An Algorithm for image removals and decompositions without inverse matrices
Journal of Computational and Applied Mathematics
Blind motion deblurring using multiple images
Journal of Computational Physics
Split Bregman Algorithm, Douglas-Rachford Splitting and Frame Shrinkage
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Augmented Lagrangian Method, Dual Methods and Split Bregman Iteration for ROF Model
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
Nonlinear filtering for sparse signal recovery from incomplete measurements
IEEE Transactions on Signal Processing
Nonlinear regularization techniques for seismic tomography
Journal of Computational Physics
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
Removing Multiplicative Noise by Douglas-Rachford Splitting Methods
Journal of Mathematical Imaging and Vision
A Fast Hybrid Algorithm for Large-Scale l1-Regularized Logistic Regression
The Journal of Machine Learning Research
On the total variation dictionary model
IEEE Transactions on Image Processing
Total variation restoration of speckled images using a split-Bregman algorithm
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Beyond Nyquist: efficient sampling of sparse bandlimited signals
IEEE Transactions on Information Theory
Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction
Journal of Scientific Computing
IEEE Transactions on Image Processing
Projected Landweber iteration for matrix completion
Journal of Computational and Applied Mathematics
Multiplicative noise removal using variable splitting and constrained optimization
IEEE Transactions on Image Processing
Minimizing nonconvex functions for sparse vector reconstruction
IEEE Transactions on Signal Processing
Fast image recovery using variable splitting and constrained optimization
IEEE Transactions on Image Processing
Solving structured sparsity regularization with proximal methods
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part II
Restoration of Poissonian images using alternating direction optimization
IEEE Transactions on Image Processing
Split Bregman method for large scale fused Lasso
Computational Statistics & Data Analysis
Gaussian beam decomposition of high frequency wave fields using expectation-maximization
Journal of Computational Physics
A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration
Journal of Scientific Computing
Exact optimization for the l1-Compressive Sensing problem using a modified Dantzig-Wolfe method
Theoretical Computer Science
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
SIAM Journal on Scientific Computing
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing
International Journal of Computer Vision
Robust principal component analysis?
Journal of the ACM (JACM)
Super-Linear Convergence of Dual Augmented Lagrangian Algorithm for Sparsity Regularized Estimation
The Journal of Machine Learning Research
EM-type algorithms for image reconstruction with background emission and Poisson noise
ISVC'11 Proceedings of the 7th international conference on Advances in visual computing - Volume Part I
A novel predual dictionary learning algorithm
Journal of Visual Communication and Image Representation
SIAM Journal on Imaging Sciences
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
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
SIAM Journal on Imaging Sciences
A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method
SIAM Journal on Imaging Sciences
A First-Order Smoothed Penalty Method for Compressed Sensing
SIAM Journal on Optimization
SIAM Journal on Optimization
SIAM Journal on Imaging Sciences
Underdetermined Sparse Blind Source Separation of Nonnegative and Partially Overlapped Data
SIAM Journal on Scientific Computing
Journal of Scientific Computing
Augmented Lagrangian Method for Generalized TV-Stokes Model
Journal of Scientific Computing
Foundations and Trends® in Machine Learning
Multidimensional Systems and Signal Processing
An augmented Lagrangian approach to general dictionary learning for image denoising
Journal of Visual Communication and Image Representation
Journal of Scientific Computing
Dual Norm Based Iterative Methods for Image Restoration
Journal of Mathematical Imaging and Vision
A relaxed split bregman iteration for total variation regularized image denoising
ICIC'12 Proceedings of the 8th international conference on Intelligent Computing Theories and Applications
A fast tri-factorization method for low-rank matrix recovery and completion
Pattern Recognition
Color demosaicking with an image formation model and adaptive PCA
Journal of Visual Communication and Image Representation
SAR image reconstruction and autofocus by compressed sensing
Digital Signal Processing
Generalized edge-weighted centroidal Voronoi tessellations for geometry processing
Computers & Mathematics with Applications
Image deconvolution using incomplete Fourier measurements
International Journal of Imaging Systems and Technology
Efficient point-to-subspace query in ℓ1 with application to robust face recognition
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part IV
Fast reduction of speckle noise in real ultrasound images
Signal Processing
Error Forgetting of Bregman Iteration
Journal of Scientific Computing
Accelerated Linearized Bregman Method
Journal of Scientific Computing
Bregmanized Domain Decomposition for Image Restoration
Journal of Scientific Computing
A Simple Compressive Sensing Algorithm for Parallel Many-Core Architectures
Journal of Signal Processing Systems
Dynamic scene understanding by improved sparse topical coding
Pattern Recognition
Dictionary learning based impulse noise removal via L1-L1 minimization
Signal Processing
Guarantees of augmented trace norm models in tensor recovery
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Nesterov's algorithm solving dual formulation for compressed sensing
Journal of Computational and Applied Mathematics
Original Article: A new nonlocal total variation regularization algorithm for image denoising
Mathematics and Computers in Simulation
An effective dual method for multiplicative noise removal
Journal of Visual Communication and Image Representation
An Iterative Scheme for Total Variation-Based Image Denoising
Journal of Scientific Computing
Poisson Noise Reduction with Non-local PCA
Journal of Mathematical Imaging and Vision
A Combined First and Second Order Variational Approach for Image Reconstruction
Journal of Mathematical Imaging and Vision
A Splitting Method for Orthogonality Constrained Problems
Journal of Scientific Computing
Hi-index | 0.09 |
We propose simple and extremely efficient methods for solving the basis pursuit problem $\min\{\|u\|_1 : Au = f, u\in\mathbb{R}^n\},$ which is used in compressed sensing. Our methods are based on Bregman iterative regularization, and they give a very accurate solution after solving only a very small number of instances of the unconstrained problem $\min_{u\in\mathbb{R}^n} \mu\|u\|_1+\frac{1}{2}\|Au-f^k\|_2^2$ for given matrix $A$ and vector $f^k$. We show analytically that this iterative approach yields exact solutions in a finite number of steps and present numerical results that demonstrate that as few as two to six iterations are sufficient in most cases. Our approach is especially useful for many compressed sensing applications where matrix-vector operations involving $A$ and $A^\top$ can be computed by fast transforms. Utilizing a fast fixed-point continuation solver that is based solely on such operations for solving the above unconstrained subproblem, we were able to quickly solve huge instances of compressed sensing problems on a standard PC.