Minimax concave penalty-based TGV model for Poissonian image restoration

As is known to all, although the denoising models based on total generalized variation regularization prevent the occurrence of staircase artifacts, they also tend to result in blurred edges in the restored images. In order to obtain high-quality images that conform human visual characteristics, we add a minimax concave penalty into the total generalized variation function, and develop a novel Kullback–Leibler divergence fidelity-based model for Poissonian image restoration. By integrating the variable splitting technique, a modified alternating direction method of multipliers is designed for numerical computation. Moreover, under proper parameter selection, the convergence of our proposed algorithm is established in detail. As the experimental validations, we have conducted a variety of numerical experiments comparing our new solver with some existing state-of-the-art methods. From the numerical experiments, it follows that our approach can not only preserve structural features well, but also achieve comparable recovery effects over other denoising schemes.