@Article{CSIAM-AM-4-4,
author = {Shao, Nian and Zhang, Rui and Sun, Jie and Wenbin, Chen},
title = {A Two-Level Simultaneous Orthogonal Matching Pursuit Algorithm for Simultaneous Sparse Approximation Problems},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2023},
volume = {4},
number = {4},
pages = {758--775},
abstract = {<p style="text-align: justify;">In this paper, we propose a two-level simultaneous orthogonal matching
pursuit (TLSOMP) algorithm for simultaneous sparse approximation (SSA) problems.
Most existing algorithms for SSA problems are directly generalized from the ones for
the sparse approximation (SA) problems, for example, the simultaneous orthogonal
matching pursuit (SOMP) method is generalized from the orthogonal matching pursuit (OMP) method. Our newly proposed algorithm is designed from another viewpoint. We first analyze the noiseless case and propose a selection algorithm. Motivated
by the analysis and presuming noise as a perturbation, we extend the selection algorithm into a TLSOMP algorithm. This novel algorithm mainly uses the information
from the subspace spanned by the multiple signals, which is not available in SA problems. Numerical experiments show the superiority of our TLSOMP algorithm over
other traditional SSA solvers.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2022-0050},
url = {https://global-sci.com/article/82305/a-two-level-simultaneous-orthogonal-matching-pursuit-algorithm-for-simultaneous-sparse-approximation-problems}
}