Inertial nonconvex alternating minimizations for the image deblurring
This is an incremental improvement for image processing researchers, enhancing deblurring methods with nonconvex formulations.
The authors tackled image deblurring by proposing a nonconvex inertial ADMM algorithm, proving its convergence and showing improved efficiency over standard ADMM in numerical simulations.
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-Łojasiewicz 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.