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In this work we address the problem of recovering sparse solutions to non linear inverse problems. We look at two variants of the basic problem, the synthesis prior problem when the solution is sparse and the analysis prior problem where…

Information Theory · Computer Science 2015-12-25 Kavya Gupta , Ankita Raj , Angshul Majumdar

The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…

Systems and Control · Electrical Eng. & Systems 2026-05-05 Yanxin Fu , Wenxiao Zhao

Sparse signal recovery deals with finding the sparsest solution of an under-determined linear system $\vx = \mQ\vs$. In this paper, we propose a novel greedy approach to addressing the challenges from such a problem. Such an approach is…

Information Theory · Computer Science 2026-04-09 Gang Li , Qiuwei Li , Shuang Li , Wu Angela Li

In this paper, we consider the problem of recovering an unknown sparse signal $\xv_0 \in \mathbb{R}^n$ from noisy linear measurements $\yv = \Hm \xv_0+ \zv \in \mathbb{R}^m$. A popular approach is to solve the $\ell_1$-norm regularized…

Information Theory · Computer Science 2018-08-14 Ayed M. Alrashdi , Ismail Ben Atitallah , Tareq Y. Al-Naffouri , Mohamed-Slim Alouini

We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…

Optimization and Control · Mathematics 2025-01-08 Dimitris Bertsimas , Jean Pauphilet , Bart Van Parys

Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…

Numerical Analysis · Mathematics 2009-05-28 Deanna Needell

We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of…

Statistics Theory · Mathematics 2014-02-25 Divyanshu Vats , Richard G. Baraniuk

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

Computational Engineering, Finance, and Science · Computer Science 2018-12-04 Ivan Dokmanić , Joan Bruna , Stéphane Mallat , Maarten de Hoop

Sensor placement for linear inverse problems is the selection of locations to assign sensors so that the entire physical signal can be well recovered from partial observations. In this paper, we propose a fast sampling algorithm to place…

Signal Processing · Electrical Eng. & Systems 2021-10-08 Fen Wang , Gene Cheung , Taihao Li , Ying Du , Yu-Ping Ruan

Inverse imaging problems that are ill-posed can be encountered across multiple domains of science and technology, ranging from medical diagnosis to astronomical studies. To reconstruct images from incomplete and distorted data, it is…

Image and Video Processing · Electrical Eng. & Systems 2023-11-30 Cesar F. Caiafa , Ramiro M. Irastorza

We address the recovery of sparse vectors in an overcomplete, linear and noisy multiple measurement framework, where the measurement matrix is known upto a permutation of its rows. We derive sparse Bayesian learning (SBL) based updates for…

Information Theory · Computer Science 2018-02-05 Ranjitha Prasad

In ill-posed dynamic inverse problems expected spatial features and temporal correlation between frames can be leveraged to improve the quality of the computed solution, in particular when the available data are limited and the…

A common task in inverse problems and imaging is finding a solution that is sparse, in the sense that most of its components vanish. In the framework of compressed sensing, general results guaranteeing exact recovery have been proven. In…

Numerical Analysis · Mathematics 2021-04-29 Monica Pragliola , Daniela Calvetti , Erkki Somersalo

The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the…

Numerical Analysis · Mathematics 2017-04-27 Yong-Xia Hao , Chong-Jun Li , Ren-Hong Wang

In this paper, we investigate the problem of optimization multivariate performance measures, and propose a novel algorithm for it. Different from traditional machine learning methods which optimize simple loss functions to learn prediction…

Machine Learning · Computer Science 2015-08-03 Jiachen Yanga , Zhiyong Dinga , Fei Guoa , Huogen Wanga , Nick Hughesb

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 consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…

Artificial Intelligence · Computer Science 2007-07-06 Onureena Banerjee , Laurent El Ghaoui , Alexandre d'Aspremont

Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…

Signal Processing · Electrical Eng. & Systems 2019-09-04 Dror Simon , Jeremias Sulam , Yaniv Romano , Yue M. Lu , Michael Elad

A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…

Information Theory · Computer Science 2012-05-22 Shirin Jalali , Arian Maleki , Richard Baraniuk

In this paper, we propose an algorithm referred to as multipath matching pursuit that investigates multiple promising candidates to recover sparse signals from compressed measurements. Our method is inspired by the fact that the problem to…

Information Theory · Computer Science 2014-03-11 Suhyuk , Kwon , Jian Wang , Byonghyo Shim