Spatially adapted parameters selection based on the local constraints for Gaussian plus impulse image deblurring

In this paper, we present a novel \(L^{1}\)-\(L^{2}\)-TV model for image deblurring that incorporates spatially varying regularization parameters, addressing the challenge of mixed Gaussian and impulse noise. The traditional Total Variation (TV) model with \(L^{1}\) and \(L^{2}\) fidelity terms is well-recognized for its effectiveness in such scenarios, but our proposed approach enhances this by allowing the regularization parameters to adapt based on local image characteristics. This ensures that fine details are better preserved while maintaining smoothness in homogeneous areas. The spatially dependent regularization parameters are automatically determined using local discrepancy functions. The discrete minimization problem that arises from this model is efficiently solved using the inexact alternating direction method (IADM). Our numerical experiments show that the proposed algorithm significantly improves the peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) by enhancing detailed regions and effectively removing both types of noise.