(v[x+ 1] v[x];

The eld of robust statistics [3, 4] is concerned with estimation problems in which the data contains gross errors, or outliers that do not conform to the statistical assumptions for the majority of the data (e.g., Gaussian noise). The main goals of robust statistics are: \(i) To describe the structure best tting the bulk of the data, (ii) To identify deviating data points (outliers) or deviating substructures for further treatment, if desired." 2 Robust Regularization. Denoising (revisited). Let us again consider the problem of denoising a one-dimensional input signal. A generalization of the previous regularization formulation is to minimize the objective function constraints: E(v) = N X x=1 (v[x] u[x];