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
Active illumination single-pixel camera based on compressive sensing
TL;DR: The active illumination concept is described along with the experimental results, which were very encouraging toward the development of compressive-sensing-based cameras for various applications, such as pixel-level programmable gain imaging.
Journal ArticleDOI
High-Resolution Fully Polarimetric ISAR Imaging Based on Compressive Sensing
TL;DR: A novel fully polarimetric ISAR imaging method based on CS that combines the merits of a full-polarization technique and CS theory has two main advantages: it can provide high-resolution ISAR images with limited measurements, which is a promising technique for reducing data storage.
Journal ArticleDOI
Improved Iterative Curvelet Thresholding for Compressed Sensing and Measurement
TL;DR: Numerical experiments show good performance of the improved ICT methods for single-pixel imaging and Fourier-domain CS imaging in remote sensing and medical engineering.
Journal ArticleDOI
Performance Analysis of Sparse Recovery Based on Constrained Minimal Singular Values
Gongguo Tang,Arye Nehorai +1 more
TL;DR: Two algorithms based on the interior point algorithm and the semidefinite relaxation are designed to verify the sufficient condition for unique ℓ1 sparse recovery.
Journal ArticleDOI
Study of dynamics in post-transient flows using Koopman mode decomposition
Hassan Arbabi,Igor Mezic +1 more
TL;DR: In this paper, the Koopman mode decomposition (KMD) was used to study the dynamics of the lid-driven flow in a two-dimensional square cavity based on theorems related to the spectral theory of the koopman operator, which is a data-analysis technique which is often used to extract the spatio-temporal patterns of complex flows.
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.