TY - GEN
T1 - Sparsity amplified
AU - Selesnick, Ivan
N1 - Funding Information:
This material is based upon work supported by the National Science Foundation under Grant No. 1525398 and the Office of Naval Research under grant No. N00014-15-1-2314.
Publisher Copyright:
© 2017 IEEE.
PY - 2017/6/16
Y1 - 2017/6/16
N2 - The L1 norm is often used as a penalty function to obtain a sparse approximate solution to a system of linear equations, but it often underestimates the true values. This paper proposes a different type of penalty that (1) estimates sparse solutions more accurately and (2) maintains the convexity of the cost function. The new penalty is a multivariate generalization of the minimax-concave (MC) penalty. To define the generalized MC (GMC) penalty we first define a multivariate generalized Huber function. The resulting cost function can be minimized by proximal algorithms comprising simple computations. The effectiveness of the GMC penalty is illustrated in a denoising example.
AB - The L1 norm is often used as a penalty function to obtain a sparse approximate solution to a system of linear equations, but it often underestimates the true values. This paper proposes a different type of penalty that (1) estimates sparse solutions more accurately and (2) maintains the convexity of the cost function. The new penalty is a multivariate generalization of the minimax-concave (MC) penalty. To define the generalized MC (GMC) penalty we first define a multivariate generalized Huber function. The resulting cost function can be minimized by proximal algorithms comprising simple computations. The effectiveness of the GMC penalty is illustrated in a denoising example.
KW - Sparse regularization
KW - basis pursuit denoising
KW - convex optimization
KW - sparse-regularized linear least squares
UR - http://www.scopus.com/inward/record.url?scp=85023759994&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85023759994&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2017.7952979
DO - 10.1109/ICASSP.2017.7952979
M3 - Conference contribution
AN - SCOPUS:85023759994
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 4356
EP - 4360
BT - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Y2 - 5 March 2017 through 9 March 2017
ER -