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A robust algorithm is proposed to reconstruct the spatial support and the Lam\'e parameters of multiple inclusions in a homogeneous background elastic material using a few measurements of the displacement field over a finite collection of…

Numerical Analysis · Mathematics 2017-02-27 Jaejun Yoo , Younghoon Jung , Mikyoung Lim , Jong Chul Ye , Abdul Wahab

We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient…

Methodology · Statistics 2019-03-13 Asad Haris , Noah Simon , Ali Shojaie

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

Optimization and Control · Mathematics 2014-12-09 Samuel Vaiter , Gabriel Peyré , Jalal M. Fadili

The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…

Machine Learning · Statistics 2025-04-07 Jinhang Chai , Jianqing Fan

In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…

Machine Learning · Computer Science 2016-10-18 Lijun Zhang , Tianbao Yang , Rong Jin , Zhi-Hua Zhou

Random and structured noise both affect seismic data, hiding the reflections of interest (primaries) that carry meaningful geophysical interpretation. When the structured noise is composed of multiple reflections, its adaptive cancellation…

Geophysics · Physics 2014-06-19 Mai Quyen Pham , Caroline Chaux , Laurent Duval , Jean-Christophe Pesquet

We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. This problem is relevant in machine learning, statistics and signal processing. It is well known that a…

Machine Learning · Statistics 2015-03-17 Charles A. Micchelli , Jean M. Morales , Massimiliano Pontil

The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…

Information Theory · Computer Science 2016-08-31 Jonathan Scarlett , Volkan Cevher

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…

Computer Vision and Pattern Recognition · Computer Science 2010-06-16 Guoshen Yu , Guillermo Sapiro , Stéphane Mallat

This note presents a unified analysis of the recovery of simple objects from random linear measurements. When the linear functionals are Gaussian, we show that an s-sparse vector in R^n can be efficiently recovered from 2s log n…

Information Theory · Computer Science 2012-03-01 Emmanuel Candes , Benjamin Recht

In order to improve the fault diagnosis capability of multivariate statistical methods, this article introduces a fault isolation framework based on structured sparsity modeling. The developed method relies on the reconstruction based…

Applications · Statistics 2020-12-22 Wei Chen , Jiusun Zeng , Xiaobin Xu , Shihua Luo , Chuanhou Gao

In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This…

Numerical Analysis · Mathematics 2019-05-28 Armenak Petrosyan , Hoang Tran , Clayton Webster

The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the sensing matrix A satisfies a rank condition, this problem…

Dynamical Systems · Mathematics 2014-11-18 David Hayden , Young Hwan Chang , Jorge Goncalves , Claire Tomlin

In this paper we present a general convex optimization approach for solving high-dimensional multiple response tensor regression problems under low-dimensional structural assumptions. We consider using convex and weakly decomposable…

Statistics Theory · Mathematics 2017-04-17 Garvesh Raskutti , Ming Yuan , Han Chen

This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature…

Methodology · Statistics 2009-05-05 Junzhou Huang , Tong Zhang , Dimitris Metaxas

The randomized version of the Kaczmarz method for the solution of linear systems is known to converge linearly in expectation. In this work we extend this result and show that the recently proposed Randomized Sparse Kaczmarz method for…

Optimization and Control · Mathematics 2016-10-11 Frank Schöpfer , Dirk A. Lorenz

We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types of nonconvex sparsity-inducing terms, bringing strong applicability to a…

Information Theory · Computer Science 2021-08-23 Hao Wang , Fan Zhang , Yuanming Shi , Yaohua Hu

Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…

Computer Vision and Pattern Recognition · Computer Science 2016-05-09 Sohil Shah , Tom Goldstein , Christoph Studer

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…

Optimization and Control · Mathematics 2010-12-24 Youwei Zhang , Alexandre d'Aspremont , Laurent El Ghaoui

Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…

Information Theory · Computer Science 2017-04-19 Sajad Daei , Farzan Haddadi