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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

Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…

Optimization and Control · Mathematics 2016-12-30 Mateo Díaz , Mauricio Junca , Felipe Rincón , Mauricio Velasco

The recently proposed modified-compressive sensing (modified-CS), which utilizes the partially known support as prior knowledge, significantly improves the performance of recovering sparse signals. However, modified-CS depends heavily on…

Information Theory · Computer Science 2012-07-10 Jun Zhang , Yuanqing Li , Zhu Liang Yu , Zhenghui Gu

Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS…

Computer Vision and Pattern Recognition · Computer Science 2017-08-29 Duc Minh Nguyen , Evaggelia Tsiligianni , Nikos Deligiannis

We consider a reconciliation problem, where two hosts wish to synchronize their respective sets. Efficient solutions for minimizing the communication cost between the two hosts have been previously proposed in the literature. However, they…

Information Theory · Computer Science 2012-12-13 H. T. Kung , Chia-Mu Yu

This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a…

Information Theory · Computer Science 2013-02-12 Xiaofu Wu , Zhen Yang , Lu Gan

Compressed sensing (CS) is on recovery of high dimensional signals from their low dimensional linear measurements under a sparsity prior and digital quantization of the measurement data is inevitable in practical implementation of CS…

Information Theory · Computer Science 2016-08-24 Zai Yang , Lihua Xie , Cishen Zhang

Compressed Sensing (CS) is a novel technique for simultaneous signal sampling and compression based on the existence of a sparse representation of signal and a projected dictionary $PD$, where $P\in\mathbb{R}^{m\times d}$ is the projection…

Information Theory · Computer Science 2018-04-25 Canyi Lu , Huan Li , Zhouchen Lin

Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…

Functional Analysis · Mathematics 2016-05-25 Axel Flinth

Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage…

Information Theory · Computer Science 2011-07-12 Wei Dai , Olgica Milenkovic , Hoa Vin Pham

Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…

Statistical Mechanics · Physics 2012-08-20 Florent Krzakala , Marc Mézard , François Sausset , Yifan Sun , Lenka Zdeborová

Recent advances in signal processing have focused on the use of sparse representations in various applications. A new field of interest based on sparsity has recently emerged: compressed sensing. This theory is a new sampling framework that…

Astrophysics · Physics 2009-11-13 J. Bobin , J-L Starck , R. Ottensamer

We propose a new technique for adaptive identification of sparse systems based on the compressed sensing (CS) theory. We manipulate the transmitted pilot (input signal) and the received signal such that the weights of adaptive filter…

Information Theory · Computer Science 2012-04-05 Seyed Hossein Hosseini , Mahrokh G. Shayesteh

Compressed sensing (CS) is an innovative technique allowing to represent signals through a small number of their linear projections. In this paper we address the application of CS to the scenario of progressive acquisition of 2D visual…

Information Theory · Computer Science 2014-03-06 Giulio Coluccia , Enrico Magli

Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and compression. CS theory enables exact reconstruction of a sparse signal from relatively few linear measurements via a suitable nonlinear…

Information Theory · Computer Science 2014-09-04 Shmuel Friedland , Qun Li , Dan Schonfeld , Edgar A. Bernal

Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…

Information Theory · Computer Science 2015-05-13 David L. Donoho , Arian Maleki , Andrea Montanari

In recent years, compressed sensing (CS) based image coding has become a hot topic in image processing field. However, since the bit depth required for encoding each CS sample is too large, the compression performance of this paradigm is…

Multimedia · Computer Science 2021-02-03 Bo Zhang , Di Xiao , Lan Wang , Sen Bai , Lei Yang

This work considers an estimation task in compressive sensing, where the goal is to estimate an unknown signal from compressive measurements that are corrupted by additive pre-measurement noise (interference, or clutter) as well as…

Machine Learning · Statistics 2013-11-25 Swayambhoo Jain , Akshay Soni , Jarvis Haupt

In the context of compressed sensing (CS), this paper considers the problem of reconstructing sparse signals with the aid of other given correlated sources as multiple side information. To address this problem, we theoretically study a…

Information Theory · Computer Science 2017-01-19 Huynh Van Luong , Jurgen Seiler , Andre Kaup , Soren Forchhammer , Nikos Deligiannis

Compressed sensing is a novel research area, which was introduced in 2006, and since then has already become a key concept in various areas of applied mathematics, computer science, and electrical engineering. It surprisingly predicts that…

Information Theory · Computer Science 2012-08-29 Gitta Kutyniok