Journal ArticleDOI
CoSaMP: iterative signal recovery from incomplete and inaccurate samples
Deanna Needell,Joel A. Tropp +1 more
TLDR
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.Abstract:
Compressive sampling (CoSa) is a new paradigm for developing data sampling technologies It is based on the principle that many types of vector-space data are compressible, which is a term of art in mathematical signal processing The key ideas are that randomized dimension reduction preserves the information in a compressible signal and that it is possible to develop hardware devices that implement this dimension reduction efficiently The main computational challenge in CoSa is to reconstruct a compressible signal from the reduced representation acquired by the sampling device This extended abstract describes a recent algorithm, called, CoSaMP, that accomplishes the data recovery task It was the first known method to offer near-optimal guarantees on resource usageread more
Citations
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Journal ArticleDOI
Message-passing algorithms for compressed sensing
TL;DR: A simple costless modification to iterative thresholding is introduced making the sparsity–undersampling tradeoff of the new algorithms equivalent to that of the corresponding convex optimization procedures, inspired by belief propagation in graphical models.
Posted Content
Subspace Pursuit for Compressive Sensing Signal Reconstruction
Wei Dai,Olgica Milenkovic +1 more
TL;DR: In this paper, the subspace pursuit algorithm was proposed for sparse signals with and without noisy perturbations, which has low computational complexity, comparable to that of orthogonal matching pursuit techniques when applied to very sparse signals, and reconstruction accuracy of the same order as that of LP optimization methods.
BookDOI
Compressed sensing : theory and applications
Yonina C. Eldar,Gitta Kutyniok +1 more
TL;DR: In this paper, the authors introduce the concept of second generation sparse modeling and apply it to the problem of compressed sensing of analog signals, and propose a greedy algorithm for compressed sensing with high-dimensional geometry.
Journal ArticleDOI
Model-Based Compressive Sensing
TL;DR: In this article, the authors introduce a new class of structured compressible signals along with a new sufficient condition for robust structured compressibility signal recovery that they dub the restricted amplification property, which is the natural counterpart to the restricted isometry property of conventional CS.
Book
Handbook of Blind Source Separation: Independent Component Analysis and Applications
Pierre Comon,Christian Jutten +1 more
TL;DR: This handbook provides the definitive reference on Blind Source Separation, giving a broad and comprehensive description of all the core principles and methods, numerical algorithms and major applications in the fields of telecommunications, biomedical engineering and audio, acoustic and speech processing.
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
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
TL;DR: In this paper, the authors considered the model problem of reconstructing an object from incomplete frequency samples and showed that with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the lscr/sub 1/ minimization problem.
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
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.