@inproceedings{4344cdc23cb9465b8c8a767d28185d60,
title = "Sharpening Sparse Regularizers",
abstract = "Non-convex penalties outperform the convex ℓ-norm, but generally sacrifice the cost function convexity. As a middle ground, we propose a framework to design non-convex penalties that induce sparsity more effectively than the ℓ-norm, but without sacrificing the cost function convexity. The non-smooth non-convex regularizers are constructed by subtracting from the non-smooth convex penalty its smoothed version. We propose a generalized infimal convolution smoothing smoothing technique to obtain the smoothed version. We call the proposed framework sharpening sparse regularizers (SSR) to imply its advantages compared to convex and non-convex regularizers. The SSR framework is applicable to any sparsity regularized ill-posed linear inverse problem. Furthermore, it recovers and generalizes several non-convex penalties in the literature as special cases. The SSR-RLS problem can be formulated as a saddle point problem, and solved by a scalable generalized primal-dual algorithm. The effectiveness of the SSR framework is demonstrated by numerical experiments.",
keywords = "Sparsity, convex analysis, convex optimization, non-convexity, smoothing",
author = "Abdullah Al-Shabili and Ivan Selesnick",
year = "2019",
month = may,
doi = "10.1109/ICASSP.2019.8683039",
language = "English (US)",
series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "4908--4912",
booktitle = "2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings",
note = "44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 ; Conference date: 12-05-2019 Through 17-05-2019",
}