  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-{\L}ojasiewicz 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.
