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Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case
Joel A. Tropp,Anna C. Gilbert +1 more
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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
An Introduction To Compressive Sampling
TL;DR: The theory of compressive sampling, also known as compressed sensing or CS, is surveyed, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition.
Journal ArticleDOI
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
Joel A. Tropp,Anna C. Gilbert +1 more
TL;DR: It is demonstrated 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(m ln d) random linear measurements of that signal.
Journal ArticleDOI
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
Deanna Needell,Joel A. Tropp +1 more
TL;DR: A new iterative recovery algorithm called CoSaMP is described that delivers the same guarantees as the best optimization-based approaches and offers rigorous bounds on computational cost and storage.
Journal ArticleDOI
Spatially Sparse Precoding in Millimeter Wave MIMO Systems
TL;DR: This paper considers transmit precoding and receiver combining in mmWave systems with large antenna arrays and develops algorithms that accurately approximate optimal unconstrained precoders and combiners such that they can be implemented in low-cost RF hardware.
Journal ArticleDOI
CoSaMP: iterative signal recovery from incomplete and inaccurate samples
Deanna Needell,Joel A. Tropp +1 more
TL;DR: This extended abstract describes a recent algorithm, called, CoSaMP, that accomplishes the data recovery task and was the first known method to offer near-optimal guarantees on resource usage.
References
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Book
The concentration of measure phenomenon
TL;DR: Concentration functions and inequalities isoperimetric and functional examples Concentration and geometry Concentration in product spaces Entropy and concentration Transportation cost inequalities Sharp bounds of Gaussian and empirical processes Selected applications References Index
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Projection Pursuit Regression
TL;DR: In this article, a nonparametric multiple regression (NMM) method is presented, which models the regression surface as a sum of general smooth functions of linear combinations of the predictor variables in an iterative manner.
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Probability in Banach Spaces: Isoperimetry and Processes
Michel Ledoux,Michel Talagrand +1 more
TL;DR: Banach Space Valued Random Variables and their strong limiting properties are discussed in this paper, where the central limit theorem and the strong law of large numbers are also considered, as well as the regularity of Gaussian and Stable Processes.
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Subset Selection in Regression
TL;DR: In this paper, Efroymson's algorithm was used to replace two variables at a time with all subsets using branch-and-bound techniques. But the results showed that one subset was better than another.
Journal ArticleDOI
Database-friendly random projections: Johnson-Lindenstrauss with binary coins
TL;DR: Two constructions of k-dimensional Euclidean embeddings with the property that all elements of the projection matrix belong in {-1, 0, +1 } are given.