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The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…

Machine Learning · Computer Science 2020-10-27 Yuhai Song , Zhong Cao , Kailun Wu , Ziang Yan , Changshui Zhang

We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the…

Numerical Analysis · Mathematics 2016-12-30 Sergey Voronin , Ingrid Daubechies

Iteratively reweighted $\ell_1$ algorithm is a popular algorithm for solving a large class of optimization problems whose objective is the sum of a Lipschitz differentiable loss function and a possibly nonconvex sparsity inducing…

Optimization and Control · Mathematics 2017-11-21 Peiran Yu , Ting Kei Pong

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

Machine Learning · Computer Science 2019-05-10 Baojian Zhou , Feng Chen , Yiming Ying

Sparse coding is typically solved by iterative optimization techniques, such as the Iterative Shrinkage-Thresholding Algorithm (ISTA). Unfolding and learning weights of ISTA using neural networks is a practical way to accelerate estimation.…

Machine Learning · Statistics 2019-05-28 Pierre Ablin , Thomas Moreau , Mathurin Massias , Alexandre Gramfort

Subspace clustering (SC) is a popular method for dimensionality reduction of high-dimensional data, where it generalizes Principal Component Analysis (PCA). Recently, several methods have been proposed to enhance the robustness of PCA and…

Data Structures and Algorithms · Computer Science 2015-06-09 Sanghyuk Chun , Yung-Kyun Noh , Jinwoo Shin

Commonly employed reconstruction algorithms in compressed sensing (CS) use the $L_2$ norm as the metric for the residual error. However, it is well-known that least squares (LS) based estimators are highly sensitive to outliers present in…

Information Theory · Computer Science 2013-11-28 Rafael E. Carrillo , Kenneth E. Barner

Ultrasound computed tomography (USCT) holds great promise for breast cancer screening. Waveform inversion-based image reconstruction methods account for higher order diffraction effects and can produce high-resolution USCT images, but are…

Medical Physics · Physics 2017-08-25 Thomas P. Matthews , Kun Wang , Cuiping Li , Neb Duric , Mark A. Anastasio

Computing the Wasserstein barycenter of a set of probability measures under the optimal transport metric can quickly become prohibitive for traditional second-order algorithms, such as interior-point methods, as the support size of the…

Optimization and Control · Mathematics 2020-01-22 Dongdong Ge , Haoyue Wang , Zikai Xiong , Yinyu Ye

Robust high-dimensional data processing has witnessed an exciting development in recent years, as theoretical results have shown that it is possible using convex programming to optimize data fit to a low-rank component plus a sparse outlier…

Computer Vision and Pattern Recognition · Computer Science 2015-04-21 Jun He , Dejiao Zhang , Laura Balzano , Tao Tao

We consider an important problem in signal processing, which consists in finding the sparsest solution of a linear system $\Phi x=b$. This problem has applications in several areas, but is NP-hard in general. Usually an alternative convex…

Optimization and Control · Mathematics 2019-06-25 Matías Valdés , Marcelo Fiori

A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…

Numerical Analysis · Mathematics 2018-10-30 Simon Foucart , Srinivas Subramanian

This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…

Numerical Analysis · Mathematics 2025-02-05 Lucas Onisk , Malena Sabaté Landman

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…

Optimization and Control · Mathematics 2012-10-10 Manya V. Afonso , José M. Bioucas-Dias , Mário A. T. Figueiredo

We present an extension of two policy-iteration based algorithms on weighted graphs (viz., Markov Decision Problems and Max-Plus Algebras). This extension allows us to solve the following inverse problem: considering the weights of the…

Discrete Mathematics · Computer Science 2009-11-18 Laurent Fribourg , Etienne André

Thresholding based iterative algorithms have the trade-off between effectiveness and optimality. Some are effective but involving sub-matrix inversions in every step of iterations. For systems of large sizes, such algorithms can be…

Information Theory · Computer Science 2017-11-08 Zhanjie Song , Shidong Li , Ningning Han

The iteratively reweighted l1 algorithm is a widely used method for solving various regularization problems, which generally minimize a differentiable loss function combined with a nonconvex regularizer to induce sparsity in the solution.…

Optimization and Control · Mathematics 2021-01-12 Hao Wang , Hao Zeng , Jiashan Wang

This work is concerned with applying iterative image reconstruction, based on constrained total-variation minimization, to low-intensity X-ray CT systems that have a high sampling rate. Such systems pose a challenge for iterative image…

Medical Physics · Physics 2016-11-17 Emil Y. Sidky , Rick Chartrand , Yuval Duchin , Christer Ullberg , Xiaochuan Pan

This paper discusses a class of thresholding-based iterative selection procedures (TISP) for model selection and shrinkage. People have long before noticed the weakness of the convex $l_1$-constraint (or the soft-thresholding) in wavelets…

Statistics Theory · Mathematics 2009-11-29 Yiyuan She

In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization. There is a lot of literature available, discussing the statistical properties of the…

Computation · Statistics 2023-03-08 Yujie Zhao , Xiaoming Huo