TY - GEN
T1 - Robust reconstruction with nonconvex subset constraints
T2 - 30th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2020
AU - Marmin, Arthur
AU - Castella, Marc
AU - Pesquet, Jean Christophe
N1 - Publisher Copyright:
© 2020 IEEE.
PY - 2020/9/1
Y1 - 2020/9/1
N2 - In this paper, we are interested in the recovery of an unknown signal corrupted by a linear operator, a nonlinear function, and an additive Gaussian noise. In addition, some of the observations contain outliers. Many robust data fit functions which alleviate sensitivity to outliers can be expressed as piecewise rational functions. Based on this fact, we reformulate the robust inverse problem as a rational optimization problem. The considered framework allows us to incorporate nonconvex constraints such as unions of subsets. The rational problem is then solved using recent optimization techniques which offer guarantees for global optimality. Finally, experimental results illustrate the validity of the recovered global solutions and the good quality of the reconstructed signals despite the presence of outliers.
AB - In this paper, we are interested in the recovery of an unknown signal corrupted by a linear operator, a nonlinear function, and an additive Gaussian noise. In addition, some of the observations contain outliers. Many robust data fit functions which alleviate sensitivity to outliers can be expressed as piecewise rational functions. Based on this fact, we reformulate the robust inverse problem as a rational optimization problem. The considered framework allows us to incorporate nonconvex constraints such as unions of subsets. The rational problem is then solved using recent optimization techniques which offer guarantees for global optimality. Finally, experimental results illustrate the validity of the recovered global solutions and the good quality of the reconstructed signals despite the presence of outliers.
KW - Global optimization
KW - Nonconvex constraints
KW - Polynomial optimization
KW - Robust estimation
KW - Union of subspaces/subsets
UR - https://www.scopus.com/pages/publications/85096475497
U2 - 10.1109/MLSP49062.2020.9231524
DO - 10.1109/MLSP49062.2020.9231524
M3 - Conference contribution
AN - SCOPUS:85096475497
T3 - IEEE International Workshop on Machine Learning for Signal Processing, MLSP
BT - Proceedings of the 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing, MLSP 2020
PB - IEEE Computer Society
Y2 - 21 September 2020 through 24 September 2020
ER -