A nonconvex nonsmooth model with convergent algorithm for image segmentation under Poisson noise

In this paper, a novel nonconvex nonsmooth variational model is proposed to segment images degraded by Poisson noise. The introduced nonconvex regularizer enhances the alignment of partition boundaries with image edges, while the non-quadratic data fidelity is incorporated to handle Poisson noise robustly. Within a proximal alternating minimization framework, the model is decomposed into two convex subproblems, each of which is efficiently solved using the alternating direction method of multipliers. The global convergence of the proposed algorithm can be established based on the Kurdyka-Łojasiewicz property of the objective function. Numerical experiments and comparisons illustrate the effectiveness and robustness of our method in terms of both visual results and quantitative metrics.