A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
Linear inversion of ban limit reflection seismograms
SIAM Journal on Scientific and Statistical Computing
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Matrix computations (3rd ed.)
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Convergence of a block coordinate descent method for nondifferentiable minimization
Journal of Optimization Theory and Applications
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
Nonmonotone Globalization Techniques for the Barzilai-Borwein Gradient Method
Computational Optimization and Applications
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming
Numerische Mathematik
Modeling Age Progression in Young Faces
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization
Journal of Mathematical Imaging and Vision
An Interior-Point Method for Large-Scale l1-Regularized Logistic Regression
The Journal of Machine Learning Research
Efficient projections onto the l1-ball for learning in high dimensions
Proceedings of the 25th international conference on Machine learning
Magneto-/Electroencephalography with Space-Time Sparse Priors
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
A sparse signal reconstruction perspective for source localization with sensor arrays
IEEE Transactions on Signal Processing - Part II
A model selection rule for sinusoids in white Gaussian noise
IEEE Transactions on Signal Processing
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Reconstruction From Noisy Random Projections
IEEE Transactions on Information Theory
Why Simple Shrinkage Is Still Relevant for Redundant Representations?
IEEE Transactions on Information Theory
Stable Recovery of Sparse Signals Via Regularized Minimization
IEEE Transactions on Information Theory
De-noising by soft-thresholding
IEEE Transactions on Information Theory
Wavelet-based image estimation: an empirical Bayes approach using Jeffrey's noninformative prior
IEEE Transactions on Image Processing
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
Majorization–Minimization Algorithms for Wavelet-Based Image Restoration
IEEE Transactions on Image Processing
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
IEEE Transactions on Image Processing
IEEE Transactions on Information Theory
Efficient Online and Batch Learning Using Forward Backward Splitting
The Journal of Machine Learning Research
A subband adaptive iterative shrinkage/thresholding algorithm
IEEE Transactions on Signal Processing
Multiplicative noise removal using variable splitting and constrained optimization
IEEE Transactions on Image Processing
Fast image recovery using variable splitting and constrained optimization
IEEE Transactions on Image Processing
Distributed sparse linear regression
IEEE Transactions on Signal Processing
Reed muller sensing matrices and the LASSO
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
An improved smoothed l0approximation algorithm for sparse representation
IEEE Transactions on Signal Processing
Restoration of Poissonian images using alternating direction optimization
IEEE Transactions on Image Processing
Image reconstruction by an alternating minimisation
Neurocomputing
Restoration of images based on subspace optimization accelerating augmented Lagrangian approach
Journal of Computational and Applied Mathematics
Dual Averaging Methods for Regularized Stochastic Learning and Online Optimization
The Journal of Machine Learning Research
Topology Selection in Graphical Models of Autoregressive Processes
The Journal of Machine Learning Research
The Journal of Machine Learning Research
Heuristic Parameter-Choice Rules for Convex Variational Regularization Based on Error Estimates
SIAM Journal on Numerical Analysis
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
SIAM Journal on Scientific Computing
A coordinate gradient descent method for l1-regularized convex minimization
Computational Optimization and Applications
A box constrained gradient projection algorithm for compressed sensing
Signal Processing
Super-Linear Convergence of Dual Augmented Lagrangian Algorithm for Sparsity Regularized Estimation
The Journal of Machine Learning Research
Proximal Methods for Hierarchical Sparse Coding
The Journal of Machine Learning Research
Composite splitting algorithms for convex optimization
Computer Vision and Image Understanding
Convex and Network Flow Optimization for Structured Sparsity
The Journal of Machine Learning Research
Analysis and Generalizations of the Linearized Bregman Method
SIAM Journal on Imaging Sciences
Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
SIAM Journal on Scientific Computing
Gradient-Based Methods for Sparse Recovery
SIAM Journal on Imaging Sciences
Large Scale Bayesian Inference and Experimental Design for Sparse Linear Models
SIAM Journal on Imaging Sciences
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
SIAM Journal on Imaging Sciences
A Regularization Parameter for Nonsmooth Tikhonov Regularization
SIAM Journal on Scientific Computing
Efficient minimization for dictionary based sparse representation and signal recovery
Proceedings of the 4th International Symposium on Applied Sciences in Biomedical and Communication Technologies
Sparsity reconstruction in electrical impedance tomography: An experimental evaluation
Journal of Computational and Applied Mathematics
Structured sparsity in structured prediction
EMNLP '11 Proceedings of the Conference on Empirical Methods in Natural Language Processing
Compressive rendering of multidimensional scenes
Proceedings of the 2010 international conference on Video Processing and Computational Video
3D imaging spectroscopy for measuring hyperspectral patterns on solid objects
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Optimization with Sparsity-Inducing Penalties
Foundations and Trends® in Machine Learning
Block-Based Compressed Sensing of Images and Video
Foundations and Trends in Signal Processing
A fast dual projected Newton method for l1-regularized least squares
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Journal of Mathematical Imaging and Vision
Directional Sparsity in Optimal Control of Partial Differential Equations
SIAM Journal on Control and Optimization
Accelerated Block-coordinate Relaxation for Regularized Optimization
SIAM Journal on Optimization
Structured sparsity via alternating direction methods
The Journal of Machine Learning Research
Manifold identification in dual averaging for regularized stochastic online learning
The Journal of Machine Learning Research
Compressive estimation for signal integration in rendering
EGSR'10 Proceedings of the 21st Eurographics conference on Rendering
Joint estimation of segmentation and structure from motion
Computer Vision and Image Understanding
On analysis-based two-step interpolation methods for randomly sampled seismic data
Computers & Geosciences
Linguistic structure prediction with the sparseptron
XRDS: Crossroads, The ACM Magazine for Students - Scientific Computing
Error Forgetting of Bregman Iteration
Journal of Scientific Computing
Bregman operator splitting with variable stepsize for total variation image reconstruction
Computational Optimization and Applications
Computational Optimization and Applications
A two-stage method for inverse medium scattering
Journal of Computational Physics
FeaFiner: biomarker identification from medical data through feature generalization and selection
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Dictionary learning based impulse noise removal via L1-L1 minimization
Signal Processing
Sparse localized deformation components
ACM Transactions on Graphics (TOG)
Sparse BRDF approximation using compressive sensing
SIGGRAPH Asia 2013 Posters
Sparse signal reconstruction using decomposition algorithm
Knowledge-Based Systems
Nesterov's algorithm solving dual formulation for compressed sensing
Journal of Computational and Applied Mathematics
Dictionary learning based reconstruction for distributed compressed video sensing
Journal of Visual Communication and Image Representation
Supervised feature selection in graphs with path coding penalties and network flows
The Journal of Machine Learning Research
Multi-stage multi-task feature learning
The Journal of Machine Learning Research
Bilinear discriminative dictionary learning for face recognition
Pattern Recognition
Journal of Global Optimization
Poisson Noise Reduction with Non-local PCA
Journal of Mathematical Imaging and Vision
An infeasible-point subgradient method using adaptive approximate projections
Computational Optimization and Applications
Hi-index | 35.70 |
Finding sparse approximate solutions to large under-determined linear systems of equations is a common problem in signal/image processing and statistics. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution and reconstruction, and compressed sensing (CS) are a few well-known areas in which problems of this type appear. One standard approach is to minimize an objective function that includes a quadratic (l2) error term added to a sparsity-inducing (usually l1) regularizater. We present an algorithmic framework for the more general problem of minimizing the sum of a smooth convex function and a nonsmooth, possibly nonconvex regularizer. We propose iterative methods in which each step is obtained by solving an optimization subproblem involving a quadratic term with diagonal Hessian (i.e., separable in the unknowns) plus the original sparsity-inducing regularizer; our approach is suitable for cases in which this subproblem can be solved much more rapidly than the original problem. Under mild conditions (namely convexity of the regularizer), we prove convergence of the proposed iterative algorithm to a minimum of the objective function. In addition to solving the standard l2 -- l1 case, our framework yields efficient solution techniques for other regularizers, such as an l∞ norm and group-separable regularizers. It also generalizes immediately to the case in which the data is complex rather than real. Experiments with CS problems show that our approach is competitive with the fastest known methods for the standard l2 -- l1 problem, as well as being efficient on problems with other separable regularization terms.