Constrained and Unconstrained Inverse Potts Modeling for Joint Image Super-Resolution and Segmentation

In this work we consider two methods for joint single-image super-resolution and image partitioning. The proposed approaches rely on a constrained and on an unconstrained version of the inverse Potts model where an l(0) regularization prior on the image gradient is used for promoting piecewise constant solutions. For the numerical solution of both models, we provide a unified implementation based on the Alternating Direction Method of Multipliers (ADMM). Upon suitable assumptions on both model operators and on the algorithmic parameters involved, we show that all the ADMM subproblems admit closed-form solutions, thus making the resulting algorithms computationally very cheap even when high-dimensional data are considered. Numerical details of the implementation of both models are given and several experiments are carried out on both synthetic and natural images to underline the accuracy and the computational efficiency of the models.