Preprint Series 2013
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2013:03
E. Livshitz and
V. Temlyakov
We study sparse approximation by greedy algorithms. Our contribution is two-fold. First, we prove exact recovery with high probability of random $K$-sparse signals within $\lceil K(1+\epsilon)\rceil$ iterations of the Orthogonal Matching Pursuit (OMP). This result shows that in a probabilistic sense the OMP is almost optimal ...
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2013:02
V. Temlyakov
We prove an inequality for the entropy numbers in terms of nonlinear Kolmogorov's widths. This inequality is in a spirit of known inequalities of this type and it is adjusted to the form convenient in applications for m-term approximations with respect to a given system. Also, we obtain ...
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2013:01
V. Temlyakov
We discuss construction of coverings of the unit ball of a finite dimensional Banach space. The well known technique of comparing volumes gives upper and lower bounds on covering numbers. This technique does not provide a construction of good coverings. Here we apply incoherent dictionaries for construction of good coverings ...
[Full Abstract]
