Signal and Noise Statistics Oblivious Sparse Reconstruction using OMP/OLS
This addresses a practical limitation in compressed sensing for applications where prior knowledge of signal statistics is unavailable, though it is incremental as it builds on existing OMP/OLS methods.
The paper tackles the problem of sparse signal reconstruction using OMP/OLS algorithms when sparsity and noise variance are unknown, developing two frameworks (TF-IGP and RRT-IGP) that achieve successful recovery under the same conditions as when these parameters are known, with numerical simulations showing highly competitive performance.
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 ($σ^2$). Both $k_0$ and $σ^2$ 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 $σ^2$ 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 $σ^2$. 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 $σ^2$.