English

Accelerated Proximal Iterative re-Weighted $\ell_1$ Alternating Minimization for Image Deblurring

Optimization and Control 2023-09-12 v1

Abstract

The quadratic penalty alternating minimization (AM) method is widely used for solving the convex 1\ell_1 total variation (TV) image deblurring problem. However, quadratic penalty AM for solving the nonconvex nonsmooth p\ell_p, 0<p<10 < p < 1 TV image deblurring problems is less studied. In this paper, we propose two algorithms, namely proximal iterative re-weighted 1\ell_1 AM (PIRL1-AM) and its accelerated version, accelerated proximal iterative re-weighted 1\ell_1 AM (APIRL1-AM) for solving the nonconvex nonsmooth p\ell_p TV image deblurring problem. The proposed algorithms are derived from the proximal iterative re-weighted 1\ell_1 (IRL1) algorithm and the proximal gradient algorithm. Numerical results show that PIRL1-AM is effective in retaining sharp edges in image deblurring while APIRL1-AM can further provide convergence speed up in terms of the number of algorithm iterations and computational time.

Keywords

Cite

@article{arxiv.2309.05204,
  title  = {Accelerated Proximal Iterative re-Weighted $\ell_1$ Alternating Minimization for Image Deblurring},
  author = {Tarmizi Adam and Alexander Malyshev and Mohd Fikree Hassan and Nur Syarafina Mohamed and Md Sah Hj Salam},
  journal= {arXiv preprint arXiv:2309.05204},
  year   = {2023}
}
R2 v1 2026-06-28T12:17:37.623Z