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EURASIP Journal on Advances in Signal Processing, ISSN 1687-6172, 12/2013, Volume 2013, Issue 1, pp. 1 - 17
Compressed sensing (CS) states that a sparse signal can exactly be recovered from very few linear measurements. While in many applications, real-world signals... 
Engineering | IRLS | Signal, Image and Speech Processing | Block-sparse recovery | Block-RIP | l 2 / l q minimization | Compressed sensing | minimization
Journal Article
Applied and Computational Harmonic Analysis, ISSN 1063-5203, 05/2012, Volume 32, Issue 3, pp. 329 - 341
In this paper, it is proved that every s-sparse vector x∈ℝ can be exactly recovered from the measurement vector z=Ax∈ via some ℓ -minimization with 0 Sparse signal | | minimization | Compressive sampling
Journal Article
by Lai, MJ and Xu, YY and Yin, WT
SIAM JOURNAL ON NUMERICAL ANALYSIS, ISSN 0036-1429, 2013, Volume 51, Issue 2, pp. 927 - 957
In this paper, we first study l(q) minimization and its associated iterative reweighted algorithm for recovering sparse vectors. Unlike most existing work, we... 
low-rank matrix recovery | MATHEMATICS, APPLIED | sparse vector recovery | compressed sensing | matrix completion | APPROXIMATION | THRESHOLDING ALGORITHM | l(q) minimization | iterative reweighted least squares | RECOVERY | SHAPE | MOTION | sparse optimization | FACTORIZATION METHOD | L-MINIMIZATION | IMAGE STREAMS
Journal Article
by Lai, MJ and Wang, JY
SIAM JOURNAL ON OPTIMIZATION, ISSN 1052-6234, 2011, Volume 21, Issue 1, pp. 82 - 101
We study an unconstrained version of the l(q) minimization for the sparse solution of underdetermined linear systems for 0 < q <= 1. Although the minimization... 
L MINIMIZATION | MATHEMATICS, APPLIED | sparse solution | compressed sensing | REPRESENTATIONS | APPROXIMATION | IMAGES | NONCONVEX MINIMIZATION | RECONSTRUCTION | SIGNAL RECOVERY | ALGORITHM | l(q) minimization
Journal Article
by Sun, QY
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, ISSN 1063-5203, 05/2012, Volume 32, Issue 3, pp. 329 - 341
In this paper, it is proved that every s-sparse vector x is an element of R-n can be exactly recovered from the measurement vector z = Ax is an element of R-m... 
l(q)-minimization | MATHEMATICS, APPLIED | MINIMIZATION | RECONSTRUCTION | Sparse signal | PHYSICS, MATHEMATICAL | Compressive sampling
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2015, Volume 37, Issue 1, pp. A536 - A563
Journal Article
by Gao, Y and Peng, JG and Yue, SG
SIGNAL PROCESSING, ISSN 0165-1684, 08/2017, Volume 137, pp. 287 - 297
This paper focuses on block sparse recovery with the l(2)/l(q)-minimization for 0 < q <= 1. We first give the l(q) stable block Null Space Property (NSP), a... 
Block sparse | BASES | l/l(q)-minimization | RECONSTRUCTION | INFORMATION | SIGNALS | Null space property | RESTRICTED ISOMETRY PROPERTY | Instance optimality | Quotient property | VARIABLE SELECTION | ENGINEERING, ELECTRICAL & ELECTRONIC | MINIMIZATION | UNCERTAINTY PRINCIPLES | MATRICES | Compressed sensing
Journal Article
SIAM JOURNAL ON SCIENTIFIC COMPUTING, ISSN 1064-8275, 2015, Volume 37, Issue 5, pp. S30 - S50
This paper presents a new efficient approach for the solution of the l(p)-l(q) minimization problem based on the application of successive orthogonal... 
FEATURE-SELECTION | TIKHONOV REGULARIZATION | MATHEMATICS, APPLIED | generalized Krylov subspaces | half-quadratic | image restoration | RECONSTRUCTION | ALGORITHM | iteratively reweighted least-squares | PARAMETER CHOICE RULES | l(p)-l(q) minimization
Journal Article
by Chen, BX and Wan, AH
NEUROCOMPUTING, ISSN 0925-2312, 10/2019, Volume 363, pp. 306 - 312
In this paper, we establish new restricted isometry conditions for sparse signal recovery via l(p) (0 < p <= 1) minimization. For any t is an element of (1,... 
Restricted isometry property (RIP) | STABLE RECOVERY | REPRESENTATION | Sparse signal recovery | l(p) minimization | Coherent tight frames | Compressed sensing | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | L(Q) MINIMIZATION
Journal Article
by Yin, PH and Lou, YF and He, Q and Xin, J
SIAM JOURNAL ON SCIENTIFIC COMPUTING, ISSN 1064-8275, 2015, Volume 37, Issue 1, pp. A536 - A563
We study minimization of the difference of l(1) and l(2) norms as a nonconvex and Lipschitz continuous metric for solving constrained and unconstrained... 
MATHEMATICS, APPLIED | simulate annealing | compressed sensing | nonconvex | SIGNAL RECOVERY | THRESHOLDING ALGORITHM | ATOMIC DECOMPOSITION | L-1/2 REGULARIZATION | l(1-2) minimization | L MINIMIZATION | difference of convex functions algorithm | L-MINIMIZATION | UNCERTAINTY PRINCIPLES | REWEIGHTED LEAST-SQUARES | SPARSE SOLUTIONS | CONVERGENCE
Journal Article
by Song, CB and Xia, ST
IEEE SIGNAL PROCESSING LETTERS, ISSN 1070-9908, 09/2014, Volume 21, Issue 9, pp. 1154 - 1158
In the context of compressed sensing, the nonconvex l(q) minimization with 0 < q < 1 has been studied in recent years. In this letter, by generalizing the... 
sparse signal recovery | restricted isometry property | l(q) minimization | Compressed sensing | ENGINEERING, ELECTRICAL & ELECTRONIC
Journal Article
by Guo, L and Liu, YL and Yan, L
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, ISSN 1004-8979, 11/2017, Volume 10, Issue 4, pp. 775 - 797
In this paper we consider the algorithm for recovering sparse orthogonal polynomials using stochastic collocation via l(q) minimization. The main results... 
MATHEMATICS, APPLIED | RANDOM INPUT DATA | DESIGN | polynomial chaos expansions | Uncertainty quantification | RESTRICTED ISOMETRY PROPERTY | stochastic collocation | ALGORITHMS | l(q)-minimization | MATHEMATICS | PARTIAL-DIFFERENTIAL-EQUATIONS | L-MINIMIZATION | POINTS | L(Q) MINIMIZATION
Journal Article
by Gao, Y and Peng, JG and Yue, SG
APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B, ISSN 1005-1031, 03/2018, Volume 33, Issue 1, pp. 1 - 24
Although Gaussian random matrices play an important role of measurement matrices in compressed sensing, one hopes that there exist other random matrices which... 
SIGNAL | MATHEMATICS, APPLIED | compressed sensing | REPRESENTATIONS | null space property | RECONSTRUCTION | STABILITY | quotient property | RESTRICTED ISOMETRY PROPERTY | l(q)-minimization | Weibull matrices | BOUNDS | UNCERTAINTY PRINCIPLES
Journal Article
Applied Mathematics-A Journal of Chinese Universities, ISSN 1005-1031, 3/2018, Volume 33, Issue 1, pp. 1 - 24
Although Gaussian random matrices play an important role of measurement matrices in compressed sensing, one hopes that there exist other random matrices which... 
15A52 | compressed sensing | Weibull matrices | l q -minimization | null space property | Mathematics, general | quotient property | Mathematics | Applications of Mathematics | 94A12 | 60E05 | 94A20
Journal Article
by Zhang, T and Tang, ZM and Liu, Q
JOURNAL OF ELECTRONIC IMAGING, ISSN 1017-9909, 05/2017, Volume 26, Issue 3
Low-rank representation (LRR) has been successfully applied to subspace clustering. However, the nuclear norm in the standard LRR is not optimal for... 
MOTION | APPROXIMATION | low-rank representation | L-q norm | ALGORITHM | motion segmentation | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | RANK | face clustering | OPTICS | weighted Schatten-p norm | ENGINEERING, ELECTRICAL & ELECTRONIC
Journal Article
by Li, S and Lin, JH
INVERSE PROBLEMS AND IMAGING, ISSN 1930-8337, 08/2014, Volume 8, Issue 3, pp. 761 - 777
Our aim of this article is to reconstruct a signal from undersampled data in the situation that the signal is sparse in terms of a tight frame. We present a... 
tight frames | l(q)-minimization | MATHEMATICS, APPLIED | coherence | D-Restricted isometry property | BOUNDS | RECONSTRUCTION | SIGNAL RECOVERY | SPARSE | sparse recovery | PHYSICS, MATHEMATICAL | Compressed sensing
Journal Article
by Liu, YF and Ma, SQ and Dai, YH and Zhang, SZ
MATHEMATICAL PROGRAMMING, ISSN 0025-5610, 07/2016, Volume 158, Issue 1-2, pp. 467 - 500
Journal Article
IEEE TRANSACTIONS ON SIGNAL PROCESSING, ISSN 1053-587X, 11/2012, Volume 60, Issue 11, pp. 5714 - 5724
Rank minimization problems, which consist of finding a matrix of minimum rank subject to linear constraints, have been proposed in many areas of engineering... 
matrix completion | l(q) optimization | SHRINKAGE | matrix rank minimization and sparse | ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC
Journal Article
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