Open Access
Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case
Joel A. Tropp,Anna C. Gilbert +1 more
Reads0
Chats0
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
More filters
Proceedings ArticleDOI
A greedy pursuit algorithm for distributed compressed sensing
TL;DR: A greedy pursuit algorithm for solving the distributed compressed sensing problem in a connected network that is based on subspace pursuit and uses the mixed support-set signal model.
Proceedings ArticleDOI
Impulsive noise estimation and cancellation in DSL using orthogonal clustering
TL;DR: This work proposes an algorithm that utilizes the guard band null carriers for the impulsive noise estimation and cancellation and exploits the structure present in the problem and the available a priori information jointly for sparse signal recovery.
Proceedings ArticleDOI
Deep Model for Classification of Hyperspectral image using Restricted Boltzmann Machine
TL;DR: An improved classification of hyperspectral images using deep learning, by extracting meaningful representations at higher levels by using a powerful regenerative model Restricted Boltzmann Machine (RBM).
Journal ArticleDOI
Wide-field multiphoton imaging through scattering media without correction
Adrià Escobet-Montalbán,Roman Spesyvtsev,Mingzhou Chen,Wardiya Afshar Saber,Melissa R. Andrews,C. Simon Herrington,Michael Mazilu,Kishan Dholakia +7 more
TL;DR: In this paper, temporal focusing and single-pixel detection was used to obtain wide-field two-photon images through various turbid media including a scattering phantom and tissue reaching a depth of up to seven scattering mean free path lengths.
Journal ArticleDOI
Cognitive Radio for Smart Grid: Theory, Algorithms, and Security
Raghuram Ranganathan,Robert C. Qiu,Zhen Hu,Shujie Hou,Marbin Pazos-Revilla,Gang Zheng,Zhe Chen,Nan Guo +7 more
TL;DR: The novel concept of incorporating a cognitive radio network as the communications infrastructure for the smart grid is presented and experimental results obtained by using dimensionality reduction techniques such as principal component analysis (PCA), kernel PCA, and landmark maximum variance unfolding (LMVU) on Wi-Fi signal measurements are presented in a spectrum sensing context.
References
More filters
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.