Average Performance Analysis for Thresholding
- 22 October 2007
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Signal Processing Letters
- Vol. 14 (11) , 828-831
- https://doi.org/10.1109/lsp.2007.903248
Abstract
In this letter, we show that with high probability, the thresholding algorithm can recover signals that are sparse in a redundant dictionary as long as the 2-Babel function is growing slowly. This implies that it can succeed for sparsity levels up to the order of the ambient dimension. The theoretical bounds are illustrated with numerical simulations. As an application of the theory, sensing dictionaries for optimal average performance are characterized, and their performance is tested numerically.Keywords
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