Sparse Signal Reconstruction for Nonlinear Models via Piecewise Rational Optimization

by   Arthur Marmin, et al.

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 ℓ_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.



page 1

page 2

page 3

page 4


Composite Optimization by Nonconvex Majorization-Minimization

Many tasks in imaging can be modeled via the minimization of a nonconvex...

Regularized asymptotic descents for a class of nonconvex optimization problems

We propose and analyze regularized asymptotic descent (RAD) methods for ...

Cross validation in sparse linear regression with piecewise continuous nonconvex penalties and its acceleration

We investigate the signal reconstruction performance of sparse linear re...

Global Optimality Guarantees for Nonconvex Unsupervised Video Segmentation

In this paper, we consider the problem of unsupervised video object segm...

Regularized asymptotic descents for nonconvex optimization

In this paper we propose regularized asymptotic descent (RAD) methods fo...

Global optimization for low-dimensional switching linear regression and bounded-error estimation

The paper provides global optimization algorithms for two particularly d...

Perfect reconstruction of sparse signals with piecewise continuous nonconvex penalties and nonconvexity control

We consider compressed sensing formulated as a minimization problem of n...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.