Reproducible Research material for : A new robust and ifficient estimator for ill-conditioned linear inverse problems with outliers.
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Regularized tau estimator

This repository contains all the code to reproduce the results of the paper A new robust and efficient estimator for ill-conditioned linear inverse problems with outliers.


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 tau 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.


Marta Martinez-Camara and Martin Vetterli are with the Laboratory for Audiovisual Communications (LCAV) at EPFL.

Michael Muma and Abdelhak M. Zoubir are with the Signal Processing Group (SPG) at TUDarmstadt.


Marta Martinez-Camara
BC Building
Station 14
1015 Lausanne

Tau estimators

The Matlab implementation of the fast tau estimator and the regularized tau estimator is given in



The scripts to generate Figures 2 and 3 from the paper are


To run them, you need the fast tau algorithms from last section, and the CVX package. Set up the CVX path in your computer in the scripts before using them.


Copyright (c) 2015, Marta Martinez-Camara, Michael Muma, Abdelhak M. Zoubir, Martin Vetterli

This code is free to reuse for non-commercial purpose such as academic or educational. For any other use, please contact the authors.

Creative Commons License
Regularized tau estimator by Marta Martinez-Camara, Michael Muma, Abdelhak M. Zoubir, Martin Vetterli is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Based on a work at