Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit
Finding the sparsest solution to underdetermined systems of linear equations y= Φ x is NP-
hard in general. We show here that for systems with “typical”/“random” Φ, a good …
hard in general. We show here that for systems with “typical”/“random” Φ, a good …
From sparse solutions of systems of equations to sparse modeling of signals and images
A full-rank matrix \bfA∈R^n*m with n<m generates an underdetermined system of linear
equations \bfAx=\bfb having infinitely many solutions. Suppose we seek the sparsest …
equations \bfAx=\bfb having infinitely many solutions. Suppose we seek the sparsest …
For most large underdetermined systems of linear equations the minimal 𝓁1‐norm solution is also the sparsest solution
DL Donoho - … on Pure and Applied Mathematics: A Journal …, 2006 - Wiley Online Library
We consider linear equations y= Φx where y is a given vector in ℝn and Φ is a given n× m
matrix with n< m≤ τn, and we wish to solve for x∈ ℝm. We suppose that the columns of Φ …
matrix with n< m≤ τn, and we wish to solve for x∈ ℝm. We suppose that the columns of Φ …
Extensions of compressed sensing
We study the notion of compressed sensing (CS) as put forward by Donoho, Candes, Tao
and others. The notion proposes a signal or image, unknown but supposed to be …
and others. The notion proposes a signal or image, unknown but supposed to be …
Fast Solution of -Norm Minimization Problems When the Solution May Be Sparse
The minimum lscr 1-norm solution to an underdetermined system of linear equations y= Ax
is often, remarkably, also the sparsest solution to that system. This sparsity-seeking property …
is often, remarkably, also the sparsest solution to that system. This sparsity-seeking property …
Error correction via linear programming
Suppose we wish to transmit a vector f ϵ R n reliably. A frequently discussed approach
consists in encoding f with an m by n coding matrix A. Assume now that a fraction of the …
consists in encoding f with an m by n coding matrix A. Assume now that a fraction of the …
Geometric approach to error-correcting codes and reconstruction of signals
M Rudelson, R Vershynin - International mathematics research …, 2005 - ieeexplore.ieee.org
We develop an approach through geometric functional analysis to reconstruction of signals
from few linear measurements and to error-correcting codes. An error-correcting code …
from few linear measurements and to error-correcting codes. An error-correcting code …
MCALab: Reproducible research in signal and image decomposition and inpainting
Morphological Component Analysis (MCA) of signals and images is an ambitious and
important goal in signal processing; successful methods for MCA have many far-reaching …
important goal in signal processing; successful methods for MCA have many far-reaching …
Sparse spatial filter optimization for EEG channel reduction in brain-computer interface
Spatial filters are useful in discriminating different classes of electroencephalogram (EEG)
signals such as those corresponding to motor activities. In the case of discriminating two …
signals such as those corresponding to motor activities. In the case of discriminating two …
RSP-Based Analysis for Sparsest and Least -Norm Solutions to Underdetermined Linear Systems
YB Zhao - IEEE Transactions on Signal Processing, 2013 - ieeexplore.ieee.org
Recently, the worse-case analysis, probabilistic analysis and empirical justification have
been employed to address the fundamental question: When does ℓ 1-minimization find the …
been employed to address the fundamental question: When does ℓ 1-minimization find the …