Robust censoring for linear inverse problems

Abstract

Existing methods for smart data reduction are typically sensitive to outlier data that do not follow postulated data models. We propose robust censoring as a joint approach unifying the concepts of robust learning and data censoring. We focus on linear inverse problems and formulate robust censoring through a sparse sensing operator, which is a non-convex bilinear problem. We propose two solvers, one using alternating descent and the other using Metropolis-Hastings sampling. Although the latter is based on the concept of Bayesian sampling, we avoid confining the outliers to a specific model. Numerical results show that the proposed Metropolis-Hastings sampler outperforms state-of-the-art robust estimators.