respectively, and uses the motion estimation method to describe the movement of muscles. An experiment was designed to collect ultrasound images of the gastrocnemius and quadriceps muscles during contraction. In addition, a motion target positioning algorithm was used to obtain some motion parameters, which provided direct help for athletes in rationally arranging training load and scientific training. The experimental results in this paper show that the muscle motion features extracted from the ultrasound sequence images can quantitatively express a lot of important information about the skeletal muscle motion form and function and have potential practical application value. And the different invariants of each type of ski trajectory vary greatly, floating between 1.5429 and 7.6759.

Level set framework based on local scalable Gaussian distribution and adaptive-scale operator for accurate image segmentation and correction

Active contour model is a popular image segmentation method, but its current development is still limited by the problem of uneven image intensity. This paper proposes a new active contour model based on level set framework using local scalable Gaussian distribution (LSGD) and adaptive-scale operator for accurate image segmentation and correction, and uses the split Bregman method to minimize the energy functional. We construct a fitting energy with local Gaussian distribution characteristics, and segment the image with the maximum posterior probability. Then we use an adaptive-scale operator to adjust the scale of the LSGD according to the degree of the intensity inhomogeneity. In addition, the bias field information is added to the model to achieve better robustness to unevenness and correction effects. Moreover, the energy functional is minimized by the split Bregman method to improve the efficiency of image segmentation. In order to meet the needs of more diverse image segmentation, we extend the two-phase energy functional to the multi-scale and the vector-valued energy functionals. To evaluate the effectiveness of the proposed methods, we select the composite images as well as brain MRI, melanoma and Berkeley nature images. We select the quantitative indexes to evaluate the image segmentation effect, including JS, Dice, CV, the Precision and Recall, correlation index, SSIM and MSE index. We compare our model with the classic traditional image segmentation models and U-net machine learning model. Experimental results show that the models can perform appropriate segmentation and bias field estimation, and the quantitative index values are better than other segmentation methods.

Hue-preserving image enhancement via complementary enhancing terms

Hue-preserving image enhancement is a very challenging and important research topic in image/video processing and computer vision fields. In the past decades, spectral methods, histogram-based methods, and spatial methods are proposed to partially tackle this problem. However, most of them still suffer from the challenges in enhancing color images while preventing hue shift. In this paper, we build two complementary terms in a variational framework for enhancing images: one is for increasing the image brightness, and the other is for strengthening the edge structure. The two enhancing terms are adaptively united to enhance color images and preserve the original hue simultaneously. The existence and uniqueness of minimizer for the proposed variational model are rigorously established. An efficient numerical implementation of our model is also accomplished via the popular split Bregman method. A number of numerical experiments and comparisons with some state-of-the-art methods are conducted to demonstrate the good performance of the newly proposed model.

Using the Split Bregman Algorithm to Solve the Self-repelling Snakes Model

Preserving contour topology during image segmentation is useful in many practical scenarios. By keeping the contours isomorphic, it is possible to prevent over-segmentation and under-segmentation, as well as to adhere to given topologies. The Self-repelling Snakes model (SR) is a variational model that preserves contour topology by combining a non-local repulsion term with the geodesic active contour model. The SR is traditionally solved using the additive operator splitting (AOS) scheme. In our paper, we propose an alternative solution to the SR using the Split Bregman method. Our algorithm breaks the problem down into simpler sub-problems to use lower-order evolution equations and a simple projection scheme rather than re-initialization. The sub-problems can be solved via fast Fourier transform or an approximate soft thresholding formula which maintains stability, shortening the convergence time, and reduces the memory requirement. The Split Bregman and AOS algorithms are compared theoretically and experimentally.

Numerical Identification of Nonlocal Potentials in Aggregation

Aggregation equations are broadly used to model population dynamics with nonlocal interactions, characterized by a potential in the equation. This paper considers the inverse problem of identifying the potential from a single noisy spatial-temporal process. The identification is challenging in the presence of noise due to the instability of numerical differentiation. We propose a robust model-based technique to identify the potential by minimizing a regularized data fidelity term, and regularization is taken as the total variation and the squared Laplacian. A split Bregman method is used to solve the regularized optimization problem. Our method is robust to noise by utilizing a Successively Denoised Differentiation technique. We consider additional constraints such as compact support and symmetry constraints to enhance the performance further. We also apply this method to identify time-varying potentials and identify the interaction kernel in an agent-based system. Various numerical examples in one and two dimensions are included to verify the effectiveness and robustness of the proposed method.