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CORR
2010
Springer

Where is Randomness Needed to Break the Square-Root Bottleneck?

9 years 7 months ago
Where is Randomness Needed to Break the Square-Root Bottleneck?
As shown by Tropp, 2008, for the concatenation of two orthonormal bases (ONBs), breaking the square-root bottleneck in compressed sensing does not require randomization over all the positions of the nonzero entries of the sparse coefficient vector. Rather the positions corresponding to one of the two ONBs can be chosen arbitrarily. The two-ONB structure is, however, restrictive and does not reveal the property that is responsible for allowing to break the bottleneck with reduced randomness. For general dictionaries we show that if a subdictionary with small enough coherence and large enough cardinality can be isolated, the bottleneck can be broken under the same probabilistic model on the sparse coefficient vector as in the two-ONB case.
Patrick Kuppinger, Giuseppe Durisi, Helmut Bö
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Patrick Kuppinger, Giuseppe Durisi, Helmut Bölcskei
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