$L_{1/2}$ Regularization: A Thresholding Representation Theory and a Fast Solver

By Zongben Xu, Xiangyu Chang, Fengmin Xu, Hai Zhang. IEEE Transactions on Neural Networks and Learning Systems, 2012

1,055 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4c764f30454667fa00577afb89c48c2499af9f57

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. Wangmeng Zuo
2. Deyu Meng
3. Xiangyu Yang
4. Hao Wang
5. Xiao Wang
6. Zheng Zhang
7. C. L. Philip Chen
8. Yichen Zhu

In Computational Mechanics

1. Wangmeng Zuo
2. Lei Zhang
3. David Dapeng Zhang
4. Xiangchu Feng
5. Yong Xu
6. Jian Yang
7. Deyu Meng
8. Xuelong Li

In Mathematical Physics

1. Wangmeng Zuo
2. Deyu Meng
3. Zheng Zhang
4. Xiangchu Feng
5. Lei Zhang
6. Yong Xu
7. Jian Yang
8. David Dapeng Zhang

Citations in the corpus

• A Survey of Sparse Representation: Algorithms and Applications (2015, methodology): “In this section, a half proximal algorithm is introduced to solve the l1/2-norm regularization problem [60], which matches the iterative shrinkage thresholding algorithm for the l1-norm regularization discussed above and the iterative hard thresholding algorithm for the l0-norm regularization.”
• Seismic sparse-spike deconvolution via Toeplitz-sparse matrix factorization (2016, background): “The principle of this algorithm can be found in Beck and Teboulle (2009) and Xu et al. (2012).”
• Underwater Image Enhancement With Hyper-Laplacian Reflectance Priors (2022, positive): “Then an iterative half thresholding algorithm [34], [35] is adopted to update the auxiliary variables d k and h k at the k th iteration : (14) where ( · ) denote the half thresholding operators concretely defined in [34] and [35]. μ > 0 is a step size parameter which is generally set to the…”
• A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding (2013, background): “Other algorithms, such as the analytic solutions in [25, 39], can only be used for some specific values of p.”
• Minimization Over the Nonconvex Sparsity Constraint Using A Hybrid First-order method (2021, methodology): “As per our knowledge, limited progress has been made in solving ( P ), in contrast to the well-explored nonconvex ℓ p (quasi)-norm penalized optimization problem [11, 25, 35, 44].”
• Broad Learning System: An Effective and Efficient Incremental Learning System Without the Need for Deep Architecture (2018, background): “Specifically, sparse feature learning models have been attractive that could explore essential characterization [12], [42], [43].”
• Universal Approximation Capability of Broad Learning System and Its Structural Variations (2019, background): “Among them, regularization is of great benefit to specific applications (see [15], [16]).”