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292
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization,”
 SIAM Review,
, 2010
"... Abstract The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and col ..."
Abstract

Cited by 562 (20 self)
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, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, the general affine rank minimization problem is NPhard, because it contains vector cardinality minimization as a special case. In this paper, we show that if a certain restricted isometry property holds
On the dynamics of isometries
 Geom. Topol
"... Abstract We provide an analysis of the dynamics of isometries and semicontractions of metric spaces. Certain subsets of the boundary at infinity play a fundamental role and are identified completely for the standard boundaries of CAT(0)spaces, Gromov hyperbolic spaces, Hilbert geometries, certain ..."
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Cited by 3 (2 self)
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Abstract We provide an analysis of the dynamics of isometries and semicontractions of metric spaces. Certain subsets of the boundary at infinity play a fundamental role and are identified completely for the standard boundaries of CAT(0)spaces, Gromov hyperbolic spaces, Hilbert geometries, certain
On the dynamics of isometries
, 2005
"... We provide an analysis of the dynamics of isometries and semicontractions of metric spaces. Certain subsets of the boundary at infinity play a fundamental role and are identified completely for the standard boundaries of CAT(0)– spaces, Gromov hyperbolic spaces, Hilbert geometries, certain pseudocon ..."
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We provide an analysis of the dynamics of isometries and semicontractions of metric spaces. Certain subsets of the boundary at infinity play a fundamental role and are identified completely for the standard boundaries of CAT(0)– spaces, Gromov hyperbolic spaces, Hilbert geometries, certain
Restricted isometries for partial random circulant matrices
 APPL. COMPUT. HARMON. ANAL
, 2010
"... In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants of the sampl ..."
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Cited by 47 (8 self)
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In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants
Pseudogroups of isometries of R: reconstruction of . . .
"... The theorem of Rips about free actions on Rtrees relies on a careful analysis of finite systems of partial isometries of R. In this paper we associate a free action on an Rtree to any finite system of isometries without reflection. Any free action may be approximated (strongly in the sense of Gi ..."
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Cited by 4 (1 self)
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The theorem of Rips about free actions on Rtrees relies on a careful analysis of finite systems of partial isometries of R. In this paper we associate a free action on an Rtree to any finite system of isometries without reflection. Any free action may be approximated (strongly in the sense
Analysis of Orthogonal Matching Pursuit using the restricted isometry property
, 2009
"... Orthogonal Matching Pursuit (OMP) is the canonical greedy algorithm for sparse approximation. In this paper we demonstrate that the restricted isometry property (RIP) can be used for a very straightforward analysis of OMP. Our main conclusion is that the RIP of order K +1 (with isometry constant δ & ..."
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Cited by 78 (6 self)
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Orthogonal Matching Pursuit (OMP) is the canonical greedy algorithm for sparse approximation. In this paper we demonstrate that the restricted isometry property (RIP) can be used for a very straightforward analysis of OMP. Our main conclusion is that the RIP of order K +1 (with isometry constant δ
ON ISOMETRY GROUPS AND MAXIMAL SYMMETRY
, 2013
"... We study problems of maximal symmetry in Banach spaces. This is done by providing an analysis of the structure of small subgroups of the general linear group GL.X/, where X is a separable reflexive Banach space. In particular, we provide the first known example of a Banach space X without any equiva ..."
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Cited by 2 (1 self)
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We study problems of maximal symmetry in Banach spaces. This is done by providing an analysis of the structure of small subgroups of the general linear group GL.X/, where X is a separable reflexive Banach space. In particular, we provide the first known example of a Banach space X without any
ON ISOMETRIES OF INTRINSIC METRICS IN COMPLEX ANALYSIS
, 2005
"... Abstract. We study isometries of the Kobayashi and Carathéodory metrics on strongly pseudoconvex and strongly convex domains in C n and prove: (i) Let Ω1 and Ω2 be strongly pseudoconvex domains in C n and f: Ω1 → Ω2 an isometry. Suppose that f extends as a C 1 map to ¯ Ω1. Then f∂Ω1: ∂Ω1 → ∂Ω2 is a ..."
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Abstract. We study isometries of the Kobayashi and Carathéodory metrics on strongly pseudoconvex and strongly convex domains in C n and prove: (i) Let Ω1 and Ω2 be strongly pseudoconvex domains in C n and f: Ω1 → Ω2 an isometry. Suppose that f extends as a C 1 map to ¯ Ω1. Then f∂Ω1: ∂Ω1 → ∂Ω2
Compressed sensing: how sharp is the restricted isometry property?
, 2009
"... Compressed sensing is a recent technique by which signals can be measured at a rate proportional to their information content, combining the important task of compression directly into the measurement process. Since its introduction in 2004 there have been hundreds of manuscripts on compressed sens ..."
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Cited by 51 (7 self)
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sensing, a large fraction of which have focused on the design and analysis of algorithms to recover a signal from its compressed measurements. The Restricted Isometry Property (RIP) has become a ubiquitous property assumed in their analysis. We present the best known bounds on the RIP, and in the process
On Support Sizes of Restricted Isometry Constants
, 2009
"... A generic tool for analyzing sparse approximation algorithms is the restricted isometry property (RIP) introduced by Candès and Tao. For qualitative comparison of sufficient conditions derived from an RIP analysis, the support size of the RIP constants is generally reduced as much as possible with t ..."
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Cited by 5 (2 self)
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A generic tool for analyzing sparse approximation algorithms is the restricted isometry property (RIP) introduced by Candès and Tao. For qualitative comparison of sufficient conditions derived from an RIP analysis, the support size of the RIP constants is generally reduced as much as possible
Results 1  10
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292