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1,026
The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices
, 2009
"... ..."
Exact Recovery of Sparsely-Used Dictionaries
- 25TH ANNUAL CONFERENCE ON LEARNING THEORY
, 2012
"... We consider the problem of learning sparsely used dictionaries with an arbitrary square dictionary and a random, sparse coefficient matrix. We prove that O(n log n) samples are sufficient to uniquely determine the coefficient matrix. Based on this proof, we design a polynomial-time algorithm, called ..."
Abstract
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Cited by 38 (2 self)
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, called Exact Recovery of Sparsely-Used Dictionaries (ER-SpUD), and prove that it probably recovers the dictionary and coefficient matrix when the coefficient matrix is sufficiently sparse. Simulation results show that ER-SpUD reveals the true dictionary as well as the coefficients with probability higher
WHEN “EXACT RECOVERY ” IS EXACT RECOVERY IN COMPRESSED SENSING SIMULATION
"... In a simulation of compressed sensing (CS), one must test whether the recovered solution x ̂ is the true solution x, i.e., “exact recovery. ” Most CS simulations employ one of two criteria: 1) the recovered support is the true support; or 2) the normalized squared error is less than 2. We analyze th ..."
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In a simulation of compressed sensing (CS), one must test whether the recovered solution x ̂ is the true solution x, i.e., “exact recovery. ” Most CS simulations employ one of two criteria: 1) the recovered support is the true support; or 2) the normalized squared error is less than 2. We analyze
Exact Recovery in the Stochastic Block Model
"... The stochastic block model (SBM) with two communities, or equivalently the planted partition model, is a popular model of random graph exhibiting a cluster behaviour. In its simplest form, the graph has two equally sized clusters and vertices connect with probability p within clusters and q across c ..."
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clusters. In the past two decades, a large body of literature in statistics and computer science has focused on providing lower-bounds on the scaling of |p − q | to ensure exact recovery. This paper identifies the sharp threshold for exact recovery. If α = pn / log(n) and β = qn / log(n) are constant (with
WHEN “EXACT RECOVERY ” IS EXACT RECOVERY IN COMPRESSED SENSING SIMULATION
, 2012
"... Accepted manuscript, peer reviewed version ..."
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
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Cited by 1397 (38 self)
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for almost any set of n coefficients provided that the number of nonzeros is of the order of n/(log m) 6 . In the case where the error term vanishes, the recovery is of course exact, and this work actually provides novel insights into the exact recovery phenomenon discussed in earlier papers. The methodology
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
Abstract
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Cited by 873 (26 self)
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We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can
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
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Cited by 1513 (20 self)
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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
Exact Recovery Threshold in the Binary Censored Block Model
, 2015
"... Binary censored block model G = ([n], E) and ∈ [0, 1/2] 1 Color the vertices in green or red arbitrarily 2 If endpoints in same color, color edge in blue (orange) w.p. 1 − () ..."
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Binary censored block model G = ([n], E) and ∈ [0, 1/2] 1 Color the vertices in green or red arbitrarily 2 If endpoints in same color, color edge in blue (orange) w.p. 1 − ()
Fuzzy extractors: How to generate strong keys from biometrics and other noisy data
, 2008
"... We provide formal definitions and efficient secure techniques for • turning noisy information into keys usable for any cryptographic application, and, in particular, • reliably and securely authenticating biometric data. Our techniques apply not just to biometric information, but to any keying mater ..."
Abstract
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Cited by 535 (38 self)
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if the input changes, as long as it remains reasonably close to the original. Thus, R can be used as a key in a cryptographic application. A secure sketch produces public information about its input w that does not reveal w, and yet allows exact recovery of w given another value that is close to w. Thus
Results 1 - 10
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