TY - JOUR
T1 - A Two-Level Simultaneous Orthogonal Matching Pursuit Algorithm for Simultaneous Sparse Approximation Problems
AU - Shao , Nian
AU - Zhang , Rui
AU - Sun , Jie
AU - Chen , Wenbin
JO - CSIAM Transactions on Applied Mathematics
VL - 4
SP - 758
EP - 775
PY - 2023
DA - 2023/10
SN - 4
DO - http://doi.org/10.4208/csiam-am.SO-2022-0050
UR - https://global-sci.org/intro/article_detail/csiam-am/22077.html
KW - Simultaneous sparse approximation, two-level simultaneous orthogonal matching pursuit, subspace approximation.
AB - <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>