Results 1  10
of
737
POSSIBLE NUMBERS OF NONZERO ENTRIES IN A MATRIX WITH A GIVEN TERM RANK
 ELA
, 2014
"... The possible numbers of nonzero entries in a matrix with a given term rank are determined respectively in the generic case, the symmetric case and the symmetric case with 0’s on the main diagonal. The matrices that attain the largest number of nonzero entries are also determined. ..."
Abstract
 Add to MetaCart
The possible numbers of nonzero entries in a matrix with a given term rank are determined respectively in the generic case, the symmetric case and the symmetric case with 0’s on the main diagonal. The matrices that attain the largest number of nonzero entries are also determined.
Lower Bound Theory of Nonzero Entries in Solutions of ℓ2ℓp Minimization
, 2009
"... Abstract. Recently, variable selection and sparse reconstruction are solved by finding an optimal solution of a minimization model where the objective function is the sum of a datafitting term in ℓ2 norm and a regularization term in ℓp norm (0 < p < 1). In this model, being able to classify ze ..."
Abstract

Cited by 25 (6 self)
 Add to MetaCart
zero and nonzero entries in its local solutions is a very important task. However, most algorithms for solving the problem can only provide an approximate local optimal solution, where nonzero entries in the solution cannot be identified theoretically. In this paper, we establish lower bounds
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
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
Maximum exponent of boolean circulant matrices with constant number of nonzero entries in their generating vector
, 2009
"... ..."
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
Abstract

Cited by 427 (36 self)
 Add to MetaCart
A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity
Sparsity and Incoherence in Compressive Sampling
, 2006
"... We consider the problem of reconstructing a sparse signal x 0 ∈ R n from a limited number of linear measurements. Given m randomly selected samples of Ux 0, where U is an orthonormal matrix, we show that ℓ1 minimization recovers x 0 exactly when the number of measurements exceeds m ≥ Const · µ 2 (U) ..."
Abstract

Cited by 238 (13 self)
 Add to MetaCart
) · S · log n, where S is the number of nonzero components in x 0, and µ is the largest entry in U properly normalized: µ(U) = √ n · maxk,j Uk,j. The smaller µ, the fewer samples needed. The result holds for “most ” sparse signals x 0 supported on a fixed (but arbitrary) set T. Given T, if the sign of x 0
Parallel Preconditioning with Sparse Approximate Inverses
 SIAM J. Sci. Comput
, 1996
"... A parallel preconditioner is presented for the solution of general sparse linear systems of equations. A sparse approximate inverse is computed explicitly, and then applied as a preconditioner to an iterative method. The computation of the preconditioner is inherently parallel, and its application o ..."
Abstract

Cited by 226 (10 self)
 Add to MetaCart
only requires a matrixvector product. The sparsity pattern of the approximate inverse is not imposed a priori but captured automatically. This keeps the amount of work and the number of nonzero entries in the preconditioner to a minimum. Rigorous bounds on the clustering of the eigenvalues
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
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
Sparse matrices in Matlab: Design and implementation
, 1991
"... We have extended the matrix computation language and environment Matlab to include sparse matrix storage and operations. The only change to the outward appearance of the Matlab language is a pair of commands to create full or sparse matrices. Nearly all the operations of Matlab now apply equally to ..."
Abstract

Cited by 164 (22 self)
 Add to MetaCart
to full or sparse matrices, without any explicit action by the user. The sparse data structure represents a matrix in space proportional to the number of nonzero entries, and most of the operations compute sparse results in time proportionaltothenumber of arithmetic operations on nonzeros.
Blocksparse signals: Uncertainty relations and efficient recovery
 IEEE TRANS. SIGNAL PROCESS
, 2010
"... We consider efficient methods for the recovery of blocksparse signals — i.e., sparse signals that have nonzero entries occurring in clusters—from an underdetermined system of linear equations. An uncertainty relation for blocksparse signals is derived, based on a blockcoherence measure, which we ..."
Abstract

Cited by 161 (17 self)
 Add to MetaCart
We consider efficient methods for the recovery of blocksparse signals — i.e., sparse signals that have nonzero entries occurring in clusters—from an underdetermined system of linear equations. An uncertainty relation for blocksparse signals is derived, based on a blockcoherence measure, which
Results 1  10
of
737