Open Access
Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case
Joel A. Tropp,Anna C. Gilbert +1 more
TLDR
In this paper, a greedy algorithm called Orthogonal Matching Pursuit (OMP) was proposed to recover a signal with m nonzero entries in dimension 1 given O(m n d) random linear measurements of that signal.Abstract:
This report demonstrates theoretically and empirically that a greedy algorithm called
Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension
d given O(mln d) random linear measurements of that signal. This is a massive improvement
over previous results, which require O(m2) measurements. The new results for OMP are comparable
with recent results for another approach called Basis Pursuit (BP). In some settings, the
OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal
recovery problems.read more
Citations
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Journal ArticleDOI
On the Achievability of Cramér–Rao Bound in Noisy Compressed Sensing
TL;DR: This correspondence generalizes the results obtained in Babadi by dropping the Gaussianity assumption on the measurement matrix and finds a theorem similar to the main theorem of Babadi for a family of randomly generated (but deterministic in the noise domain) measurement matrices that satisfy a generalized condition known as “the concentration of measures inequality.”
Journal ArticleDOI
Reconstruction of Moving Target's HRRP Using Sparse Frequency-Stepped Chirp Signal
TL;DR: This paper introduces a novel reconstruction method of high-resolution range profile (HRRP) using sparse frequency-stepped chirp signal (FSCS), where Compressed Sensing theory is utilized to reconstruct the moving target's HRRP.
Journal ArticleDOI
Distributed Compressive Sensing Augmented Wideband Spectrum Sharing for Cognitive IoT
Xingjian Zhang,Yuan Ma,Haoran Qi,Yue Gao,Zhixun Xie,Zhiqin Xie,Zhang Minxiu,Wang Xiaodong,Wei Guangliang,Li Zheng +9 more
TL;DR: A blind joint sub-Nyquist sensing scheme is proposed by utilizing the surround IoT devices to jointly sample the spectrum based on the multicoset sampling theory and it is shown that the adaptive number of coset samplers could be adopted without causing the degradation of the detection performance and the number ofcoset sampler could be further reduced with the assists from geo-location database even when the obtained information is partially correct.
Journal ArticleDOI
Real-time ECG monitoring using compressive sensing on a heterogeneous multicore edge-device
Hamza Djelouat,Mohamed Al Disi,Issam Boukhenoufa,Abbes Amira,Abbes Amira,Faycal Bensaali,Christos Kotronis,Elena Politi,Mara Nikolaidou,George Dimitrakopoulos +9 more
TL;DR: It is concluded that multicore processors have the computational capacity and energy efficiency to promote gateway-centric solution rather than cloud-centric platforms.
Journal ArticleDOI
Symbol-Level Precoding for Low Complexity Transmitter Architectures in Large-Scale Antenna Array Systems
TL;DR: This paper considers three transmitter designs for symbol-level-precoding (SLP), a technique that mitigatesMultiuser interference in multiuser systems by designing the transmitted signals using the channel state information and the information-bearing symbols.
References
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Book
Compressed sensing
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
Journal ArticleDOI
Atomic Decomposition by Basis Pursuit
TL;DR: Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
Journal ArticleDOI
Matching pursuits with time-frequency dictionaries
Stéphane Mallat,Zhifeng Zhang +1 more
TL;DR: The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions, chosen in order to best match the signal structures.
Journal ArticleDOI
Least angle regression
Bradley Efron,Trevor Hastie,Iain M. Johnstone,Robert Tibshirani,Hemant Ishwaran,Keith Knight,Jean-Michel Loubes,Jean-Michel Loubes,Pascal Massart,Pascal Massart,David Madigan,David Madigan,Greg Ridgeway,Greg Ridgeway,Saharon Rosset,Saharon Rosset,Ji Zhu,Robert A. Stine,Berwin A. Turlach,Sanford Weisberg +19 more
TL;DR: A publicly available algorithm that requires only the same order of magnitude of computational effort as ordinary least squares applied to the full set of covariates is described.