Primal-Dual Approach for Uniform Noise Removal

Zhang, Zhan; Wei, Wenyou

doi:10.2991/iset-15.2015.27

Cited by 6 publications

(2 citation statements)

References 10 publications

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“…When encountering heavy-tailed or heterogeneous noises, the data fidelity of Ax − b 1 is robust [2,22,32,33]. In the case of uniformly distributed and quantization error, the data fidelity of Ax − b ∞ is more suitable [34,36]. Recently, based on p (p = 1, 2, ∞) norm data fidelity and elastic net regularization, Ding et al [10] proposed a flexible and robust reconstruction model:…”

Section: Introductionmentioning

confidence: 99%

A fast and effective algorithm for sparse linear regression with $\ell_p$-norm data fidelity and elastic net regularization

2024

J. Nonlinear Var. Anal.

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Elastic net model is widely used in high-dimensional statistics for parameter regression and variable selection, which has been proved that the performance is often better than the lasso. However, it can only deals with data containing Gaussian noise, so it is not suitable for modern complex highdimensional data. Fortunately, an adaptive and robust minimization model, which combines the p -norm data fidelity and elastic net regularization, has been proposed to deal with different types of noises and inherit the advantages of the elastic net in prediction accuracy. The double non-smoothness in objective function makes it challenging to minimize the model. After investigation, we find that the optimization algorithm is currently limited to the first-order alternating direction method of multipliers (ADMM), which is relatively lower in the recovered solutions' accuracy and relatively slower in the calculation speed. Therefore, we are committed to developing a fast and effective algorithm based on second-order information. Specifically, we propose a preconditioned proximal point algorithm (abbreviated as P-PPA) to solve the considered model by adding a proximal term. In theory, we analyze the consistency between the solution of the surrogate model and the original model. In addition, a key subproblem in P-PPA is solved by superlinear or even quadratically convergent semismooth Newton methods from the dual perspective. Finally, a large number of numerical experiments on high-dimensional simulated and real examples fully verify that our proposed algorithm is superior to ADMM in terms of calculation accuracy and speed.Keywords. Alternating direction method of multipliers; High-dimensional sparse linear regression; p 1 -2 minimization; Preconditioned proximal point algorithm; Semismooth Newton method.

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Section: Introductionmentioning

confidence: 99%

A fast and effective algorithm for sparse linear regression with $\ell_p$-norm data fidelity and elastic net regularization

2024

J. Nonlinear Var. Anal.

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“…The data fidelity with form Ax−b 1 has also been evidently shown to be more robust when the noises are not normal but heavy-tailed or heterogeneous, see e.g., ; Lu (2014); Wang (2013); Xiu et al (2018). Besides, the data fidelity with form Ax − b ∞ is also known to be very suitable for dealing with the uniformly distributed noise and quantization error, see e.g., Wen et al (2018); Xue et al (2019); Zhang and Wei (2015). Therefore, a more natural question is whether or not one can design a more flexible and robust reconstruction model as well as an efficient algorithm which is capable of dealing with all the three types of noise mentioned above?…”

Section: Introductionmentioning

confidence: 99%

An Efficient Semismooth Newton Method for Adaptive Sparse Signal Recovery Problems

Ding¹,

Zhang²,

Li³

et al. 2021

Preprint

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We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional methods might work not so well. Recently, it was shown that using the difference between 1-and 2-norm as a regularization always has superior performance. In this paper, we propose an adaptive p-1−2 model where the p-norm with p ≥ 1 measures the data fidelity and the 1−2-term measures the sparsity. This proposed model has the ability to deal with different types of noises and extract the sparse property even under high coherent condition. We use a proximal majorization-minimization technique to handle the nonconvex regularization term and then employ a semismooth Newton method to solve the corresponding convex relaxation subproblem. We prove that the sequence generated by the semismooth Newton method admits fast local convergence rate to the subproblem under some technical assumptions. Finally, we do some numerical experiments to demonstrate the superiority of the proposed model and the progressiveness of the proposed algorithm.

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Hierarchical Ensemble of AutoEncoder for Restoration of Images Corrupted by Cumulative Combination of Noise

Ganguly,

Katham,

Agrawal

et al. 2024

Lecture Notes in Computer Science

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Primal-Dual Approach for Uniform Noise Removal

Cited by 6 publications

References 10 publications

A fast and effective algorithm for sparse linear regression with $\ell_p$-norm data fidelity and elastic net regularization

A fast and effective algorithm for sparse linear regression with $\ell_p$-norm data fidelity and elastic net regularization

An Efficient Semismooth Newton Method for Adaptive Sparse Signal Recovery Problems

Hierarchical Ensemble of AutoEncoder for Restoration of Images Corrupted by Cumulative Combination of Noise

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