Image Denoising via Group Sparse Representations over Local SVD and Variational Model

We propose a novel two-stage model for image denoising. With the group sparse representations over local singular value decomposition stage (locally), one can remove the noise effectively and keep the texture well. The final denoising by a first-order variational model stage (globally) can help us to remove artifacts, maintain the image contrast, suppress the staircase effect, while preserving sharp edges. The existence and uniqueness of global minimizers of the low-rank problem based on group sparse representations are analyzed and proved. Alternating direction method of multipliers is utilized to minimize the associated functional, and the convergence analysis of the proposed optimization algorithm are established. Numerical experiments are conducted to showcase the distinctive features of our method and to provide a comparison with other image denoising techniques.