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Robust principal component analysis?
TLDR
It is proved that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, this suggests the possibility of a principled approach to robust principal component analysis.
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
TLDR
It is shown how one can reconstruct a piecewise constant object from incomplete frequency samples - provided that the number of jumps (discontinuities) obeys the condition above - by minimizing other convex functionals such as the total variation of f.
Decoding by linear programming
  • E. Candès, T. Tao
  • Computer Science, Mathematics
    IEEE Transactions on Information Theory
  • 15 February 2005
TLDR
F can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program) and numerical experiments suggest that this recovery procedure works unreasonably well; f is recovered exactly even in situations where a significant fraction of the output is corrupted.
An Introduction To Compressive Sampling
TLDR
The theory of compressive sampling, also known as compressed sensing or CS, is surveyed, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition.
Enhancing Sparsity by Reweighted ℓ1 Minimization
TLDR
A novel method for sparse signal recovery that in many situations outperforms ℓ1 minimization in the sense that substantially fewer measurements are needed for exact recovery.
Stable signal recovery from incomplete and inaccurate measurements
Suppose we wish to recover a vector x_0 Є R^m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax_0 + e; A is an n by m matrix with far fewer rows than columns (n «
A Singular Value Thresholding Algorithm for Matrix Completion
TLDR
This paper develops a simple first-order and easy-to-implement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank, and develops a framework in which one can understand these algorithms in terms of well-known Lagrange multiplier algorithms.
The Dantzig selector: Statistical estimation when P is much larger than n
In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y=Xβ+z, where β∈Rp is a
The restricted isometry property and its implications for compressed sensing
Abstract It is now well-known that one can reconstruct sparse or compressible signals accurately from a very limited number of measurements, possibly contaminated with noise. This technique known as
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
  • E. Candès, T. Tao
  • Mathematics, Computer Science
    IEEE Transactions on Information Theory
  • 25 October 2004
TLDR
If the objects of interest are sparse in a fixed basis or compressible, then it is possible to reconstruct f to within very high accuracy from a small number of random measurements by solving a simple linear program.
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