TY - JOUR
T1 - Sparse Recovery Based on the Generalized Error Function
AU - Zhou , Zhiyong
JO - Journal of Computational Mathematics
VL - 3
SP - 679
EP - 704
PY - 2024
DA - 2024/04
SN - 42
DO - http://doi.org/10.4208/jcm.2204-m2021-0288
UR - https://global-sci.org/intro/article_detail/jcm/23032.html
KW - Sparse recovery, Generalized error function, Nonconvex regularization, Iterative reweighted L1, Difference of convex functions algorithms.
AB - <p style="text-align: justify;">In this paper, we offer a new sparse recovery strategy based on the generalized error
function. The introduced penalty function involves both the shape and the scale parameters, making it extremely flexible. For both constrained and unconstrained models,
the theoretical analysis results in terms of the null space property, the spherical section
property and the restricted invertibility factor are established. The practical algorithms
via both the iteratively reweighted $ℓ_1$ and the difference of convex functions algorithms
are presented. Numerical experiments are carried out to demonstrate the benefits of the
suggested approach in a variety of circumstances. Its practical application in magnetic
resonance imaging (MRI) reconstruction is also investigated.</p>