Kernel Correntropy Conjugate Gradient Algorithms Based on Half-Quadratic Optimization

Xiong, Kui; Iu, Herbert Ho-Ching; Wang, Shiyuan

doi:10.1109/tcyb.2019.2959834

Cited by 38 publications

(19 citation statements)

References 40 publications

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“…The behavior of the minimizing sequence is also a challenging problem, which is closely related to Perona and Malik anisotropic diffusion [23] whose associated potential is nonconvex also. In spite of the lack of a rigorous mathematical theory for the continuous minimization problem with nonconvex potential, its associated discrete version can be solved numerically, for example, with the gradient decent algorithm [23], the simulated annealing algorithm [24], the half-quadratic algorithms [18,20,21,[25][26][27][28][29], and so on. The nonconvex potential always leads to the backward diffusion equation or the forward-backward diffusion equation, which can sharpen the edges, corners, as well as the singular features.…”

Section: Nonconvex Variational Model and Backward Diffusion Equationmentioning

confidence: 99%

A class of singular diffusion equations based on the convex–nonconvex variation model for noise removal

Dong

2021

Bound Value Probl

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This paper focuses on the problem of noise removal. First, we propose a new convex–nonconvex variation model for noise removal and consider the nonexistence of solutions of the variation model. Based on the new variation method, we propose a class of singular diffusion equations and prove the of solutions and comparison rule for the new equations. Finally, experimental results illustrate the effectiveness of the model in noise reduction.

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Section: Nonconvex Variational Model and Backward Diffusion Equationmentioning

confidence: 99%

A class of singular diffusion equations based on the convex–nonconvex variation model for noise removal

Dong

2021

Bound Value Probl

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“…By making use of the orthogonal search direction, such method can achieve faster convergence than the SG method [121]. Recently, the CG method and its variants have received increased attention in kernel adaptive filters [122], [123] and beamforming [124], [125]. However, there is scarce literature focused on using the CG-type algorithm for combating impulsive noise.…”

Section: Introductionmentioning

confidence: 99%

Conjugate Gradient Adaptive Learning with Tukey's Biweight M-Estimate

Lu¹,

Chen²,

Lamare³

et al. 2022

Preprint

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We propose a novel M-estimate conjugate gradient (CG) algorithm, termed Tukey's biweight M-estimate CG (TbMCG), for system identification in impulsive noise environments. In particular, the TbMCG algorithm can achieve a faster convergence while retaining a reduced computational complexity as compared to the recursive least-squares (RLS) algorithm. Specifically, the Tukey's biweight M-estimate incorporates a constraint into the CG filter to tackle impulsive noise environments. Moreover, the convergence behavior of the TbMCG algorithm is analyzed. Simulation results confirm the excellent performance of the proposed TbMCG algorithm for system identification and active noise control applications.

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Section: Introductionmentioning

confidence: 99%

“…However, these algorithms are not robust to non-Gaussian noises. By utilizing the kernel function, researchers have developed a series of adaptive filtering algorithms based on correntropy in [12][13][14][15][16][17][18][19][20][21] to make adaptive filtering algorithms robust in a non-Gaussian noise environment. In addition, some correntropy based spare adaptive filtering algorithms have also been proposed in [22][23][24][25], such as general zero attraction proportionate normalized maximum correntropy criterion (GZA-PNMCC) [22], correntropy induced metric maximum correntropy criterion (CIMMCC) [23], and group-constrained maximum correntropy criterion (GC-MCC) [24].Since signals are represented in the complex-valued form in many scenarios, adaptive filtering in the complex-valued domain attracts considerable critical attention of researchers, then a series of adaptive filtering algorithms are followed, including complex LMS (CLMS) algorithm [26] and complex correntropy based algorithms [27][28][29][30][31].…”

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confidence: 99%

Maximum Total Improper Complex Correntropy Algorithm for Widely Linear Adaptive Filtering

Fu¹,

Li²

2022

IEEE Access

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The maximum total complex correntropy (MTCC) algorithm improves the performance of adaptive filtering under the error in variable (EIV) model by integrating both input and output noise information into the total complex correntropy. However, the MTCC algorithm cannot be applied to the widely linear model, directly. Compared with a strictly linear model, the widely linear model provides the complete statistical information of signals for adaptive filtering. This paper first constructs a novel cost function for the widely linear model by incorporating the input and output noise information into the improper complex correntropy. Then, a novel widely linear adaptive filter algorithm named widely linear maximum total improper complex correntropy (WL-MTICC) is proposed using the gradient descent method under the maximum total improper correntropy criterion. Finally, the analysis of local stability and convergence in the mean sense regarding the proposed WL-MTICC algorithm is provided. Simulations are used to show the performance advantage of the proposed WL-MTICC algorithm in the presence of both input and output noises.INDEX TERMS adaptive filter, convergence, stability, total complex correntropy, widely linear model. I. INTRODUCTIONSince adaptive filtering adjusts the filter parameters flexibly by combining the input and expected signals, it has been developed well in signal processing, control, communication, and other scenarios [1-2]. The original adaptive filtering algorithm aimed at the real-valued field, and its classical representative is the least-mean-square (LMS) [3][4][5] algorithm. LMS has the good properties of fast convergence and simple structure. Researchers have made certain improvements in developing a series of LMS algorithm variations to further improve the convergence performance and steady-state performance of LMS in a Gaussian environment [6][7][8][9]. In addition, to improve the performance of LMS type algorithms for colored inputs, affine projection algorithm (APA) and recursive least-squares (RLS) were also developed in [10][11]. However, these algorithms are not robust to non-Gaussian noises. By utilizing the kernel function, researchers have developed a series of adaptive filtering algorithms based on correntropy in [12][13][14][15][16][17][18][19][20][21] to make adaptive filtering algorithms robust in a non-Gaussian noise environment. In addition, some correntropy based spare adaptive filtering algorithms have also been proposed in [22][23][24][25], such as general zero attraction proportionate normalized maximum correntropy criterion (GZA-PNMCC) [22], correntropy induced metric maximum correntropy criterion (CIMMCC) [23], and group-constrained maximum correntropy criterion (GC-MCC) [24].Since signals are represented in the complex-valued form in many scenarios, adaptive filtering in the complex-valued domain attracts considerable critical attention of researchers, then a series of adaptive filtering algorithms are followed, including complex LMS (CLMS) algorithm [26] and complex correntr...

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Kernel Correntropy Conjugate Gradient Algorithms Based on Half-Quadratic Optimization

Cited by 38 publications

References 40 publications

A class of singular diffusion equations based on the convex–nonconvex variation model for noise removal

A class of singular diffusion equations based on the convex–nonconvex variation model for noise removal

Conjugate Gradient Adaptive Learning with Tukey's Biweight M-Estimate

Maximum Total Improper Complex Correntropy Algorithm for Widely Linear Adaptive Filtering

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