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
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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Journal ArticleDOI
An affine scaling methodology for best basis selection
TL;DR: A methodology is developed to derive algorithms for optimal basis selection by minimizing diversity measures proposed by Wickerhauser (1994) and Donoho (1994), which include the p-norm-like (l/sub (p/spl les/1)/) diversity measures and the Gaussian and Shannon entropies.
Proceedings ArticleDOI
Homotopy continuation for sparse signal representation
TL;DR: This work describes a homotopy continuation-based algorithm to find and trace efficiently all solutions of basis pursuit as a function of the regularization parameter, and shows the effectiveness of this algorithm in accurately and efficiently generating entire solution paths for basis pursuit.
Journal ArticleDOI
Nonlinear Methods of Approximation
TL;DR: Nonlinear approximation is focused on both in the classical form of m -term approximation (where several important problems remain unsolved) and in the form of highly nonlinear approximation where a theory is only now emerging.