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(6 citation statements)

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“…We next consider the case when x / ∈ C I . By Item (ii) of Proposition 2.7, we conclude that there exists δ 2 > 0 such that The sufficient condition for a pair (x * , y * ) to be a local minimizer of the minimization problem (4.1) presented in Corollary 4.9 for a special example of convex function g was obtained in Proposition 2.3 of [32].…”

confidence: 78%

“…We next consider the case when x / ∈ C I . By Item (ii) of Proposition 2.7, we conclude that there exists δ 2 > 0 such that The sufficient condition for a pair (x * , y * ) to be a local minimizer of the minimization problem (4.1) presented in Corollary 4.9 for a special example of convex function g was obtained in Proposition 2.3 of [32].…”

confidence: 78%

“…Form (4.2) relates to regularization by the envelope of the ℓ 0 norm and form (4.3) relates to regularization by the capped ℓ 1 norm [11]. For specific examples of f , see [31] for inverting incomplete Fourier transform, [32,33] for image/signal processing, [34] for medical image reconstruction and machine learning [16,17,21,29]. Employing the partition A j , j ∈ Z d+1 , of R d and the definition of • 0 , we have an alternative representation of function f :…”

confidence: 99%

“…In this subsection we propose subiteration-dependent preconditioners that originated from generalization of the momentum approach. The momentum is an acceleration technique widely used in optimization [25]- [27]. The Nesterov's momentum [25] has been combined with ordered-subsets (OS) by Kim et al [28] for CT image reconstruction.…”

confidence: 99%

“…The resulting model is always convex and can be solved efficiently with many available tools. However, compared with the convex 1 norm-based model, a nonconvex 0 norm-based model has certain advantages in the context of image processing [4,58]. Here, we propose a novel regularization model that combines the sparsity maximization and denoising task, and we introduce the Moreau envelope of the 0 norm to reformulate the problem.…”

confidence: 99%