TY - GEN
T1 - A two-term penalty function for inverse problems with sparsity constrains
AU - Rodriguez, Paul
N1 - Publisher Copyright:
© EURASIP 2017.
PY - 2017/10/23
Y1 - 2017/10/23
N2 - Inverse problems with sparsity constrains, such Basis Pursuit denoising (BPDN) and Convolutional BPDN (CBPDN), usually use the '1-norm as the penalty function; however such choice leads to a solution that is biased towards zero. Recently, several works have proposed and assessed the properties of other non-standard penalty functions (most of them non-convex), which avoid the above mentioned drawback and at the same time are intended to induce sparsity more strongly than the '1-norm. In this paper we propose a two-term penalty function consisting of a synthesis between the '1-norm and the penalty function associated with the Non-Negative Garrote (NNG) thresholding rule. Although the proposed two-term penalty function is nonconvex, the total cost function for the BPDN/CBPDN problems is still convex. The performance of the proposed twoterm penalty function is compared with other reported choices for practical denoising, deconvolution and convolutional sparse coding (CSC) problems within the BPDN/CBPDN frameworks. Our experimental results show that the proposed two-term penalty function is particularly effective (better reconstruction with sparser solutions) for the CSC problem while attaining competitive performance for the denoising and deconvolution problems.
AB - Inverse problems with sparsity constrains, such Basis Pursuit denoising (BPDN) and Convolutional BPDN (CBPDN), usually use the '1-norm as the penalty function; however such choice leads to a solution that is biased towards zero. Recently, several works have proposed and assessed the properties of other non-standard penalty functions (most of them non-convex), which avoid the above mentioned drawback and at the same time are intended to induce sparsity more strongly than the '1-norm. In this paper we propose a two-term penalty function consisting of a synthesis between the '1-norm and the penalty function associated with the Non-Negative Garrote (NNG) thresholding rule. Although the proposed two-term penalty function is nonconvex, the total cost function for the BPDN/CBPDN problems is still convex. The performance of the proposed twoterm penalty function is compared with other reported choices for practical denoising, deconvolution and convolutional sparse coding (CSC) problems within the BPDN/CBPDN frameworks. Our experimental results show that the proposed two-term penalty function is particularly effective (better reconstruction with sparser solutions) for the CSC problem while attaining competitive performance for the denoising and deconvolution problems.
UR - http://www.scopus.com/inward/record.url?scp=85023761050&partnerID=8YFLogxK
U2 - 10.23919/EUSIPCO.2017.8081585
DO - 10.23919/EUSIPCO.2017.8081585
M3 - Conference contribution
AN - SCOPUS:85023761050
T3 - 25th European Signal Processing Conference, EUSIPCO 2017
SP - 2126
EP - 2130
BT - 25th European Signal Processing Conference, EUSIPCO 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 25th European Signal Processing Conference, EUSIPCO 2017
Y2 - 28 August 2017 through 2 September 2017
ER -