Regularization of _1 minimization for dealing with outliers and noise in Statistics and Signal Recovery

Abstract

We study the robustness properties of _1 norm minimization for the classical linear regression problem with a given design matrix and contamination restricted to the dependent variable. We perform a fine error analysis of the _1 estimator for measurements errors consisting of outliers coupled with noise. We introduce a new estimation technique resulting from a regularization of _1 minimization by inf-convolution with the _2 norm. Concerning robustness to large outliers, the proposed estimator keeps the breakdown point of the _1 estimator, and reduces to least squares when there are not outliers. We present a globally convergent forward-backward algorithm for computing our estimator and some numerical experiments confirming its theoretical properties.

Tasks

Reproductions