Sparse signal recovery from noisy measurements via searching forward OMP

Abstract

Recovering sparse signals from compressed measurements has received much attention in recent years. Considering that measurement errors always exist, an improved orthogonal matching pursuit (OMP) method which is called Searching Forward OMP (SFOMP), is proposed in this letter. The proposed SFOMP method is designed for compressive sensing and sparse signal recovery in the noisy environment. To improve the recovery performance, the SFOMP method incorporates a searching forward strategy to find the column leading to a minimum norm of residual error among the added candidates in each iteration. Numerical results show that, compared with other commonly used methods, this method provides a higher recovery signal‐to‐noise ratio, more accurate reconstruction of support set, and a competitive computational complexity with noisy measurements.

The statistical properties analysis of reconstruction error in greedy pursuit algorithms: Taking OMP as an example

“…Orthogonal matching pursuit (OMP) [2,3], the most classical greedy pursuit algorithm, encompasses two fundamental aspects of greedy pursuit algorithms: matching pursuit and least squares. Over the years, numerous novel greedy pursuit algorithms have been proposed to refine support set selection strategies based on OMP, such as generalized OMP (gOMP) [4], stagewise OMP (StOMP) [5], searching forward OMP (SFOMP) [6], regularized OMP (ROMP) [7], compressive sampling MP (CoSaMP) [8], subspace pursuit (SP) [9], and sparsity adaptive MP (SAMP) [10]. All of the above algorithms select multiple column vectors at each iteration, and the latter three algorithms employ techniques like backtracking or pruning to replace incorrect column vectors from the support set.…”

Sparse regularization method combining SVA for feature enhancement of SAR images

“…Introduction: Sparse synthetic aperture radar (SAR) imaging is an emerging imaging scheme with the development of compressed sensing [1], which exploits sparse signal processing to replace matched filtering (MF) for image focusing. It can reconstruct SAR images and improve the image quality in down and full-sampling conditions [2,3].…”