Splitting Algorithm Research Articles

Blind deblurring text images via Beltrami regularization

This article proposes a blind image deblurring model based on Beltrami regularization. The existence and uniqueness of the Beltrami model are proved, and we perform a theoretical analysis of the convergence and error estimation of the algorithm for solving the Beltrami regularization model. Meanwhile, we apply a half-quadratic splitting algorithm to solve it and obtain the blur kernel of the blurred image. Furthermore, we get a clean image through some non-blind deblurring algorithms. Finally, we compare this with the state-of-art methods, and our algorithm has specific performance improvements and advantages in the text images.© 2024 Elsevier Ltd. All rights reserved.

Stereoscopic artificial compound eyes for spatiotemporal perception in three-dimensional space.

Arthropods' eyes are effective biological vision systems for object tracking and wide field of view because of their structural uniqueness; however, unlike mammalian eyes, they can hardly acquire the depth information of a static object because of their monocular cues. Therefore, most arthropods rely on motion parallax to track the object in three-dimensional (3D) space. Uniquely, the praying mantis (Mantodea) uses both compound structured eyes and a form of stereopsis and is capable of achieving object recognition in 3D space. Here, by mimicking the vision system of the praying mantis using stereoscopically coupled artificial compound eyes, we demonstrated spatiotemporal object sensing and tracking in 3D space with a wide field of view. Furthermore, to achieve a fast response with minimal latency, data storage/transportation, and power consumption, we processed the visual information at the edge of the system using a synaptic device and a federated split learning algorithm. The designed and fabricated stereoscopic artificial compound eye provides energy-efficient and accurate spatiotemporal object sensing and optical flow tracking. It exhibits a root mean square error of 0.3 centimeter, consuming only approximately 4 millijoules for sensing and tracking. These results are more than 400 times lower than conventional complementary metal-oxide semiconductor-based imaging systems. Our biomimetic imager shows the potential of integrating nature's unique design using hardware and software codesigned technology toward capabilities of edge computing and sensing.

An efficient hybrid genetic algorithm for the traveling salesman problem with release dates

This paper deals with a generalization of the classic traveling salesman problem where each customer is associated with a release date, defined as the time at which the desired product becomes available at the depot. In this problem, a single uncapacitated vehicle is allowed to perform multiple trips in order to satisfy all demands. However, the vehicle cannot start a route unless all the products associated with the demands in the route are released. As a consequence, there might be a waiting time before starting the next route. The objective of the problem is to minimize the completion time of the service, defined as the time at which the vehicle returns to the depot after satisfying all demands. We propose a hybrid genetic algorithm that incorporates more advanced mechanisms to evaluate individuals and to ensure population diversity. We also introduce a novel dynamic programming splitting algorithm that converts a sequence of visits to customers, the so-called giant-tour, into the best set of routes that respects the sequence. Computational experiments performed on 522 benchmark instances show that our approach is able to find all 154 known optimal solutions from the literature. In addition, we were able to improve the best-known upper bounds for 364 instances in significantly shorter computational times when compared to the state-of-the-art.

Short message encryption technology of Beidou communication based on SM9

AbstractTo reduce the security authentication time cost, forwarding delay, and enhance message security of Beidou communication short messages, this paper proposes a Beidou communication short message encryption technology based on SM9 (Mobile Code Secure Communication). This technology uses split hierarchical clustering algorithm to cluster the short message data of Beidou Communication, in order to unify the processing of similar short message data and improve the encryption efficiency of subsequent short messages. Based on the data clustering results, this paper constructs a short message forwarding verification model using the SM9 identification password algorithm, and provides the message content of the communication application protocol and the communication receiving information protocol to achieve low‐cost and efficient forwarding verification. In addition, this article improves the initial value selection of Logistic chaotic mapping by coupling the tent map with coupled mapping lattice (CML) in the spatiotemporal chaos model to generate a chaotic initial value sequence, thereby expanding the key space, enhancing the ability to resist exhaustive attacks, enhancing the randomness of the generated key parameters, and optimizing the encryption effect of short messages. The experimental results show that the short message security authentication time of the technology proposed in this article is basically controlled within 25 ms, and the minimum forwarding delay is only 23.9 ms, which can effectively resist attacks and improve the security of Beidou communication.

Improved quantification in CEST-MRI by joint spatial total generalized variation.

In this work, the use of joint Total Generalized Variation (TGV) regularization to improve Multipool-Lorentzian fitting of chemical exchange saturation transfer (CEST) Spectra in terms of stability and parameter signal-to-noise ratio (SNR) was investigated. The joint TGV term was integrated into the nonlinear parameter fitting problem. To increase convergence and weight the gradients, preconditioning using a voxel-wise singular value decomposition was applied to the problem, which was then solved using the iteratively regularized Gauss-Newton method combined with a Primal-Dual splitting algorithm. The TGV method was evaluated on simulated numerical phantoms, 3T phantom data and 7T in vivo data with respect to systematic errors and robustness. Three reference methods were also implemented: The standard nonlinear fitting, a method using a nonlocal-means filter for denoising and the pyramid scheme, which uses downsampled images to acquire accurate start values. The proposed regularized fitting method showed significantly improved robustness (compared to the reference methods). In testing, over a range of SNR values the TGV fit outperformed the other methods and showed accurate results even for large amounts of added noise. Parameter values found were closer or comparable to the ground truth. For in vivo datasets, the added regularization increased the parameter map SNR and prevented instabilities. The proposed fitting method using TGV regularization leads to improved results over a range of different data-sets and noise levels. Furthermore, it can be applied to all Z-spectrum data, with different amounts of pools, where the improved SNR and stability can increase diagnostic confidence.

Tseng-type splitting projection algorithms for equilibrium problems in Hilbert spaces

In this work, based on the subgradient-type projection method considered by Santos and Scheimberg (Optimization, 2017), we propose some Tseng-type splitting algorithms for solving equilibrium problems whose bifunction is decomposed into the sum of two bifunctions in Hilbert spaces. We establish the weak and strong convergence of the proposed algorithm under standard assumptions. Numerical results in Nash–Cournot oligopolistic electricity market equilibrium model and comparisons with other related methods demonstrate the effectiveness of the proposed algorithm.

Knockoffs-SPR: Clean Sample Selection in Learning With Noisy Labels.

A noisy training set usually leads to the degradation of the generalization and robustness of neural networks. In this article, we propose a novel theoretically guaranteed clean sample selection framework for learning with noisy labels. Specifically, we first present a Scalable Penalized Regression (SPR) method, to model the linear relation between network features and one-hot labels. In SPR, the clean data are identified by the zero mean-shift parameters solved in the regression model. We theoretically show that SPR can recover clean data under some conditions. Under general scenarios, the conditions may be no longer satisfied; and some noisy data are falsely selected as clean data. To solve this problem, we propose a data-adaptive method for Scalable Penalized Regression with Knockoff filters (Knockoffs-SPR), which is provable to control the False-Selection-Rate (FSR) in the selected clean data. To improve the efficiency, we further present a split algorithm that divides the whole training set into small pieces that can be solved in parallel to make the framework scalable to large datasets. While Knockoffs-SPR can be regarded as a sample selection module for a standard supervised training pipeline, we further combine it with a semi-supervised algorithm to exploit the support of noisy data as unlabeled data. Experimental results on several benchmark datasets and real-world noisy datasets show the effectiveness of our framework and validate the theoretical results of Knockoffs-SPR.

Evaluation of low-dose computed tomography reconstruction using spatial-radon domain total generalized variation regularization

The x-ray radiation dose in computed tomography (CT) examination has been a major concern for patients. Lowing the tube current and exposure time in data acquisition is a straightforward and cost-effective strategy to reduce the x-ray radiation dose. However, this will inevitably increase the noise fluctuations in measured projection data, and the corresponding CT image quality will be severely degraded if noise suppression is not performed during image reconstruction. To reconstruct high-quality low-dose CT image, we present a spatial-radon domain total generalized variation (SRDTGV) regularization for statistical iterative reconstruction based on penalized weighted least-squares (PWLS) principle, which is called PWLS-SRDTGV for simplicity. The presented PWLS-SRDTGV model can simultaneously reconstruct high-quality CT image in space domain and its corresponding projection in radon domain. An efficient split Bregman algorithm was applied to minimize the cost function of the proposed reconstruction model. Qualitative and quantitative studies were performed to evaluate the effectiveness of the PWLS-SRDTGV image reconstruction algorithm using a digital 3D XCAT phantom and an anthropomorphic torso phantom. The experimental results demonstrate that PWLS-SRDTGV algorithm achieves notable gains in noise reduction, streak artifact suppression, and edge preservation compared with competing reconstruction approaches.

Relaxed Inertial Projective Forward-backward Splitting Algorithms for Regularized Least Square Problems

This study presents flexible conditions of the inertial extrapolation parameter for easy implementation that is added to the algorithm in faster convergence. Modified inertial forward-backward splitting algorithms for solving variational inclusion problems are introduced to apply to solve the LASSO problem for image restoration and signal recovery, and the elastic net model for classification problem. Projection methods are used in the final step for narrowing down the search field, resulting in a better solution.

A hybrid genetic search and dynamic programming-based split algorithm for the multi-trip time-dependent vehicle routing problem

We design a hybrid algorithm for the multi-trip time-dependent vehicle routing problem (MT-TD-VRP). One of its components is the Time-Dependent SPlit Algorithm (TD-SPA), which is a dynamic programming-based algorithm specifically designed to handle both the multi-trip per vehicle and the time-dependent aspects of the problem. The hybrid algorithm combines the proposed TD-SPA, designed to efficiently split a giant tour into complete vehicle routes, with a genetic algorithm for generating these tours. We introduce a monotone queue optimization (MQO) technique to accelerate the TD-SPA. The effectiveness of MQO is evaluated by comparing computation times between the original split algorithm for the capacitated vehicle routing problem (CVRP) and its MQO-enhanced counterpart. Extensive numerical experiments with a real-world dataset from a Singapore food and beverage company are conducted to assess our algorithm’s performance on various MT-TD-VRP instances. The results indicate that our algorithm surpasses the performance of the commercial solver Gurobi, with an average improvement of 25.13% on the best solutions found within a prescribed duration. Our numerical simulations further reveal the algorithm’s ability to efficiently solve both the capacitated vehicle routing problem (CVRP) and the multi-trip vehicle routing problem (MTVRP), consistently producing competitive solutions. Moreover, to highlight the importance of incorporating the time-dependent (TD) factor into our model and algorithm, we demonstrate a notable enhancement in performance–averaging at 7.47% for the best solutions under TD conditions for an MTVRP dataset.

Robust image segmentation and bias field correction model based on image structural prior constraint

In this paper, we propose an advanced variational model for image segmentation and bias correction. In contrast to the majority of existing level set segmentation models that only consider illumination bias fields, we additionally consider the impact of image reflectance on segmentation accuracy. Our method is capable of effectively segmenting images with blurry edge structures affected by non-uniform illumination. In order to enhance segmentation efficiency, we directly segment the underlying structures of the images, construct spatial prior and apply adaptive regularization constraints on the structural component. Therefore, in the process of segmentation, the proposed algorithm can accurately identify object boundaries without being affected by the environment. Besides, the GL operator is applied to enhance the robustness of the model against noise. Furthermore, we use the alternating direction method of multipliers and the operator splitting algorithm for numerical solution. The experimental results obtained from various sorts of images illustrate that our model outperforms many leading-edge level set models with regard to robustness, corrected results and accuracy.

Splitting algorithms for solving state-dependent maximal monotone inclusion problems

We consider the state-dependent maximal monotone inclusion problem and propose forward-backward splitting algorithms for solving it. Strong convergence of the proposed algorithms is established under suitable conditions. For the special separable case, we present an improved Douglas–Rachford variant that can be easily implemented. Moreover, some accelerated forward-backward splitting algorithms are also presented. Preliminary numerical experiments with comparisons to existing results are presented, illustrating the advantages of our methods.

Pre-service mathematics teachers' performance prediction using a modified Mann-Tseng forward-backward splitting algorithm

Pre-service mathematics teachers' performance prediction using a modified Mann-Tseng forward-backward splitting algorithm

Split Bregman quantum noise removal algorithm for 3D reconstruction of neutron computed tomography image

The low intensity of the neutron source for neutron computed tomography (CT) results in a long acquisition time for a single projection, which causes the neutron projection data to contain a large amount of quantum noise. Quantum noise will degrade the quality of neutron CT reconstruction images. Therefore, an efficient quantum noise removal algorithm must be used in CT reconstruction. In this paper, an efficient quantum noise removal algorithm for neutron CT 3D image reconstruction is proposed by analysing classical image processing algorithms and quantum image processing algorithms, which employs the maximum likelihood expectation maximization to reconstruct the image and split Bregman algorithm to solve for the total variation (MLEM-SBTV). Experimental results show that MLEM-SBTV performs well in removing quantum noise and reconstructing the detailed structure of images.

Local regularization assisted split augmented Lagrangian shrinkage algorithm for feature selection in condition monitoring

Feature selection plays a vital role in improving the efficiency and accuracy of condition monitoring by constructing sparse but effective models. In this study, an advanced feature selection algorithm named the local regularization assisted split augmented Lagrangian shrinkage algorithm (LR-SALSA) is proposed. The feature selection is realized by solving a l1-norm optimization problem, which usually selects more sparse and representative features at less computational costs. The proposed algorithm operates in two stages, namely variable selection and coefficient estimation. In the stage of variable selection, the primal problem is converted into three subproblems which can be solved separately. Then individual penalty parameters are applied to every coefficient of the model when dealing with the first subproblem. Under the Bayesian evidence framework, an iterative algorithm is derived to optimize these hyperparameters. During the optimization process, redundant variables will be pruned to guarantee model sparsity and improve computational efficiency at the same time. In the second stage, the coefficients for the selected model terms are determined using the least squares technique. The superior performance and efficiency of the proposed LR-SALSA method are validated through two numerical examples and a real-world cutting tool wear prediction case study. Compared with the existing methods, the proposed method can generate a sparse model and ensure a good trade-off between estimation accuracy and computational efficiency.

Forward-backward-half forward splitting algorithm with deviations

ABSTRACT In this paper, we present a forward-backward-half forward splitting algorithm with deviations for solving the structured monotone inclusion problem composed of a maximally monotone operator, a maximally monotone and Lipschitz continuous operator and a cocoercive operator. The weak and linear convergence of the proposed algorithms is established. The aim of introducing deviations is to improve the performance of the forward-backward-half forward splitting algorithm through suitable choices of the deviations. A numerical example is given to show that the two-step inertial variant of the forward-backward-half forward splitting algorithms with deviations outperforms the existing methods in Briceño-Arias and Davis [Forward-backward-half forward algorithm for solving monotone inclusions, SIAM J Optimiz, 2017;28(4):2839–2871. doi: 10.1137/17M1120099], Zong et al. [An accelerated forward-backward-half forward splitting algorithm for monotone inclusion with applications to image restoration, Optimization, 2022;73(2):401–428. doi: 10.1080/02331934.2022.2107926] and Fan et al. [Convergence of an inertial shadow Douglas–Rachford splitting algorithm for monotone inclusions, Numer Func Anal Optim, 2021;42(14):1627–1644. doi: 10.1080/01630563.2021.2001749].

Two-echelon time-dependent vehicle routing problem with simultaneous pickup and delivery and satellite synchronization

The multi-echelon distribution strategy has been widely applied in city logistics systems. This study develops a mixed-integer linear programming model for a new variant of vehicle routing problem, namely, a two-echelon time-dependent vehicle routing problem with simultaneous pickup and delivery and satellite synchronization, in which customers are divided into multiple customer regions according to different geographical characteristics. The pickup and delivery activities with hard time windows are performed simultaneously by the same vehicles from depots to satellites in the first echelon and from satellites to customers in different customer regions in the second echelon. A vehicle speed function is developed for each echelon based on traffic conditions. The function depends on commuter traffic and urbanization level. Satellites with storage buffer capacities for split and consolidation are allowed. Thus, demand unloading, storage, and reloading are synchronized. Costs of transportation, loading/unloading, inventory, and environment during one complete distribution process are considered. A memetic algorithm (MA) is proposed including a split algorithm for chromosome decoding and a three-phase construction heuristic for initial population generation. Self-adaptive operators of crossover, mutation, and local search are designed, and a neighborhood route improvement strategy is devised that includes distance-related destroy, route-based destroy, distance-based greedy repair, and time-distance cluster repair operators. Results of different scales of numerical experiments and sensitivity analysis show the effectiveness of the model and MA by comparing it with an exact algorithm, CPLEX, and adaptive large neighborhood search.

The International Association for the Study of Lung Cancer Mesothelioma Staging Project: Proposals for Revisions of the “T” Descriptors in the Forthcoming Ninth Edition of the TNM Classification for Pleural Mesothelioma

IntroductionThe primary tumor (T) component in the eighth edition of pleural mesothelioma (PM) staging system is based on pleural involvement and extent of invasion. Quantitative assessment of pleural tumor has been found to be prognostic. We explored quantitative and qualitative metrics to develop recommendations for T descriptors in the upcoming ninth edition of the PM staging system. MethodsThe International Association for the Study of Lung Cancer prospectively collected data on patients with PM. Sum of maximum pleural thickness (Psum) was recorded. Optimal combinations of Psum and eighth edition cT descriptors were assessed using recursive binary splitting algorithm, with bootstrap resampling to correct for the adaptive nature of the splitting algorithm, and validated in the eighth edition data. Overall survival (OS) was calculated by the Kaplan-Meier method and differences in OS assessed by the log-rank test. ResultsOf 7338 patients submitted, 3598 were eligible for cT analysis and 1790 had Psum measurements. Recursive partitioning identified optimal cutpoints of Psum at 12 and 30 mm, which, in combination with extent of invasion, yielded four prognostic groups for OS. Fmax greater than 5 mm indicated poor prognosis. cT4 category (based on invasion) revealed similar performance to eighth edition. Three eighth edition descriptors were eliminated based on low predictive accuracy. Eighth edition pT descriptors remained valid in ninth edition analyses. ConclusionGiven reproducible prognostication by Psum, size criteria will be incorporated into cT1 to T3 categories in the ninth edition. Current cT4 category and all pT descriptors will be maintained, with reclassification of fissural invasion as pT2.

A novel predictive–reactive scheduling method for parallel batch processor lot-sizing and scheduling with sequence-dependent setup time

In practical printed circuit boards (PCB) drilling production systems, multiple spindle processing capabilities and uncertainties are commonplace. This paper addresses predictive–reactive scheduling, considering parallel batch processor lot-sizing and scheduling with sequence-dependent setup times in a dynamic environment. We propose a predictive scheduling algorithm named S-AGAIG to balance machine spindle utilization and order tardiness in steps. Multiple splitting solutions are first formed by using a split heuristic algorithm to size the sub-lots of orders. Then the adaptive genetic algorithm with iterated greedy search is applied to select the solutions and scheduling. Furthermore, we present a schedule repair strategy based on sub-lot co-processing considering the impact of critical sub-lots, and construct a scheduling stability metric for rescheduling. In 36 sets of case experiments encompassing diverse load and machine type configurations, S-AGAIG showcases a 21.27% enhancement in average tardiness performance when compared to its closest rival. Across 28 cases involving varying disturbances, the framework demonstrates exceptional robustness.

Supplier selection for carbon emission reduction collaboration in green supply chain using an improved multi-criteria decision-making method

PurposePlatform-based enterprises, as micro-entities in the platform economy, have the potential to effectively promote the low-carbon development of both supply and demand sides in the supply chain. Therefore, this paper aims to provide a multi-criteria decision-making method in a probabilistic hesitant fuzzy environment to assist platform-type companies in selecting cooperative suppliers for carbon reduction in green supply chains.Design/methodology/approachThis paper combines the advantages of probabilistic hesitant fuzzy sets (PHFS) to address uncertainty issues and proposes an improved multi-criteria decision-making method called PHFS-DNMEREC-MABAC for aiding platform-based enterprises in selecting carbon emission reduction collaboration suppliers in green supply chains. Within this decision-making method, we enhance the standardization process of both the DNMEREC and MABAC methods by directly standardizing probabilistic hesitant fuzzy elements. Additionally, a probability splitting algorithm is introduced to handle probabilistic hesitant fuzzy elements of varying lengths, mitigating information bias that traditional approaches tend to introduce when adding values based on risk preferences.FindingsIn this paper, we apply the proposed method to a case study involving the selection of carbon emission reduction collaboration suppliers for Tmall Mart and compare it with the latest existing decision-making methods. The results demonstrate the applicability of the proposed method and the effectiveness of the introduced probability splitting algorithm in avoiding information bias.Originality/valueFirstly, this paper proposes a new multi-criteria decision making method for aiding platform-based enterprises in selecting carbon emission reduction collaboration suppliers in green supply chains. Secondly, in this method, we provided a new standard method to process probability hesitant fuzzy decision making information. Finally, the probability splitting algorithm was introduced to avoid information bias in the process of dealing with inconsistent lengths of probabilistic hesitant fuzzy elements.