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

2023/09/11 by Tarmizi Adam, Alexander Malyshev, Adam, Tarmizi +7
Computer Science · Engineering · #Advanced Image Processing Techniques #FOS: Mathematics #Image and Signal Denoising Methods #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2309.05204

openalex publication_date 2023/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 ℓ_p, 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 ℓ_p 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.

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