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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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Tensor LRR and Sparse Coding-Based Subspace Clustering
TL;DR: Experimental results on both synthetic and real-world data sets show that TLRRSC outperforms several established state-of- the-art methods and can well capture the global structure and inherent feature information of data and provide a robust subspace segmentation from corrupted data.
Proceedings ArticleDOI
Model-based compressive sensing for signal ensembles
TL;DR: This paper provides experimental results using synthetic and real-world signals that confirm the benefits of a new framework for CS based on unions of subspaces that provides recovery algorithms with theoretical performance guarantees and scales naturally to large sensor networks.
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Verification Decoding of High-Rate LDPC Codes With Applications in Compressed Sensing
Fan Zhang,Henry D. Pfister +1 more
TL;DR: The high-rate scaling law for MP decoding of LDPC codes on the binary erasure channel and the q-ary symmetric channel is derived and leads to the result that strictly sparse signals can be reconstructed efficiently with high probability using a constant oversampling ratio.
Journal ArticleDOI
Deterministic Construction of Sparse Sensing Matrices via Finite Geometry
Shuxing Li,Gennian Ge +1 more
TL;DR: This work investigates a series of packing designs originated from finite geometry, which gives rise to deterministic sparse matrices with low coherence, and constructs a set of binary and modified matrices that outperform several typical sensing matrices.
Journal ArticleDOI
Projection-Based and Look-Ahead Strategies for Atom Selection
TL;DR: This paper devise two new schemes to select an atom from a set of potential atoms in each iteration of iterative greedy search algorithms, and proposes a look-ahead strategy such that the selection of an atom in the current iteration has an effect on the future iterations.
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.