@inproceedings{c0c3aa4841e8458d9d3552d4562a9f8c,
title = "Can we allow linear dependencies in the dictionary in the sparse synthesis framework?",
abstract = "Signal recovery from a given set of linear measurements using a sparsity prior has been a major subject of research in recent years. In this model, the signal is assumed to have a sparse representation under a given dictionary. Most of the work dealing with this subject has focused on the reconstruction of the signal's representation as the means for recovering the signal itself. This approach forced the dictionary to be of low coherence and with no linear dependencies between its columns. Recently, a series of contributions that focus on signal recovery using the analysis model find that linear dependencies in the analysis dictionary are in fact permitted and beneficial. In this paper we show theoretically that the same holds also for signal recovery in the synthesis case for the ℓ0-synthesis minimization problem. In addition, we demonstrate empirically the relevance of our conclusions for recovering the signal using an ℓ1-relaxation.",
keywords = "Sparse representations, analysis versus synthesis, compressed sensing, inverse problems",
author = "Raja Giryes and Michael Elad",
year = "2013",
month = oct,
day = "18",
doi = "10.1109/ICASSP.2013.6638707",
language = "אנגלית",
isbn = "9781479903566",
series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",
pages = "5459--5463",
booktitle = "2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings",
note = "null ; Conference date: 26-05-2013 Through 31-05-2013",
}