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An adaptive fractional-order regularization primal-dual image denoising algorithm based on non-convex function

APPLIED MATHEMATICAL MODELLING 2024年 131卷 67-83页

作者： Li, Minmin Bi, Shaojiu Cai, Guangcheng Kunming Univ Sci & Technol Dept Math Kunming 650500 Yunnan Peoples R China

In this paper, a novel non-convex fractional-order image denoising model is proposed to suppress the staircase effect produced by the TV model while maintaining a neat contour. The model combines l(q) (0<q<1) qu... 详细信息

关键词： Image denoising Diffusion coefficient Fractional-order non-convex function Primal-dual algorithm Complexity analysis

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Intelligent optimization algorithm of non-convex function based on genetic algorithm

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2018年第4期35卷 4289-4297页

作者： Zhao, Xi Li, Ying Boonen, P. Guangdong Polytech Sci & Technol Comp Engn Tech Coll Zhuhai 519090 Peoples R China Tilburg Univ Dept Econometr & Operat Res Tilburg Netherlands

There are many local optimums for the non-convex function. The traditional algorithm is easy to fall into the local optimum and cannot obtain the optimal solution of non-convex function. To address this problem, a new intelligent optimization algorithm for non-convex function based on genetic algorithm is proposed in this paper. A proximal point sequence is obtained by using the idea of proximal point algorithm. Two simple and easily solved non-convex function subproblems are constructed by convexity technique, cutting plane method, and alternating linearization method. The basic operation process of genetic algorithm is analyzed. The combination selection operator, the initial population molding, the cross probability and the mutation probability are improved to ensure the global optimum. The processing result of the non-convex function is taken as the objective function. The mapping relationship between the fitness function and the objective function is constructed. Intelligent optimization of non-convex function is achieved by optimized genetic algorithm. Experimental results show that the proposed algorithm can obtain the global optimal solution of the non-convex function, and the optimization performance is better.

关键词： Genetic algorithm non-convex function intelligence optimization global optimal solution

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Network resource information scheduling based on non-convex function optimization algorithm

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2018年第4期35卷 4215-4224页

作者： Liang, Peng Zhao, Huimin Caner, G. Guangdong Polytech Normal Univ Dept Comp Sci Guangzhou 510665 Guangdong Peoples R China San Diego State Univ Dept Geog San Diego CA 92182 USA

When the network resource information is scheduled with the current algorithm, the execution time of the resource scheduling task cannot be improved. The utilization of network resources is reduced in the case of the heavy scheduling task. To address this problem, a network resource information scheduling based on non-convex function optimization algorithm is proposed in this paper. The network resource is modeled as a non-convex function. The execution interval of task is divided into subspaces of multiple units. Task density is introduced into network resource scheduling model. In this model, computing resources and storage resources of the network are considered. Ant colony particle swarm optimization algorithm is used for scheduling with the built network resource scheduling model. The initial solution is obtained by initial search with the particle swarm algorithm. Then the initial solution is transformed into the initial pheromone distribution of the ant colony. The resource information is searched by using ant colony algorithm until the optimal solution is found, so as to achieve network resource information scheduling. Experimental results show that the proposed algorithm can reduce the execution time of task and improve the utilization rate of network resource information.

关键词： non-convex function network resource information scheduling joint scheduling algorithm

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A New Fractional-Order Regularization for Speckle Image Denoising: Preserving Edges and Features

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2025年第5期44卷 3570-3598页

作者： Laghrib, A. Nachaoui, A. Univ Sultan Moulay Slimane Equipe LMA ENSA Khouribga Beni Mellal Morocco Univ Nantes Lab Math Jean Leray CNRS UMR6629 2 Rue Houssiniere Nantes France

In this paper, we elaborate a novel variational model for image denoising, particularly focusing on scenarios with high levels of speckle noise. Our approach integrates fractional-order regularizers to better preserve image edges, overcoming the limitations of traditional methods in handling small gradient variations. The main contributions of our work include the introduction of a non-convex attached term with a fractional-order gradient penalization to mitigate the staircasing effect. Additionally, we incorporate a controlled parameter to manage gradient magnitudes while preserving image contours and texture. Experimental results demonstrate the effectiveness and robustness of our proposed method, yielding competitive performance against state-of-the-art speckle noise removal techniques.

关键词： non-convex function Speckle noise Fractional-order regularization AMM optimization

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An overlapping group sparse variation method for enhancing time-frequency modulation bispectrum characteristics and its applications in bearing fault diagnosis

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MEASUREMENT 2025年 249卷

作者： Zou, Xue Zhang, Kun Liu, Tongtong Jiang, Zuhua Xu, Yonggang Beijing Univ Technol Coll Mech & Energy Engn Beijing Engn Res Ctr Precis Measurement Technol & Beijing 100124 Peoples R China Inner Mongolia Univ Sci & Technol Inner Mongolia Key Lab Intelligent Diag & Control Baotou 014017 Peoples R China Shanghai Jiao Tong Univ State Key Lab Mech Syst & Vibrat Shanghai 200240 Peoples R China

Rolling bearings are essential for machines and their faults can cause significant losses. Extracting pulse components from vibrations is difficult due to complicated working conditions. In this paper, a two-dimensional overlapping group sparse variation method based on non-convex function for enhancing time-frequency modulation bispectrum characteristics (OGSVMB) to identify bearing faults is proposed. The time-frequency modulation bispectrum (TFMB) demodulates signals into bispectra, highlighting the relationship between resonance band and modulation frequency. A mathematical model is established with a non-convex penalty term to constrain the distribution of two-dimensional reconstructed signal. The optimization-minimization method is used to find an optimal solution, producing a bispectrum with clearer modulation characteristics and a high SNR by reducing noise and irrelevant components while preserving the group sparsity of TFMB. The modulation Gini index is introduced to adaptively determine group size. Finally, the optimal enhanced envelope spectrum is calculated through slice optimization to identify fault characteristics. The effectiveness of the proposed method in diagnosing rolling bearing faults is verified through simulation and experiments. Compared to MSB, original TFMB, Fast Kurtogram, and Autogram, the OGSVMB method is better at identifying bearing fault characteristics.

关键词： Overlapping group sparsity non-convex function Time-frequency modulation bispectrum Bearing fault diagnosis Signal processing

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Mixed Gaussian-impulse noise removal using non-convex high-order TV penalty

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APPLIED NUMERICAL MATHEMATICS 2024年 201卷 72-84页

作者： Liu, Xinwu Sun, Ting Guangxi Minzu Univ Sch Math & Phys Nanning 530006 Guangxi Peoples R China Hunan Univ Sci & Technol Sch Math & Computat Sci Xiangtan 411201 Hunan Peoples R China

To restore images with clear edge details and no staircase artifacts from degraded versions, this paper incorporates the C2 plus C0 data fidelity and non-convex high-order total variation regularizer to establish an optimization model for eliminating mixed Gaussian-impulse noise. Among them, the C2 fidelity is adopted to suppress Gaussian noise, while the C0-norm is more suitable for detecting and removing impulse noise. In addition, the non-convex regularization displays excellent performance in overcoming the staircase effect and preserving edge details. Computationally, by using the iteratively reweighted C1 algorithm and variable splitting method, this work designs a modified alternating minimization method to solve the optimization problem we construct. In theory, the convergence proof of our resulting algorithm is also presented. Finally, in the experimental section, we conduct extensive numerical experiments on degraded images and compare with other existing techniques. From the intuitive effects and restoration accuracy, it follows that our newly proposed method is effective and competitive for image deblurring and mixed noise removal.

关键词： Gaussian-impulse noise non-convex function High-order total variation C0-norm fidelity Alternating minimization method

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GLOBAL CONVERGENCE OF ALTERNATING DIRECTION METHOD OF MULTIPLIERS FOR INVEX OBJECTIVE LOSSES 49

GLOBAL CONVERGENCE OF ALTERNATING DIRECTION METHOD OF MULTIP...

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49th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Pinilla, Samuel Yeung, Siu-Lun Thiyagalingam, Jeyan Sci & Technol Facil Council Sci Comp Dept Harwell Berks England

ISBN: (纸本)9798350344868;9798350344851

The Alternating Direction Method of Multipliers (ADMM) is uniquely suited for large-scale signal restoration problems, owing to its parallelizability. ADMM has been successfully deployed into several imaging modalities, including blind ptychography, phase retrieval, computer tomography, network unrolling, and magnetic resonance imaging. It is not an overstatement to say that while global convergence guarantees of ADMM under convex objective losses cement its utility, non-convex objectives offer superior reconstruction quality at the expense of these guarantees. In this paper, we break new ground with the development of invex ADMM which retains global optima guarantees for a novel class of non-convex, invex losses - an invex function is a mapping where any critical point is a global minimizer. More specifically, we propose a family of invex losses for which ADMM converges to the global minima, along with their guarantees. Our experimental evaluation and theoretical results shows that the proposed approach is very promising, and can aid in extending existing convergences guarantees of ADMM beyond traditional convex settings.

关键词： ADMM Invexity convexity non-convex function Global optima

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non-convex variational model for image restoration under impulse noise

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SIGNAL IMAGE AND VIDEO PROCESSING 2022年第6期16卷 1549-1557页

作者： Liu, Xinwu Hunan Univ Sci & Technol Sch Math & Computat Sci Xiangtan 411201 Hunan Peoples R China

This paper proposes a novel non-convex regularization model for recovering the degraded images corrupted by impulse noise. The introduced model closely incorporates the advantages of total generalized variation and non-convex prior. This combination helps to eliminate the remaining staircase artifacts while preserving sharp edges and then results in the highly desirable restorations. To optimize the resulting minimizations, we develop in great detail two efficient numerical algorithms called primal-dual method and alternating minimization method. Several visual experiments and measurable comparisons, which indicate the visualization quality and restoration accuracy, are presented to demonstrate the outstanding performance of our new methods for image restoration under impulse noise over some well-developed numerical methods.

关键词： Impulse noise non-convex function Total generalized variation Primal-dual method Alternating minimization method

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non-convex High-Order TV and 0-Norm Wavelet Frame-Based Speckle Noise Reduction

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2022年第12期69卷 5174-5178页

作者： Liu, Xinwu Lian, Wenhui Hunan Univ Sci & Technol Sch Math & Computat Sci Xiangtan 411201 Hunan Peoples R China

To obtain natural restorations from the noisy images contaminated by speckle noise, this brief presents a novel hybrid non-convex regularizers model for image denoising. The proposed new variational model closely combines the superiorities of non-convex high-order total variation function and l(0)-norm wavelet frame. This combination helps to avoid the staircase artifacts and maintain discontinuities while removing noise. Numerically, by integrating two popular tools: iteratively reweighted l(1) algorithm and variable splitting method, a modified alternating minimization method is adopted to optimize the resulting minimization problem. Finally, compared with several despeckling methods, numerical experiments indicate the competitive performance of our solver in visual improvement and objective measurement.

关键词： TV Speckle Noise measurement Image edge detection Computational modeling Optimization Noise reduction Speckle noise total variation non-convex function l0-norm wavelet frame alternating minimization method

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A novel shrinkage operator for tensor completion with low-tubal-rank approximation

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DIGITAL SIGNAL PROCESSING 2024年 152卷

作者： Wu, Guangrong Li, Haiyang Tang, Yuchao Huang, Wenli Peng, Jigen Guangzhou Univ Sch Math & Informat Sci Guangzhou Peoples R China

The problem of tensor completion (TC) has significant practical significance and a wide range of application backgrounds. Various approaches have been used to solve this problem, including approximating the rank function through its convex envelope, the tensor nuclear norm. However, because of the gap between the rank function and its convex envelope, this method is often unsatisfactory in terms of achieving recovery. As a result, researchers have widely studied explicit non-convex functions that can better approximate the rank function. In this paper, we construct a novel shrinkage operator that functions as the proximal operator of non-convex function satisfying three critical properties: unbiasedness, sparsity, and continuity. While an explicit analytical expression for the induced non-convex function cannot be obtained, simulation experiments show that it approximates the rank function. By implementing the shrinkage operator in the TC framework, we can show that our iterative sequence converges to the Karush-Kuhn-Tucker (KKT) point. We have discovered that the convergence of the model can be guaranteed as long as certain properties hold for the shrinkage operator. Hence, this result can be extended to a class of shrinkage operators. Extensive experimental results illustrate that our proposed method achieves better recovery performance at the same sampling rate compared to other methods.

关键词： Low-tubal-rank approximation Tensor completion non-convex function The fraction shrinkage operator

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