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Lower Bounds for Sparse Recovery
"... We consider the following ksparse recovery problem: design an m × n matrix A, such that for any signal x, given Ax we can efficiently recover ˆx satisfying ..."
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Cited by 60 (23 self)
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We consider the following ksparse recovery problem: design an m × n matrix A, such that for any signal x, given Ax we can efficiently recover ˆx satisfying
On the Power of Adaptivity in Sparse Recovery
, 2011
"... The goal of (stable) sparse recovery is to recover a ksparse approximation x ∗ of a vector x from linear measurements of x. Specifically, the goal is to recover x ∗ such that ‖x − x ∗ ‖ ..."
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Cited by 14 (4 self)
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The goal of (stable) sparse recovery is to recover a ksparse approximation x ∗ of a vector x from linear measurements of x. Specifically, the goal is to recover x ∗ such that ‖x − x ∗ ‖
Sparse Recovery Using Sparse Matrices
"... We survey algorithms for sparse recovery problems that are based on sparse random matrices. Such matrices has several attractive properties: they support algorithms with low computational complexity, and make it easy to perform incremental updates to signals. We discuss applications to several areas ..."
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Cited by 72 (12 self)
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We survey algorithms for sparse recovery problems that are based on sparse random matrices. Such matrices has several attractive properties: they support algorithms with low computational complexity, and make it easy to perform incremental updates to signals. We discuss applications to several
Sparse Recovery and Fourier Sampling
, 2013
"... the last decade a broad literature has arisen studying sparse recovery, the estimation of sparse vectors from low dimensional linear projections. Sparse recovery has a wide variety of applications such as streaming algorithms, image acquisition, and disease testing. A particularly important subclass ..."
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Cited by 1 (0 self)
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the last decade a broad literature has arisen studying sparse recovery, the estimation of sparse vectors from low dimensional linear projections. Sparse recovery has a wide variety of applications such as streaming algorithms, image acquisition, and disease testing. A particularly important
Sparse recovery using sparse matrices
, 2008
"... We consider the approximate sparse recovery problem, where the goal is to (approximately) recover a highdimensional vector x from its lowerdimensional sketch Ax. A popular way of performing this recovery is by finding x # such that Ax = Ax # , and ‖x # ‖1 is minimal. It is known that this approach ..."
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Cited by 11 (1 self)
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We consider the approximate sparse recovery problem, where the goal is to (approximately) recover a highdimensional vector x from its lowerdimensional sketch Ax. A popular way of performing this recovery is by finding x # such that Ax = Ax # , and ‖x # ‖1 is minimal. It is known
AN ALPS VIEW OF SPARSE RECOVERY
"... We provide two compressive sensing (CS) recovery algorithms based on iterative hardthresholding. The algorithms, collectively dubbed as algebraic pursuits (ALPS), exploit the restricted isometry properties of the CS measurement matrix within the algebra of Nesterov’s optimal gradient methods. We th ..."
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Cited by 15 (7 self)
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We provide two compressive sensing (CS) recovery algorithms based on iterative hardthresholding. The algorithms, collectively dubbed as algebraic pursuits (ALPS), exploit the restricted isometry properties of the CS measurement matrix within the algebra of Nesterov’s optimal gradient methods. We
On Partially Sparse Recovery
, 2011
"... In this paper we consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the ℓ1norm of the part of the solution vector which is known to be sparse. Such a problem is closely related to the classical problem in Compressed Sensing ..."
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where the ℓ1norm of the whole solution vector is minimized. We introduce analogues of restricted isometry and null space properties for the recovery of partially sparse vectors and show that these new properties are implied by their original counterparts. We show also how to extend recovery under noisy
Results 1  10
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