Results 1  10
of
3,921
SIGNAL RECOVERY BY PROXIMAL FORWARDBACKWARD SPLITTING
 MULTISCALE MODEL. SIMUL. TO APPEAR
"... We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a unifi ..."
Abstract

Cited by 509 (24 self)
 Add to MetaCart
We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a
Stable signal recovery from incomplete and inaccurate measurements,”
 Comm. Pure Appl. Math.,
, 2006
"... Abstract Suppose we wish to recover a vector x 0 ∈ R m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax 0 + e; A is an n × m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x 0 accurately based on the data y? To r ..."
Abstract

Cited by 1397 (38 self)
 Add to MetaCart
Abstract Suppose we wish to recover a vector x 0 ∈ R m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax 0 + e; A is an n × m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x 0 accurately based on the data y
Signal recovery from random measurements via Orthogonal Matching Pursuit
 IEEE TRANS. INFORM. THEORY
, 2007
"... This technical 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(m ln d) random linear measurements of that signal. This is a massive improvement over previous ..."
Abstract

Cited by 802 (9 self)
 Add to MetaCart
previous results for OMP, which require O(m 2) measurements. The new results for OMP are comparable with recent results for another algorithm called Basis Pursuit (BP). The OMP algorithm is faster and easier to implement, which makes it an attractive alternative to BP for signal recovery problems.
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
 California Institute of Technology, Pasadena
, 2008
"... Abstract. Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery alg ..."
Abstract

Cited by 770 (13 self)
 Add to MetaCart
Abstract. Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
Abstract

Cited by 1513 (20 self)
 Add to MetaCart
Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear
Dualization of Signal Recovery Problems
, 2009
"... In convex optimization, duality theory can sometimes lead to simpler solution methods than those resulting from direct primal analysis. In this paper, this principle is applied to a class of composite variational problems arising in particular in signal recovery. These problems are not easily amenab ..."
Abstract

Cited by 16 (6 self)
 Add to MetaCart
In convex optimization, duality theory can sometimes lead to simpler solution methods than those resulting from direct primal analysis. In this paper, this principle is applied to a class of composite variational problems arising in particular in signal recovery. These problems are not easily
Combining geometry and combinatorics: a unified approach to sparse signal recovery
, 2008
"... There are two main algorithmic approaches to sparse signal recovery: geometric and combinatorial. The geometric approach starts with a geometric constraint on the measurement matrix Φ and then uses linear programming to decode information about x from Φx. The combinatorial approach constructs Φ an ..."
Abstract

Cited by 157 (14 self)
 Add to MetaCart
There are two main algorithmic approaches to sparse signal recovery: geometric and combinatorial. The geometric approach starts with a geometric constraint on the measurement matrix Φ and then uses linear programming to decode information about x from Φx. The combinatorial approach constructs Φ
Signal recovery from partial information via Orthogonal Matching Pursuit
 IEEE TRANS. INFORM. THEORY
, 2005
"... This article 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(m ln d) random linear measurements of that signal. This is a massive improvement over previous results ..."
Abstract

Cited by 191 (8 self)
 Add to MetaCart
results for OMP, which require O(m 2) measurements. The new results for OMP are comparable with recent results for another algorithm called Basis Pursuit (BP). The OMP algorithm is much faster and much easier to implement, which makes it an attractive alternative to BP for signal recovery problems.
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
Abstract

Cited by 483 (2 self)
 Add to MetaCart
that convex relaxation succeeds. As evidence of the broad impact of these results, the paper describes how convex relaxation can be used for several concrete signal recovery problems. It also describes applications to channel coding, linear regression, and numerical analysis.
Uniform Uncertainty Principle and signal recovery via Regularized Orthogonal Matching Pursuit
, 2007
"... This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements – L1minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantage ..."
Abstract

Cited by 188 (8 self)
 Add to MetaCart
This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements – L1minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has
Results 1  10
of
3,921