  We consider the task of robust non-linear regression in the presence of both
inlier noise and outliers. Assuming that the unknown non-linear function
belongs to a Reproducing Kernel Hilbert Space (RKHS), our goal is to estimate
the set of the associated unknown parameters. Due to the presence of outliers,
common techniques such as the Kernel Ridge Regression (KRR) or the Support
Vector Regression (SVR) turn out to be inadequate. Instead, we employ sparse
modeling arguments to explicitly model and estimate the outliers, adopting a
greedy approach. The proposed robust scheme, i.e., Kernel Greedy Algorithm for
Robust Denoising (KGARD), is inspired by the classical Orthogonal Matching
Pursuit (OMP) algorithm. Specifically, the proposed method alternates between a
KRR task and an OMP-like selection step. Theoretical results concerning the
identification of the outliers are provided. Moreover, KGARD is compared
against other cutting edge methods, where its performance is evaluated via a
set of experiments with various types of noise. Finally, the proposed robust
estimation framework is applied to the task of image denoising, and its
enhanced performance in the presence of outliers is demonstrated.
