A Derivative Fidelity-Based Total Generalized Variation Method for Image Restoration

Image edge is the most indicative feature that forms a significant role in image analysis and image understanding, but edge-detail preservation is a difficult task in image restoration due to noise and blur during imaging. The balance between edge preservation and noise removal has always been a difficult problem in image restoration. This paper proposes a derivative fidelity-based total generalized variation method (D-TGV) to improve this balance. First, an objective function model that highlights the ability to maintain details is proposed for the image restoration problem, which is combined with a fidelity term in derivative space and a total generalized variation regularization term. This is designed to achieve the advantage of preserving details in derivative space and eliminate the staircase effect caused by traditional total variation. Second, the alternating direction method of the multipliers (ADMM) is used to solve the model equations by decomposing the original, highly complex model into several simple sub-problems to attain rapid convergence. Finally, a series of experiments conducted on standard grayscale images showed that the proposed method exhibited a good balance between detail preservation and denoising but also reached completion with the fewest iterations compared with the currently established methods.