A new robust and efficient estimator for ill-conditioned linear inverse problems with outliers

Marta Martinez-Camara; Michael Muma; Abdelhak M. Zoubir; Martin Vetterli

ICASSP 2015accepted0 citations

A new robust and efficient estimator for ill-conditioned linear inverse problems with outliers

Marta Martinez-Camara, Michael Muma, Abdelhak M. Zoubir, Martin Vetterli

Abstract

Solving a linear inverse problem may include difficulties such as the presence of outliers and a mixing matrix with a large condition number. In such cases a regularized robust estimator is needed. We propose a new-type regularized robust estimator that is simultaneously highly robust against outliers, highly efficient in the presence of purely Gaussian noise, and also stable when the mixing matrix has a large condition number. We also propose an algorithm to compute the estimates, based on a regularized iterative reweighted least squares algorithm. A basic and a fast version of the algorithm are given. Finally, we test the performance of the proposed approach using numerical experiments and compare it with other estimators. Our estimator provides superior robustness, even up to 40% of outliers, while at the same time performing quite close to the optimal maximum likelihood estimator in the outlier-free case.

BibTeX

@inproceedings{icassp2015_anewrobustandeff,
  title = {A new robust and efficient estimator for ill-conditioned linear inverse problems with outliers},
  author = {Marta Martinez-Camara and Michael Muma and Abdelhak M. Zoubir and Martin Vetterli},
  booktitle = {ICASSP 2015},
  year = {2015}
}