  Orthogonal matching pursuit (OMP) and orthogonal least squares (OLS) are
widely used for sparse signal reconstruction in under-determined linear
regression problems. The performance of these compressed sensing (CS)
algorithms depends crucially on the \textit{a priori} knowledge of either the
sparsity of the signal ($k_0$) or noise variance ($\sigma^2$). Both $k_0$ and
$\sigma^2$ are unknown in general and extremely difficult to estimate in under
determined models. This limits the application of OMP and OLS in many practical
situations. In this article, we develop two computationally efficient
frameworks namely TF-IGP and RRT-IGP for using OMP and OLS even when $k_0$ and
$\sigma^2$ are unavailable. Both TF-IGP and RRT-IGP are analytically shown to
accomplish successful sparse recovery under the same set of restricted isometry
conditions on the design matrix required for OMP/OLS with \textit{a priori}
knowledge of $k_0$ and $\sigma^2$. Numerical simulations also indicate a highly
competitive performance of TF-IGP and RRT-IGP in comparison to OMP/OLS with
\textit{a priori} knowledge of $k_0$ and $\sigma^2$.
