Accelerated Proximal Iterative re-Weighted ℓ1 Alternating Minimization for Image Deblurring

The quadratic penalty alternating minimization (AM) method is widely used for solving the convex ℓ1 total variation (TV) image deblurring problem. However, quadratic penalty AM for solving the nonconvex nonsmooth ℓp, 0 < p < 1 TV image deblurring problems is less studied. In this paper, we propose two algorithms, namely proximal iterative re-weighted ℓ1 AM (PIRL1-AM) and its accelerated version, accelerated proximal iterative re-weighted ℓ1 AM (APIRL1-AM) for solving the nonconvex nonsmooth ℓp TV image deblurring problem. The proposed algorithms are derived from the proximal iterative re-weighted ℓ1 (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.