Efficient box-constrained “nonconvex + nonconvex” approach for image deblurring with impulse noise
Journal of Applied and Numerical Optimization · 2024
To overcome the biases in estimating the L 1 -norm data fidelity term and staircase artifacts of the total variation regularization term, we propose a nonconvex+nonconvex model with box constraints to recover images degraded by blurring and impulse noise.Owing to the data fidelity term and the regularization term being nonconvex, we apply a proximal linearized minimization algorithm to solve the problem.To deal with a subproblem, we utilize the alternating direction multiplier method.The global convergence of the proposed algorithm is established under the assumption that the objective function satisfies the Kurdyka-Lojasiewicz property.We also present numerical results to demonstrate that the proposed nonconvex+nonconvex model outperforms existing models in terms of both numerical accuracy and visual quality.The proposed model also exhibits much better performance than the other methods, especially for piecewise-constant images.