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

No abstract is available for this paper.

• Publication year

  2012

• Venue

  IEEE Transactions on Neural Networks and Learning Systems

• Publication date

  2012-05-25

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1109/TNNLS.2012.2197412
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Regularization: Convergence of Iterative Half Thresholding Algorithm

  2014cited by this paper
• Embedding Prior Knowledge Within Compressed Sensing by Neural Networks

  2011cited by this paper
• Data Modeling: Visual Psychology Approach and L1/2 Regularization Theory

  2011cited by this paper
• $\ell_{p}-\ell_{q}$ Penalty for Sparse Linear and Sparse Multiple Kernel Multitask Learning

  2011cited by this paper
• Lower Bound Theory of Nonzero Entries in Solutions of ℓ2-ℓp Minimization

  2010cited by this paper
• L1/2 regularization

  2010cited by this paper
• Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data

  2009cited by this paper
• Fast Image Deconvolution using Hyper-Laplacian Priors

  2009cited by this paper
• 双対平坦空間におけるLeast Angle Regressionと情報量規準

  2009cited by this paper
• Exact Matrix Completion via Convex Optimization

  2008cited by this paper
• LASSO-TYPE RECOVERY OF SPARSE REPRESENTATIONS FOR HIGH-DIMENSIONAL DATA

  2008cited by this paper
• Iterative Hard Thresholding for Compressed Sensing

  2008cited by this paper
• Iterative Thresholding for Sparse Approximations

  2008cited by this paper
• Iterated Hard Shrinkage for Minimization Problems with Sparsity Constraints

  2008cited by this paper
• Signal Recovery From Incomplete and Inaccurate Measurements Via Regularized Orthogonal Matching Pursuit

  2007cited by this paper
• Restricted isometry properties and nonconvex compressive sensing

  2007cited by this paper
• Exact Reconstruction of Sparse Signals via Nonconvex Minimization

  2007cited by this paper
• PATHWISE COORDINATE OPTIMIZATION

  2007cited by this paper
• Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit

  2007cited by this paper
• Highly Robust Error Correction byConvex Programming

  2006cited by this paper
• High-Dimensional Centrally Symmetric Polytopes with Neighborliness Proportional to Dimension

  2006cited by this paper
• On the exponential convergence of matching pursuits in quasi-incoherent dictionaries

  2006cited by this paper
• Sparse Approximation Via Iterative Thresholding

  2006cited by this paper
• The Adaptive Lasso and Its Oracle Properties

  2006cited by this paper
• Compressed sensing

  2006cited by this paper
• Stable signal recovery from incomplete and inaccurate measurements

  2005cited by this paper
• Signal Recovery by Proximal Forward-Backward Splitting

  2005cited by this paper
• Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information

  2004cited by this paper
• Greed is good: algorithmic results for sparse approximation

  2004cited by this paper
• Investigation on Solutions of Cubic Equations with One Unknown

  2003cited by this paper
• An iterative thresholding algorithm for linear inverse problems with a sparsity constraint

  2003cited by this paper
• Greedy function approximation: A gradient boosting machine.

  2001cited by this paper
• Complex Wavelets for Shift Invariant Analysis and Filtering of Signals

  2001cited by this paper
• Introduction to Inverse Problems in Imaging

  1998cited by this paper
• Atomic Decomposition by Basis Pursuit

  1998cited by this paper
• Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm

  1997cited by this paper
• Emergence of simple-cell receptive field properties by learning a sparse code for natural images

  1996cited by this paper
• Regression Shrinkage and Selection via the Lasso

  1996cited by this paper
• Sparse Approximate Solutions to Linear Systems

  1995cited by this paper
• De-noising by soft-thresholding

  1995cited by this paper
• Matching pursuits with time-frequency dictionaries

  1993cited by this paper
• Estimating the Dimension of a Model

  1978cited by this paper
• Information Theory and an Extension of the Maximum Likelihood Principle

  1973cited by this paper
• Fonctions convexes duales et points proximaux dans un espace hilbertien

  1962cited by this paper

• $\ell_{1\text{-}2}$ Regularization for Sparse Optimization: Consistency and Global Convergence

  2026cites this paper
• An Efficient and Sparse Kernelized Grey RVFL Network for Energy Forecasting

  2026cites this paper
• Acoustic Beamforming for Source Localization With Laplace Norm Joint Constraint

  2026cites this paper
• Tensor band restricted thresholding algorithms for affine tensor rank minimization

  2026cites this paper
• Promoting sparsity in Bayesian learning through Laplace priors and evidential thresholding for equation discovery of nonlinear dynamical systems

  2026cites this paper
• Dynamic Proximal Gradient Algorithms for Schatten-$p$ Quasi-Norm Regularized Problems

  2026influential citation
• A Modified Proximal Gradient Algorithm for Nonconvex Regularized Least Squares in Compressed Sensing

  2026cites this paper
• Sparse learning of interval type-2 fuzzy model with embedded feature and rule selection

  2026cites this paper
• Robust RIS-Assisted DOA Estimation Under Impulsive Noise

  2026cites this paper
• A θ-inertial ADMM for efficient and stable nonconvex optimization

  2026cites this paper
• Inertial proximal stochastic gradient method with adaptive sampling for non-convex and non-smooth problems

  2026cites this paper
• A fusion sparse learning algorithm for fault identification of rolling bearings

  2026influential citation
• Impact load identification on ship stiffened structures using L1/2 regularization and shape functions

  2026cites this paper
• A partially symmetric linearized Bregman ADMM for three-block nonconvex nonsmooth optimization

  2026cites this paper
• Logarithmic function minimization to compressed sensing with application to magnetic resonance imaging

  2025cites this paper
• Detection and mitigation of TCP-based DDoS attacks in cloud environments using a self-attention and intersample attention transformer model

  2025cites this paper
• Sparse dual-graph regularized quadratic dimensionality reduction algorithm based on subspace learning

  2025cites this paper
• Efficient Sparse Recovery With Arctangent Regularization: A Novel Iterative Thresholding Algorithm

  2025influential citation
• Iterative mix thresholding algorithm with continuation technique for mix sparse optimization and application

  2025influential citation
• Virtual sensing of blade strain distribution using tip-timing method

  2025cites this paper
• Sparsity-enhanced Compressive Beamforming for Partial Discharge Localization via Laplace Norm

  2025cites this paper
• Fan noise radial mode detection based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si5.svg"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo stretchy="true">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> regularization method

  2025cites this paper
• Sparse Optimization Mechanism and Application of Recurrent Neural Network via Fractional-Order Gradient Descent Learning

  2025cites this paper
• Difference-of-Convex Elastic Net for Compressed Sensing

  2025cites this paper
• A comprehensive survey of transfer dictionary learning

  2025cites this paper
• Tailored Channel Pruning: Achieve Targeted Model Complexity Through Adaptive Sparsity Regularization

  2025cites this paper
• A Modified Approach to Distributed Bregman ADMM for a Class of Nonconvex Consensus Problems

  2025cites this paper
• Adaptive Multiorder Graph Regularized NMF With Dual Sparsity for Hyperspectral Unmixing

  2025cites this paper
• The Prediction Performance Analysis of the Lasso Model with Convex Non-Convex Sparse Regularization

  2025cites this paper
• ν-Accelerated ADMM Algorithm with Safe Guard Conditions

  2025cites this paper
• Convergence analysis of recurrent neural networks based on sparse mechanism and its application to time series and multiple classification problems

  2025cites this paper
• A Half-Proximal Symmetric Splitting Method for Non-Convex Separable Optimization

  2025influential citation
• An efficient proximal algorithm for squared L1 over L2 regularized sparse recovery

  2025influential citation
• Binary Kernel Logistic Regression: a sparsity-inducing formulation and a convergent decomposition training algorithm

  2025cites this paper
• Hölder network for improved adversarial robustness

  2025cites this paper
• A Globalized Semismooth Newton Method for Prox-regular Optimization Problems

  2025cites this paper
• Moving objects detection based on tensor ring low rank decomposition

  2025cites this paper
• A joint sparse self-representation learning method for multiview clustering

  2025cites this paper
• Smooth gradient loss: a loss function for gradient regularization in deep learning optimization

  2025cites this paper
• A Bregman-Type Improved ADMM Method with Extrapolation and Its Linear Variant for Nonconvex and Nonsmooth Optimization

  2025cites this paper
• Efficient and Robust Sparse Linear Discriminant Analysis for Data Classification

  2025influential citation
• Poisson Image Denoising via Generalized Gaussian Scale Mixture Modeling in the Wavelet Domain

  2025cites this paper
• Recovery Thresholding Hyperinterpolations in Signal Processing

  2025cites this paper
• Riemannian Multiplicative Update for Sparse Simplex constraint using oblique rotation manifold

  2025cites this paper
• Transformed L1 Regularization for Sparse Photoacoustic Tomography

  2025cites this paper
• Biologically informed cortical models predict optogenetic perturbations

  2025cites this paper
• An Efficient ADMM Method for Ratio-Type Nonconvex and Nonsmooth Minimization in Sparse Recovery

  2025cites this paper
• Robust incremental random RNN for process industries soft sensing

  2025cites this paper
• $\ell_{1}^{2}-\eta\ell_{2}^{2}$ regularization for sparse recovery

  2025cites this paper
• A second-order projection neurodynamic optimization approach for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alph

  2025cites this paper
• Manifold-aware and sparsity discriminant collaborative representation model and its application to multimode process monitoring

  2025cites this paper
• A Novel Biclustering Algorithm Based on Differential Sparsity Constraints and Dynamic Graph Regularization for Cancer Gene Expression Data

  2025cites this paper
• A fast iterative thresholding and support-and-scale shrinking algorithm (fits3) for non-lipschitz group sparse optimization (i): the case of least-squares fidelity

  2025cites this paper
• An inexact ADMM for separable nonconvex and nonsmooth optimization

  2025cites this paper
• Advanced fault diagnosis in industrial robots through hierarchical hyper-laplacian priors and singular spectrum analysis

  2025influential citation
• Velocity Analysis Using High-resolution Hyperbolic Radon Transform with Lq1-Lq2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{do

  2025cites this paper
• The joint quantile regression modeling of mixed ordinal and continuous responses with its application to an obesity risk data

  2025cites this paper
• From Target Tracking to Targeting Track - Part II: Regularized Polynomial Trajectory Optimization

  2025cites this paper
• Echo state network with a non-convex penalty for nonlinear time series prediction

  2025cites this paper
• Riemannian Optimization on the Oblique Manifold for Sparse Simplex Constraints via Multiplicative Updates

  2025cites this paper
• A Novel Nonconvex Penalty Method for a Rank Constrained Matrix Optimization Problem and its Applications

  2025cites this paper
• Undistorted and Consistent Enhancement of Automotive SAR Image via Multi-Segment-Reweighted Regularization

  2025cites this paper
• A General Framework for Group Sparsity in Hyperspectral Unmixing Using Endmember Bundles

  2025cites this paper
• A Novel Symmetrical Inertial Alternating Direction Method of Multipliers with Proximal Term for Nonconvex Optimization with Applications

  2025cites this paper
• Deterministic Convergence Analysis and Application of Elman Neural Network via Sparse Mechanism and Entropy Error Function

  2025cites this paper
• Robust Sparse Phase Retrieval: Statistical Guarantee, Optimality Theory and Convergent Algorithm

  2025cites this paper
• Under-determined audio source separation using the convolutive narrowband approximation and flexible ℓ regularizer

  2025cites this paper
• SVD method for sparse recovery

  2025influential citation
• Proximal Operators of Sorted Nonconvex Penalties

  2025cites this paper
• An Efficient Sparse Synthetic Aperture Radar Imaging Method Based on L1-Norm and Total Variation Regularization

  2025cites this paper
• OneMoreTest: A Learning-Based Approach to Generating and Selecting Fault-Revealing Unit Tests

  2025cites this paper
• Batch gradient based smoothing L2/3 regularization for training pi-sigma higher-order networks

  2025cites this paper
• A Relaxed Alternating Direction Method Of Multipliers For Separable Nonconvex Minimization Problems

  2025cites this paper
• Non-Asymptotic Analysis of Hybrid SPG for Non-Convex Stochastic Composite Optimization

  2025cites this paper
• Discriminative attention based weighted sparse representation of visual objects in complex scenarios

  2025cites this paper
• Accelerated Proximal Dogleg Majorization for Sparse Regularized Quadratic Optimization Problem

  2025cites this paper
• Limited-angle CT reconstruction by minimizing L1 over L2 based on linearized alternating direction method

  2025cites this paper
• Regularized Periodic Gaussian Process for Nonparametric Sparse Feature Extraction From Noisy Periodic Signals

  2025cites this paper
• Inertial proximal Bregman ADMM with dual relaxation approach for nonconvex optimization

  2025cites this paper
• A springback TV algorithm for image reconstruction from sparse view data in CT

  2025influential citation
• DualHash: A Stochastic Primal-Dual Algorithm with Theoretical Guarantee for Deep Hashing

  2025cites this paper
• Knowledge-Informed Neural Network for Complex-Valued SAR Image Recognition

  2025cites this paper
• A new limited shrinkage thresholding iterative ADMM algorithm for compressed sensing signal reconstruction

  2025cites this paper
• Signal and Image Recovery with Scale and Signed Permutation Invariant Sparsity-Promoting Functions

  2025cites this paper
• A Fast Sparse NMF Optimization Algorithm for Hyperspectral Unmixing

  2024cites this paper
• Analytical selection of hidden parameters through expanded enhancement matrix stability for functional-link neural networks and broad learning systems

  2024cites this paper
• 3-D Sparse SAR Imaging Based on Complex-Valued Nonconvex Regularization for Scattering Diagnosis

  2024cites this paper
• A Generalized Formulation for Group Selection via ADMM

  2024cites this paper
• Two-Timescale Optimization Framework for Sparse-Feedback Linear-Quadratic Optimal Control

  2024cites this paper
• Gaussian mixture-learned approximate message passing (GM-LAMP) based hybrid precoders for mmWave massive MIMO systems

  2024cites this paper
• ISAR High Resolution Imaging Algorithm Based on Weighted Adaptive Mixed Norm

  2024cites this paper
• Impact Force Localization and Reconstruction via ADMM-based Sparse Regularization Method

  2024influential citation
• Efficient Image Classification via Structured Low-Rank Matrix Factorization Regression

  2024cites this paper
• Joint Generalized Lq and Convolutional Regularization: Enhancing mmW Automotive SAR Sparse Imaging

  2024cites this paper
• Sparsity penalized mean–variance portfolio selection: analysis and computation

  2024cites this paper
• Bi-Sparse Unsupervised Feature Selection

  2024cites this paper
• A distributed Douglas-Rachford splitting method for solving linear constrained multi-block weakly convex problems

  2024cites this paper
• Sparse Feature-Weighted Double Laplacian Rank Constraint Non-Negative Matrix Factorization for Image Clustering

  2024cites this paper
• Integrating Regularization and PnP Priors for SAR Image Reconstruction Using Multiagent Consensus Equilibrium

  2024cites this paper
• Robust Underwater Direction-of-Arrival Estimation Method Using Acoustic Sensor Array under Unknown Swing Deviation Elements

  2024cites this paper