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Shirong Deng, Yuchao Tang, Efficient box-constrained “nonconvex + nonconvex” approach for image deblurring with impulse noise

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DOI: 10.23952/jano.6.2024.3.06
Volume 6, Issue 3, 1 December 2024, Pages 391-409

 

Abstract. 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.

 

How to Cite this Article:
S. Deng, Y. Tang, Efficient box-constrained “nonconvex + nonconvex” approach for image deblurring with impulse noise, J. Appl. Numer. Optim. 6 (2024), 391-409.