Title: Tuning Free Orthogonal Matching Pursuit,
Abstract: Orthogonal matching pursuit (OMP) is a widely used compressive sensing (CS)
algorithm for recovering sparse signals in noisy linear regression models. The
performance of OMP depends on its stopping criteria (SC). SC for OMP discussed
in literature typically assumes knowledge of either the sparsity of the signal
to be estimated $k_0$ or noise variance $\sigma^2$, both of which are
unavailable in many practical applications. In this article we develop a
modified version of OMP called tuning free OMP or TF-OMP which does not require
a SC. TF-OMP is proved to accomplish successful sparse recovery under the usual
assumptions on restricted isometry constants (RIC) and mutual coherence of
design matrix. TF-OMP is numerically shown to deliver a highly competitive
performance in comparison with OMP having \textit{a priori} knowledge of $k_0$
or $\sigma^2$. Greedy algorithm for robust de-noising (GARD) is an OMP like
algorithm proposed for efficient estimation in classical overdetermined linear
regression models corrupted by sparse outliers. However, GARD requires the
knowledge of inlier noise variance which is difficult to estimate. We also
produce a tuning free algorithm (TF-GARD) for efficient estimation in the
presence of sparse outliers by extending the operating principle of TF-OMP to
GARD. TF-GARD is numerically shown to achieve a performance comparable to that
of the existing implementation of GARD.