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We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…

Systems and Control · Computer Science 2016-06-16 Reza Arablouei

In this note, we analyze an iterative soft / hard thresholding algorithm with homotopy continuation for recovering a sparse signal $x^\dag$ from noisy data of a noise level $\epsilon$. Under suitable regularity and sparsity conditions, we…

Numerical Analysis · Mathematics 2017-05-24 Yuling Jiao , Bangti Jin , Xiliang Lu

We analyze an Iteratively Re-weighted Least Squares (IRLS) algorithm for promoting l1-minimization in sparse and compressible vector recovery. We prove its convergence and we estimate its local rate. We show how the algorithm can be…

Numerical Analysis · Mathematics 2008-07-04 Ingrid Daubechies , Ronald DeVore , Massimo Fornasier , C. Sinan Gunturk

Weighted $\ell_1$-minimization has been studied as a technique for the reconstruction of a sparse signal from compressively sampled measurements when prior information about the signal, in the form of a support estimate, is available. In…

Information Theory · Computer Science 2016-12-09 Deanna Needell , Rayan Saab , Tina Woolf

We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…

Information Theory · Computer Science 2012-04-04 Seyed Hossein Hosseini , Mahrokh G. Shayesteh

It is now well understood that $\ell_1$ minimization algorithm is able to recover sparse signals from incomplete measurements [2], [1], [3] and sharp recoverable sparsity thresholds have also been obtained for the $\ell_1$ minimization…

Probability · Mathematics 2009-04-07 Weiyu Xu , M. Amin Khajehnejad , Salman Avestimehr , Babak Hassibi

This paper is about iteratively reweighted basis-pursuit algorithms for compressed sensing and matrix completion problems. In a first part, we give a theoretical explanation of the fact that reweighted basis pursuit can improve a lot upon…

Information Theory · Computer Science 2011-07-11 Stéphane Gaïffas , Guillaume Lecué

Broadband wireless channels usually have the sparse nature. Based on the assumption of Gaussian noise model, adaptive filtering algorithms for reconstruction sparse channels were proposed to take advantage of channel sparsity. However,…

Information Theory · Computer Science 2015-02-20 Guan Gui , Li Xu , Wentao Ma , Badong Chen

We study the problem of recovering the underlining sparse signals from clean or noisy phaseless measurements. Due to the sparse prior of signals, we adopt an L0regularized variational model to ensure only a small number of nonzero elements…

Optimization and Control · Mathematics 2016-12-09 Yuping Duan , Chunlin Wu , Zhi-Feng Pang , Huibin Chang

Noise robust compressive sensing algorithm is considered. This algorithm allows an efficient signal reconstruction in the presence of different types of noise due to the possibility to change minimization norm. For instance, the commonly…

Information Theory · Computer Science 2015-02-23 Maja Lakicevic , Mitar Moracanin , Nadja Djerkovic

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 paper considers the problem of minimizing the sum of a smooth function and the Schatten-$p$ norm of the matrix. Our contribution involves proposing accelerated iteratively reweighted nuclear norm methods designed for solving the…

Optimization and Control · Mathematics 2024-06-27 Hao Wang , Ye Wang , Xiangyu Yang

This paper presents a novel hybrid algorithm for minimizing the sum of a continuously differentiable loss function and a nonsmooth, possibly nonconvex, sparse regularization function. The proposed method alternates between solving a…

Optimization and Control · Mathematics 2025-04-01 Hao Wang , Xiangyu Yang , Yichen Zhu

This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements -- L_1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized…

Numerical Analysis · Mathematics 2008-03-15 Deanna Needell , Roman Vershynin

Vector valued data appearing in concrete applications often possess sparse expansions with respect to a preassigned frame for each vector component individually. Additionally, different components may also exhibit common sparsity patterns.…

Numerical Analysis · Mathematics 2007-05-23 Massimo Fornasier , Holger Rauhut

In numerous substitution models for the $\l_{0}$-norm minimization problem $(P_{0})$, the $\l_{p}$-norm minimization $(P_{p})$ with $0<p<1$ have been considered as the most natural choice. However, the non-convex optimization problem…

Optimization and Control · Mathematics 2018-04-27 Angang Cui , Jigen Peng , Haiyang Li

Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…

Information Theory · Computer Science 2013-09-24 Ljubisa Stankovic , Milos Dakovic , Stefan Vujovic

Sparse decision trees are one of the most common forms of interpretable models. While recent advances have produced algorithms that fully optimize sparse decision trees for prediction, that work does not address policy design, because the…

Machine Learning · Computer Science 2022-10-27 Ali Behrouz , Mathias Lecuyer , Cynthia Rudin , Margo Seltzer

In this paper, we present a novel yet simple homotopy proximal mapping algorithm for compressive sensing. The algorithm adopts a simple proximal mapping of the $\ell_1$ norm at each iteration and gradually reduces the regularization…

Information Theory · Computer Science 2016-08-29 Tianbao Yang , Lijun Zhang , Rong Jin , Shenghuo Zhu , Zhi-Hua Zhou

Broadband frequency-selective fading channels usually have the inherent sparse nature. By exploiting the sparsity, adaptive sparse channel estimation (ASCE) algorithms, e.g., least mean square with reweighted L1-norm constraint (LMS-RL1)…

Information Theory · Computer Science 2015-04-29 Guan Gui , Li Xu