2017/07/27 by Sreejith Kallummil, Sheetal Kalyani, Kallummil, Sreejith +1
Computer Science · Engineering · #FOS: Computer and information sciences #Image and Signal Denoising Methods #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.1707.08712
openalex publication_date 2017/07/27 · openalex created_date 2017/08/08 · openalex updated_date 2026/07/28
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 a priori knowledge of either the sparsity of the signal (k0) or noise variance (σ2). Both k0 and σ2 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 k0 and σ2 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 a priori knowledge of k0 and σ2. Numerical simulations also indicate a highly competitive performance of TF-IGP and RRT-IGP in comparison to OMP/OLS with a priori knowledge of k0 and σ2.