Maximum correntropy adaptation approach for robust compressive sensing reconstruction

He, Yicong; Wang, Fei; Wang, Shiyuan; Cao, Jiuwen; Chen, Badong

doi:10.1016/j.ins.2018.12.039

Cited by 25 publications

(9 citation statements)

References 70 publications

(85 reference statements)

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“…The main property of correntropy is that it provides an effective mechanism to mitigate the influence of large outliers. Recently, correntropy has been successfully applied in various areas, such as signal processing [23], machine learning [24][25][26], adaptive filtering [27][28][29], and others [30][31][32].…”

Section: Mixture Correntropymentioning

confidence: 99%

Kernel Mixture Correntropy Conjugate Gradient Algorithm for Time Series Prediction

Xue

Luo

Gao

et al. 2019

Entropy

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Kernel adaptive filtering (KAF) is an effective nonlinear learning algorithm, which has been widely used in time series prediction. The traditional KAF is based on the stochastic gradient descent (SGD) method, which has slow convergence speed and low filtering accuracy. Hence, a kernel conjugate gradient (KCG) algorithm has been proposed with low computational complexity, while achieving comparable performance to some KAF algorithms, e.g., the kernel recursive least squares (KRLS). However, the robust learning performance is unsatisfactory, when using KCG. Meanwhile, correntropy as a local similarity measure defined in kernel space, can address large outliers in robust signal processing. On the basis of correntropy, the mixture correntropy is developed, which uses the mixture of two Gaussian functions as a kernel function to further improve the learning performance. Accordingly, this article proposes a novel KCG algorithm, named the kernel mixture correntropy conjugate gradient (KMCCG), with the help of the mixture correntropy criterion (MCC). The proposed algorithm has less computational complexity and can achieve better performance in non-Gaussian noise environments. To further control the growing radial basis function (RBF) network in this algorithm, we also use a simple sparsification criterion based on the angle between elements in the reproducing kernel Hilbert space (RKHS). The prediction simulation results on a synthetic chaotic time series and a real benchmark dataset show that the proposed algorithm can achieve better computational performance. In addition, the proposed algorithm is also successfully applied to the practical tasks of malware prediction in the field of malware analysis. The results demonstrate that our proposed algorithm not only has a short training time, but also can achieve high prediction accuracy.

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Section: Mixture Correntropymentioning

confidence: 99%

Kernel Mixture Correntropy Conjugate Gradient Algorithm for Time Series Prediction

Xue

Luo

Gao

et al. 2019

Entropy

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“…Recently, the correntropy [29] which is derived from the information theoretic learning has gained increasing attention in various applications such as robust compressive sensing [30], robust adaptive filtering [17], [18] and robust principal component analysis [31]. Correntropy denotes a local similarity measure between two random variables B and C, which can be expressed as…”

Section: B Maximum Correntropy Criterionmentioning

confidence: 99%

Robust Sparse Recovery in Impulsive Noise via M-Estimator and Non-Convex Regularization

Gao

Peng

et al. 2019

IEEE Access

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Robust sparse recovery aims at recovering a sparse signal or image from its compressed and contaminated measurements. Under the impulsive noise condition, the performance of traditional sparse recovery algorithms may deteriorate seriously for exploiting 2 -norm to model the non-Gaussian noise. In this paper, a novel formulation which combines the M-estimator and the non-convex regularization term is presented to address the issue of robust sparse recovery in the impulsive noise environment. Since the 2 -norm is highly sensitive to the large outliers appearing in impulse interference, we replace it with the robust M-estimators that have exhibited the powerful capability of suppressing impulsive noise in various scenarios. Meanwhile, the non-convex regularization is capable of overcoming the biased estimation problem induced by the convex 1 -norm regularization and thus can obtain more accurate reconstruction results. Furthermore, to solve the resulting non-convex formulation, an efficient first-order algorithm with low computational complexity is developed by utilizing the alternating direction method of multipliers framework and the half-quadratic optimization. The reconstruction experiments under the circumstance of impulsive noise are conducted to demonstrate the superior performance of the proposed algorithm over several typical sparse recovery algorithms.INDEX TERMS Robust sparse recovery, alternating direction method of multipliers (ADMM), half-quadratic (HQ) optimization, M-estimator, impulsive noise.

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“…The 0 -MCC algorithm was first introduced in [44]. It uses the MCC to filter outliers in a compressive sensing problem, but although the good performance in the presence of impulsive noise, its application is restricted for real-valued data only.…”

Section: -Maximum Complex Correntropy Criterionmentioning

confidence: 99%

“…It uses the MCC to filter outliers in a compressive sensing problem, but although the good performance in the presence of impulsive noise, its application is restricted for real-valued data only. Since many compressive sensing problems deal with complex-valued data, instead of doing the minimization showed in (1), let us define a new cost function J inspired in [44] as…”

Section: -Maximum Complex Correntropy Criterionmentioning

confidence: 99%

“…Correntropy was also used in CS analysis in [27] showing a great potential for nonlinear signal processing and defined a new algorithm called 0 -Maximum Correntropy Criterion ( 0 -MCC). It puts together an 0 gradient approxi-mation strategy, previously used in the 0 -Least Mean Square ( 0 -LMS) [28] and the Maximum Correntropy Criterion (MCC).…”

Section: Introductionmentioning

confidence: 99%

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Complex Correntropy Applied to a Compressive Sensing Problem in an Impulsive Noise Environment

et al. 2019

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Correntropy is a similarity function capable of extracting high-order statistical information from data. It has been used in different kinds of applications as a cost function to overcome traditional methods in non-Gaussian noise environments. One of the recent applications of correntropy was in the theory of compressive sensing, which takes advantage of sparsity in a transformed domain to reconstruct the signal from a few measurements. Recently, an algorithm called 0 -MCC was introduced. It applies the Maximum Correntropy Criterion (MCC) in order to deal with a non-Gaussian noise environment in a compressive sensing problem. However, because correntropy was only defined for real-valued data, it was not possible to apply the 0 -MCC algorithm in a straightforward way to compressive sensing problems dealing with complex-valued measurements. This paper presents a generalization of the 0 -MCC algorithm to complex-valued measurements. Simulations show that the proposed algorithm can outperform traditional minimization algorithms such as Nesterov's algorithm (NESTA) and the 0 -Least Mean Square ( 0 -LMS) in the presence of non-Gaussian noise.

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Maximum correntropy adaptation approach for robust compressive sensing reconstruction

Cited by 25 publications

References 70 publications

Kernel Mixture Correntropy Conjugate Gradient Algorithm for Time Series Prediction

Kernel Mixture Correntropy Conjugate Gradient Algorithm for Time Series Prediction

Robust Sparse Recovery in Impulsive Noise via M-Estimator and Non-Convex Regularization

Complex Correntropy Applied to a Compressive Sensing Problem in an Impulsive Noise Environment

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