A Truncated L1-L2 Total Variational Method for Image Restoration with Impulse Noise

Image restoration is a key step in the field of image processing. Total Variation (TV) model is widely applied in image denoising because it preserves edges and image details. However, TV model has some shortcomings, such as staircase artifacts and excessive smoothing of image texture area. Then we purpose a truncated L1-L2 Total Variational model, which is nonconvex and nonsmooth, for image restoration with impulse noise. In this proper, two algorithms, the alternating direction method of multiplier (ADMM) and the penalty-Gaussian Seidel type inertial proximal alternating linearized minimization (P-GiPALM), are designed to solve the nonconvex optimization. The subproblems are solved by the proximal difference-of -convex algorithm with extrapolation (pDCAe) and GiPALM with global convergence, respectively. The experimental results show that the new model has higher peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) values than those of median filter and the cutting-edge Cauchy denoising method.