A nonconvex TVcapped-L1 model for image restoration with impulse noise

This paper addresses the problem of image deblurring in the presence of impulse noise. While methods based on total variation regularization have a long-standing history in image processing, the traditional convex TVL1 model that using the L₁ fidelity may introduce bias in the recovery results. To overcome this drawback, we propose a novel image deblurring model for impulse noise, called TVcapped-L₁ model, which integrates the nonconvex capped-L₁ fidelity with total variation regularization. We also provide an algorithmic framework that employs the difference-of-convex algorithm to solve the proposed model. Numerical experiments demonstrate that our proposed method outperforms existing methods in recovering images degraded by Gaussian blur and various types of impulse noise.