Edge-preserving reconstruction with contour-line smoothing and non-quadratic data-fidelity (Q2437913)

The image reconstruction problem can be formulated as the minimization of a cost function, which has the limitation of noisy contour lines and the staircase effect with piecewise-constant regions. The authors propose a regularization model by incorporating the smoothness features of the edge field implicitly to encourage the formulation of smooth contour lines and to reduce the staircase effect. A deterministic relaxation algorithm under differentiability and coercivity assumptions is proposed. The proposed scheme allows to enforce inequality constraints on the pixel values, and to use continuation sequences to reveal the complexity of minimizing the cost function which is not convex. The convergence properties of the algorithm are derived. Some numerical experimental results are presented to show the effectiveness of the algorithms.