TY - GEN
T1 - Can we allow linear dependencies in the dictionary in the sparse synthesis framework?
AU - Giryes, Raja
AU - Elad, Michael
PY - 2013/10/18
Y1 - 2013/10/18
N2 - 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.
AB - 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.
KW - Sparse representations
KW - analysis versus synthesis
KW - compressed sensing
KW - inverse problems
UR - http://www.scopus.com/inward/record.url?scp=84890507372&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2013.6638707
DO - 10.1109/ICASSP.2013.6638707
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AN - SCOPUS:84890507372
SN - 9781479903566
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 5459
EP - 5463
BT - 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings
T2 - 2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013
Y2 - 26 May 2013 through 31 May 2013
ER -