Improved Sparsity Thresholds Through Dictionary Splitting

Details Improved Sparsity Thresholds Through Dictionary Splitting Improved Sparsity Thresholds Through Dictionary Splitting

2009-08-12

arxiv.org/abs/0908.1676v1

Computer Science

Information Theory

IEEE Information Theory Workshop (ITW), Taormina, Italy, Oct. 2009, to appear

Scientific paper

Known sparsity thresholds for basis pursuit to deliver the maximally sparse solution of the compressed sensing recovery problem typically depend on the dictionary's coherence. While the coherence is easy to compute, it can lead to rather pessimistic thresholds as it captures only limited information about the dictionary. In this paper, we show that viewing the dictionary as the concatenation of two general sub-dictionaries leads to provably better sparsity thresholds--that are explicit in the coherence parameters of the dictionary and of the individual sub-dictionaries. Equivalently, our results can be interpreted as sparsity thresholds for dictionaries that are unions of two general (i.e., not necessarily orthonormal) sub-dictionaries.

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