Robust censoring for linear inverse problems

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.