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Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate…

Numerical Analysis · Mathematics 2009-04-27 Deanna Needell

Compressed sensing is a paradigm within signal processing that provides the means for recovering structured signals from linear measurements in a highly efficient manner. Originally devised for the recovery of sparse signals, it has become…

Information Theory · Computer Science 2021-12-09 Jens Eisert , Axel Flinth , Benedikt Groß , Ingo Roth , Gerhard Wunder

As an alternative to the traditional sampling theory, compressed sensing allows acquiring much smaller amount of data, still estimating the spectra of frequency-sparse signals accurately. However, compressed sensing usually requires random…

Information Theory · Computer Science 2016-07-22 Shan Huang , Hong Sun , Haijian Zhang , Lei Yu

Intensively growing approach in signal processing and acquisition, the Compressive Sensing approach, allows sparse signals to be recovered from small number of randomly acquired signal coefficients. This paper analyses some of the commonly…

Signal Processing · Electrical Eng. & Systems 2018-02-21 Tamara Koljensic , Caslav Labudovic

As a lossy compression framework, compressed sensing has drawn much attention in wireless telemonitoring of biosignals due to its ability to reduce energy consumption and make possible the design of low-power devices. However, the…

Information Theory · Computer Science 2014-04-22 Zhilin Zhang , Bhaskar D. Rao , Tzyy-Ping Jung

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

Compressed sensing is the art of reconstructing a sparse vector from its inner products with respect to a small set of randomly chosen measurement vectors. It is usually assumed that the ensemble of measurement vectors is in isotropic…

Information Theory · Computer Science 2014-02-25 Richard Kueng , David Gross

Sparsity is a ubiquitous feature of many real world signals such as natural images and neural spiking activities. Conventional compressed sensing utilizes sparsity to recover low dimensional signal structures in high ambient dimensions…

Statistics Theory · Mathematics 2018-07-02 Abbas Kazemipour

Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Cand\`{e}s and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all $\boldsymbol{k}$-sparse…

Information Theory · Computer Science 2009-10-18 Robert Calderbank , Stephen Howard , Sina Jafarpour

Dimension reduction is widely regarded as an effective way for decreasing the computation, storage and communication loads of data-driven intelligent systems, leading to a growing demand for statistical methods that allow analysis (e.g.,…

Computer Vision and Pattern Recognition · Computer Science 2019-08-23 Guangcan Liu , Zhao Zhang , Qingshan Liu , Kongkai Xiong

Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have…

Information Theory · Computer Science 2014-05-02 Armin Eftekhari , Michael B. Wakin

Advances of information-theoretic understanding of sparse sampling of continuous uncoded signals at sampling rates exceeding the Landau rate were reported in recent works. This work examines sparse sampling of coded signals at sub-Landau…

Information Theory · Computer Science 2013-03-04 Michael Peleg , Shlomo Shamai

We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the optimal cost function and resulting sparse state feedback for these systems can be…

Optimization and Control · Mathematics 2023-11-07 David Ohlin , Emma Tegling , Anders Rantzer

Sign truncated matching pursuit (STrMP) algorithm is presented in this paper. STrMP is a new greedy algorithm for the recovery of sparse signals from the sign measurement, which combines the principle of consistent reconstruction with…

Information Theory · Computer Science 2013-12-13 Wenhui Liu , Da Gong , Zhiqiang Xu

We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…

Information Theory · Computer Science 2015-03-19 David L. Donoho , Adel Javanmard , Andrea Montanari

Sparse wideband sensor array design for sensor location optimisation is highly nonlinear and it is traditionally solved by genetic algorithms, simulated annealing or other similar optimization methods. However, this is an extremely…

Information Theory · Computer Science 2014-03-20 Matthew B. Hawes , Wei Liu

The one-bit compressed sensing framework aims to reconstruct a sparse signal by only using the sign information of its linear measurements. To compensate for the loss of scale information, past studies in the area have proposed recovering…

Information Theory · Computer Science 2016-09-21 Yingying Xu , Yoshiyuki Kabashima

Compressive sensing claims that the sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. One of issues ensuring the successful compressive sensing is to deal with the…

Information Theory · Computer Science 2009-03-31 Lianlin Li , Fang Li

Compressed sensing (sparse signal recovery) has been a popular and important research topic in recent years. By observing that natural signals are often nonnegative, we propose a new framework for nonnegative signal recovery using…

Methodology · Statistics 2013-10-04 Ping Li , Cun-Hui Zhang , Tong Zhang

As a paradigm to recover the sparse signal from a small set of linear measurements, compressed sensing (CS) has stimulated a great deal of interest in recent years. In order to apply the CS techniques to wireless communication systems,…

Information Theory · Computer Science 2016-12-21 Jun Won Choi , Byonghyo Shim , Yacong Ding , Bhaskar Rao , Dong In Kim