# Inertial nonconvex alternating minimizations for the image deblurring

arXiv: https://arxiv.org/abs/1907.12945 · HTML: https://mlsanity.com/paper/1907.12945/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimization](https://mlsanity.com/paper/2102.05433/) (2021)

## Abstract (arXiv)

In image processing, Total Variation (TV) regularization models are commonly used to recover blurred images. One of the most efficient and popular methods to solve the convex TV problem is the Alternating Direction Method of Multipliers (ADMM) algorithm, recently extended using the inertial proximal point method. Although all the classical studies focus on only a convex formulation, recent articles are paying increasing attention to the nonconvex methodology due to its good numerical performance and properties. In this paper, we propose to extend the classical formulation with a novel nonconvex Alternating Direction Method of Multipliers with the Inertial technique (IADMM). Under certain assumptions on the parameters, we prove the convergence of the algorithm with the help of the Kurdyka-Lojasiewicz property. We also present numerical simulations on classical TV image reconstruction problems to illustrate the efficiency of the new algorithm and its behavior compared with the well established ADMM method.