Average Performance Analysis for Thresholding

Karin Schnass, Pierre Vandergheynst
2007 IEEE Signal Processing Letters  
In this article is shown 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 characterised and their performance is tested numerically.
more » ... s tested numerically.
doi:10.1109/lsp.2007.903248 fatcat:nnqt5uv2f5ay3bbdbtiksj5pyy