Title: Noise Statistics Oblivious GARD For Robust Regression With Sparse Outliers,
Abstract: Linear regression models contaminated by Gaussian noise (inlier) and possibly
unbounded sparse outliers are common in many signal processing applications.
Sparse recovery inspired robust regression (SRIRR) techniques are shown to
deliver high quality estimation performance in such regression models.
Unfortunately, most SRIRR techniques assume \textit{a priori} knowledge of
noise statistics like inlier noise variance or outlier statistics like number
of outliers. Both inlier and outlier noise statistics are rarely known
\textit{a priori} and this limits the efficient operation of many SRIRR
algorithms. This article proposes a novel noise statistics oblivious algorithm
called residual ratio thresholding GARD (RRT-GARD) for robust regression in the
presence of sparse outliers. RRT-GARD is developed by modifying the recently
proposed noise statistics dependent greedy algorithm for robust de-noising
(GARD). Both finite sample and asymptotic analytical results indicate that
RRT-GARD performs nearly similar to GARD with \textit{a priori} knowledge of
noise statistics. Numerical simulations in real and synthetic data sets also
point to the highly competitive performance of RRT-GARD.