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Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
- E. Candès, J. Romberg, T. Tao
- Computer ScienceIEEE Transactions on Information Theory
- 10 September 2004
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
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.
Stable signal recovery from incomplete and inaccurate measurements
It is shown that it is possible to recover x0 accurately based on the data y from incomplete and contaminated observations.
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
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.
Endpoint Strichartz estimates
<abstract abstract-type="TeX"><p>We prove an abstract Strichartz estimate, which implies previously unknown endpoint Strichartz estimates for the wave equation (in dimension <i>n</i> ≥ 4) and the…
Nonlinear dispersive equations : local and global analysis
- T. Tao
- 8 June 2006
Ordinary differential equations Constant coefficient linear dispersive equations Semilinear dispersive equations The Korteweg de Vries equation Energy-critical semilinear dispersive equations Wave…
The Power of Convex Relaxation: Near-Optimal Matrix Completion
This paper shows that, under certain incoherence assumptions on the singular vectors of the matrix, recovery is possible by solving a convenient convex program as soon as the number of entries is on the order of the information theoretic limit (up to logarithmic factors).
Topics in Random Matrix Theory
- T. Tao
- 21 March 2012
The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field…
The primes contain arbitrarily long arithmetic progressions
We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. The first is Szemeredi�s theorem, which asserts that any subset of the integers of…
On the multilinear restriction and Kakeya conjectures
We prove d-linear analogues of the classical restriction and Kakeya conjectures in Rd. Our approach involves obtaining monotonicity formulae pertaining to a certain evolution of families of…