تقرير
Sparse Signal Reconstruction for Nonlinear Models via Piecewise Rational Optimization
| العنوان: | Sparse Signal Reconstruction for Nonlinear Models via Piecewise Rational Optimization |
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| المؤلفون: | Marmin, Arthur, Castella, Marc, Pesquet, Jean-Christophe, Duval, Laurent |
| المصدر: | Signal Processing, Volume 179, February 2021, 107835 Signal Processing Volume 179, February 2021, 107835 |
| سنة النشر: | 2020 |
| المجموعة: | Computer Science Mathematics Physics (Other) Statistics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Computer Science - Machine Learning, Physics - Data Analysis, Statistics and Probability, Statistics - Applications, 46N10, G.1, I.6, G.1.2, G.1.6, I.4.5 |
| الوصف: | We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and a penalization term. In contrast with most previous works which settle for approximated local solutions, we seek for a global solution to the obtained challenging nonconvex problem. Our global approach relies on the so-called Lasserre relaxation of polynomial optimization. We here specifically include in our approach the case of piecewise rational functions, which makes it possible to address a wide class of nonconvex exact and continuous relaxations of the $\ell_0$ penalization function. Additionally, we study the complexity of the optimization problem. It is shown how to use the structure of the problem to lighten the computational burden efficiently. Finally, numerical simulations illustrate the benefits of our method in terms of both global optimality and signal reconstruction. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.sigpro.2020.107835 |
| URL الوصول: | http://arxiv.org/abs/2010.15427 |
| رقم الأكسشن: | edsarx.2010.15427 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.sigpro.2020.107835 |
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