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Related papers: Iterative Hard Thresholding for Compressed Sensing

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In this paper, we consider the problem of compressed sensing where the goal is to recover almost all the sparse vectors using a small number of fixed linear measurements. For this problem, we propose a novel partial hard-thresholding…

Information Theory · Computer Science 2011-06-15 Prateek Jain , Ambuj Tewari , Inderjit S. Dhillon

Compressive sensing is a signal acquisition framework based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable recovery. In this paper we introduce a new theory for…

Information Theory · Computer Science 2009-01-23 Dror Baron , Marco F. Duarte , Michael B. Wakin , Shriram Sarvotham , Richard G. Baraniuk

The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$ norm minimization - a sparse quaternion signal from a limited number of its real linear…

Functional Analysis · Mathematics 2016-05-26 Agnieszka Badenska , Łukasz Błaszczyk

For compressive sensing of dynamic sparse signals, we develop an iterative pursuit algorithm. A dynamic sparse signal process is characterized by varying sparsity patterns over time/space. For such signals, the developed algorithm is able…

Statistics Theory · Mathematics 2012-10-15 Dave Zachariah , Saikat Chatterjee , Magnus Jansson

Sparse signal recovery is one of the most fundamental problems in various applications, including medical imaging and remote sensing. Many greedy algorithms based on the family of hard thresholding operators have been developed to solve the…

Signal Processing · Electrical Eng. & Systems 2023-06-09 Rachel Grotheer , Shuang Li , Anna Ma , Deanna Needell , Jing Qin

We address the problem of recovering a sparse signal from clipped or quantized measurements. We show how these two problems can be formulated as minimizing the distance to a convex feasibility set, which provides a convex and differentiable…

Signal Processing · Electrical Eng. & Systems 2018-12-05 Lucas Rencker , Francis Bach , Wenwu Wang , Mark D. Plumbley

In this paper we consider the problem of recovering a low-rank Tucker approximation to a massive tensor based solely on structured random compressive measurements. Crucially, the proposed random measurement ensembles are both designed to be…

Information Theory · Computer Science 2023-08-29 Cullen Haselby , Mark A. Iwen , Deanna Needell , Elizaveta Rebrova , William Swartworth

During the last decade, the paradigm of compressed sensing has gained significant importance in the signal processing community. While the original idea was to utilize sparsity assumptions to design powerful recovery algorithms of vectors…

Functional Analysis · Mathematics 2016-07-07 Axel Flinth

In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…

Information Theory · Computer Science 2015-06-18 Jun Fang , Jing Li , Yanning Shen , Hongbin Li , Shaoqian Li

Compressed sensing aims at reconstructing sparse signals from significantly reduced number of samples, and a popular reconstruction approach is $\ell_1$-norm minimization. In this correspondence, a method called orthonormal expansion is…

Information Theory · Computer Science 2015-05-30 Zai Yang , Cishen Zhang , Jun Deng , Wenmiao Lu

We consider the problem of recovering a set of correlated signals (e.g., images from different viewpoints) from a few linear measurements per signal. We assume that each sensor in a network acquires a compressed signal in the form of linear…

Networking and Internet Architecture · Computer Science 2015-03-19 Alhussein Fawzi , Tamara Tosic , Pascal Frossard

Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…

Numerical Analysis · Mathematics 2018-01-08 Lenny Fukshansky , Deanna Needell , Benny Sudakov

Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy this…

Computational Complexity · Computer Science 2012-11-06 Pascal Koiran , Anastasios Zouzias

In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to…

Machine Learning · Statistics 2020-04-28 Mahsa Lotfi , Mathukumalli Vidyasagar

As a signal recovery algorithm, compressed sensing is particularly useful when the data has low-complexity and samples are rare, which matches perfectly with the task of quantum phase estimation (QPE). In this work we present a new…

Quantum Physics · Physics 2025-01-01 Changhao Yi , Cunlu Zhou , Jun Takahashi

An accelerated class of adaptive scheme of iterative thresholding algorithms is studied analytically and empirically. They are based on the feedback mechanism of the null space tuning techniques (NST+HT+FB). The main contribution of this…

Information Theory · Computer Science 2020-05-15 Ningning Han , Shidong Li , Zhanjie Song

In this paper, based on a successively accuracy-increasing approximation of the $\ell_0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class…

Information Theory · Computer Science 2016-11-03 Mohammadreza Malek-Mohammadi , Ali Koochakzadeh , Massoud Babaie-Zadeh , Magnus Jansson , Cristian R. Rojas

Various iterative reconstruction algorithms for inverse problems can be unfolded as neural networks. Empirically, this approach has often led to improved results, but theoretical guarantees are still scarce. While some progress on…

Statistics Theory · Mathematics 2021-08-16 Arash Behboodi , Holger Rauhut , Ekkehard Schnoor

It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…

Information Theory · Computer Science 2010-04-06 M. Amin Khajehnejad , Weiyu Xu , Salman Avestimehr , Babak Hassibi

In this paper the authors describe the problem of acquisition of interfered signals and formulate a filtering problem. A frequency-selective compressed sensing technique is proposed as a solution to this problem. Signal acquisition is…

Information Theory · Computer Science 2015-01-19 Jacek Pierzchlewski , Thomas Arildsen