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Compressed Sensing.
, 2011
"... The central problem of Compressed Sensing is to recover a sparse signal from fewer measurements than its ambient dimension. Recent results by Donoho, and Candes and Tao giving theoretical guarantees that ( 1minimization succeeds in recovering the signal in a large number of cases have stirred up mu ..."
Abstract
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The central problem of Compressed Sensing is to recover a sparse signal from fewer measurements than its ambient dimension. Recent results by Donoho, and Candes and Tao giving theoretical guarantees that ( 1minimization succeeds in recovering the signal in a large number of cases have stirred up
Compressed Sensing
"... The theoretical problem of finding the solution to an underdetermined set of linear equations has for several years attracted considerable attention in the literature. This problem has many practical applications. One example of such an application is compressed sensing (cs), which has the potentia ..."
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The theoretical problem of finding the solution to an underdetermined set of linear equations has for several years attracted considerable attention in the literature. This problem has many practical applications. One example of such an application is compressed sensing (cs), which has
Distributed compressed sensing
, 2005
"... Compressed sensing is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. In this paper we introduce a new theory for distributed compressed sensing (DCS) that enables new distributed coding algori ..."
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Cited by 136 (26 self)
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Compressed sensing is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. In this paper we introduce a new theory for distributed compressed sensing (DCS) that enables new distributed coding
Compressed sensing and best kterm approximation
 J. Amer. Math. Soc
, 2009
"... Compressed sensing is a new concept in signal processing where one seeks to minimize the number of measurements to be taken from signals while still retaining the information necessary to approximate them well. The ideas have their origins in certain abstract results from functional analysis and app ..."
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Cited by 282 (10 self)
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Compressed sensing is a new concept in signal processing where one seeks to minimize the number of measurements to be taken from signals while still retaining the information necessary to approximate them well. The ideas have their origins in certain abstract results from functional analysis
Compressed Sensing: Theory and Applications
, 2012
"... Compressed sensing is a novel research area, which was introduced in 2006, and since then has already become a key concept in various areas of applied mathematics, computer science, and electrical engineering. It surprisingly predicts that highdimensional signals, which allow a sparse representati ..."
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Cited by 120 (30 self)
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Compressed sensing is a novel research area, which was introduced in 2006, and since then has already become a key concept in various areas of applied mathematics, computer science, and electrical engineering. It surprisingly predicts that highdimensional signals, which allow a sparse
1Bit Compressive Sensing
"... Abstract—Compressive sensing is a new signal acquisition technology with the potential to reduce the number of measurements required to acquire signals that are sparse or compressible in some basis. Rather than uniformly sampling the signal, compressive sensing computes inner products with a randomi ..."
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Cited by 98 (12 self)
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Abstract—Compressive sensing is a new signal acquisition technology with the potential to reduce the number of measurements required to acquire signals that are sparse or compressible in some basis. Rather than uniformly sampling the signal, compressive sensing computes inner products with a
Combinatorial Algorithms for Compressed Sensing
 In Proc. of SIROCCO
, 2006
"... Abstract — In sparse approximation theory, the fundamental problem is to reconstruct a signal A ∈ R n from linear measurements 〈A, ψi 〉 with respect to a dictionary of ψi’s. Recently, there is focus on the novel direction of Compressed Sensing [1] where the reconstruction can be done with very few—O ..."
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Cited by 113 (1 self)
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Abstract — In sparse approximation theory, the fundamental problem is to reconstruct a signal A ∈ R n from linear measurements 〈A, ψi 〉 with respect to a dictionary of ψi’s. Recently, there is focus on the novel direction of Compressed Sensing [1] where the reconstruction can be done with very few
Iteratively reweighted algorithms for compressive sensing
 in 33rd International Conference on Acoustics, Speech, and Signal Processing (ICASSP
, 2008
"... The theory of compressive sensing has shown that sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. In [1], it was shown empirically that using ℓ p minimization with p < 1 can do so with fewer measurements than with p = 1. In this paper ..."
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Cited by 185 (8 self)
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The theory of compressive sensing has shown that sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. In [1], it was shown empirically that using ℓ p minimization with p < 1 can do so with fewer measurements than with p = 1
Compressed Sensing
"... ◮ Think of a grayscale image as a vector of pixel intensities x ∈ R m. ◮ The idea is to choose m × m matrix F whose rows are basis for R m for which θ = F x has many small entries (i.e. θ is approximately sparse). ◮ Then only need to store the K largest magnitude coefficients θi. Discrete Cosine Tra ..."
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◮ Think of a grayscale image as a vector of pixel intensities x ∈ R m. ◮ The idea is to choose m × m matrix F whose rows are basis for R m for which θ = F x has many small entries (i.e. θ is approximately sparse). ◮ Then only need to store the K largest magnitude coefficients θi. Discrete Cosine Transform ◮ Sample m cosine functions of different periods at m places to make a basis for Rm. For m = 3 we could let
Results 11  20
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