TY - GEN
T1 - Weighted sparse signal decomposition
AU - Babaie-Zadeh, Massoud
AU - Mehrdad, Behzad
AU - Giannakis, Georgios B.
PY - 2012
Y1 - 2012
N2 - Standard sparse decomposition (with applications in many different areas including compressive sampling) amounts to finding the minimum ℓ 0-norm solution of an underdetermined system of linear equations. In this decomposition, all atoms are treated 'uniformly' for being included or not in the decomposition. However, one may wish to weigh more or less certain atoms, or, assign higher costs to some other atoms to be included in the decomposition. This can happen for example when there is prior information available on each atom. This motivates generalizing the notion of minimal ℓ 0-norm solution to that of minimal weighted ℓ 0-norm solution. On the other hand, relaxing weighted ℓ 0-norm via the weighted ℓ 1-norm is challenging. This paper deals with minimal weighted ℓ 0-norm solutions of underdetermined linear systems, provides conditions for their uniqueness, and develops an algorithm for their estimation.
AB - Standard sparse decomposition (with applications in many different areas including compressive sampling) amounts to finding the minimum ℓ 0-norm solution of an underdetermined system of linear equations. In this decomposition, all atoms are treated 'uniformly' for being included or not in the decomposition. However, one may wish to weigh more or less certain atoms, or, assign higher costs to some other atoms to be included in the decomposition. This can happen for example when there is prior information available on each atom. This motivates generalizing the notion of minimal ℓ 0-norm solution to that of minimal weighted ℓ 0-norm solution. On the other hand, relaxing weighted ℓ 0-norm via the weighted ℓ 1-norm is challenging. This paper deals with minimal weighted ℓ 0-norm solutions of underdetermined linear systems, provides conditions for their uniqueness, and develops an algorithm for their estimation.
KW - Compressive sampling
KW - Sparse decomposition
KW - Weighted sparse decomposition
KW - weighted compressive sampling
UR - http://www.scopus.com/inward/record.url?scp=84867600375&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84867600375&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2012.6288652
DO - 10.1109/ICASSP.2012.6288652
M3 - Conference contribution
AN - SCOPUS:84867600375
SN - 9781467300469
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 3425
EP - 3428
BT - 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings
T2 - 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012
Y2 - 25 March 2012 through 30 March 2012
ER -