The Proximity Operator of the Log-Sum Penalty

Prater-Bennette, Ashley; Shen, Lixin; Tripp, Erin E.

doi:10.1007/s10915-022-02021-4

Cited by 6 publications

(2 citation statements)

References 28 publications

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“…The proximal operator of some commonly used nonconvex separable ℓ 0 -norm surrogates, such as SCAD [9], MCP [12], CaP [10], Log [43], TL1 [24] are well-known.…”

Section: Proximal Operator Of Piementioning

confidence: 99%

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High efficiency sensing - dominates "compressed sensing"

Liu¹

2023

Preprint

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<p>In this paper, we exemplify a new mathematical theory and method for data prediction, interpolation and acquisition, called “high efficiency sensing.” Compressed sensing theory is the most sensational topic of scientific research in the past century. The original paper was unprecedentedly cited over 30,000 times in only 15 years. Compressed sensing purports to exert data compression at the phase of data acquisition, but turns out to massively lose data quality. Based on insight into flaws of compressed sensing theory and crucial discovery of a series of new logical phenomena, our high efficiency sensing method radically rectifies mathematical rationale and immensely improves technical performance in vast dominance. The core method is simple yet powerful. It runs hundreds of thousand times faster in computation. Even better, it duplicates data information in various domains altogether while boosting data dimension. In consequence, prediction and interpolation conform to the waveform of samples without loss or distortion. The deep copy ensures the high quality of resulting data set. Demo software and test data are downloadable at website www.lucidsee.ca.</p>

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“…The proximal operator of some commonly used nonconvex separable ℓ 0 -norm surrogates, such as SCAD [9], MCP [12], CaP [10], Log [43], TL1 [24] are well-known.…”

Section: Proximal Operator Of Piementioning

confidence: 99%

“…Let us explain the choices of those parameters in TABLE IV. The shape parameter a = 3.7 was suggested for SCAD and MCP in [9], [11] and a ∈ {0.1, 0.5} was used for Log in [43]. Remember that for a ρ-weakly convex penalty, the maximum step size of ISTA is µ max = 2 νmax+ρ .…”

Section: Comparative Analysis Of Various Penalty Functionsmentioning

confidence: 99%

High efficiency sensing - dominates "compressed sensing"

Liu¹

2023

Preprint

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Augmented Lagrangian method for tensor low-rank and sparsity models in multi-dimensional image recovery

Zhu,

Liu,

Huang

et al. 2024

Adv Comput Math

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A lifted ℓ1 framework for sparse recovery

Rahimi,

Kang,

Lou

2023

Information and Inference: A Journal of the IMA

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We introduce a lifted $\ell _1$ (LL1) regularization framework for the recovery of sparse signals. The proposed LL1 regularization is a generalization of several popular regularization methods in the field and is motivated by recent advancements in re-weighted $\ell _1$ approaches for sparse recovery. Through a comprehensive analysis of the relationships between existing methods, we identify two distinct types of lifting functions that guarantee equivalence to the $\ell _0$ minimization problem, which is a key objective in sparse signal recovery. To solve the LL1 regularization problem, we propose an algorithm based on the alternating direction method of multipliers and provide proof of convergence for the unconstrained formulation. Our experiments demonstrate the improved performance of the LL1 regularization compared with state-of-the-art methods, confirming the effectiveness of our proposed framework. In conclusion, the LL1 regularization presents a promising and flexible approach to sparse signal recovery and invites further research in this area.

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The Proximity Operator of the Log-Sum Penalty

Cited by 6 publications

References 28 publications

High efficiency sensing - dominates "compressed sensing"

High efficiency sensing - dominates "compressed sensing"

Augmented Lagrangian method for tensor low-rank and sparsity models in multi-dimensional image recovery

A lifted ℓ1 framework for sparse recovery

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