A nonmonotone adaptive projected gradient method for primal-dual total variation image restoration

•A nonmonotone adaptive projected gradient (NAPG) method is proposed.•The proposed method implements image restoration by deblurring and denoising alternatively at each iteration.•The per-iteration computational complexity of the algorithm is dominated by two fast Fourier transforms (FFTs).•It is competitive to some restoration functions in Matlab image processing toolbox and some state-of-the-art algorithms, such as FISTA, FTVd, and TwIST.

This paper studies image restoration problems from noisy and blurred observation. Based on a primal-dual total variation model, a nonmonotone adaptive projected gradient method is proposed and tested. By introducing an auxiliary variable, the proposed method implements image restoration by de-blurring and de-noising alternatively at each iteration. Convergence result of the proposed method is established. Numerical results illustrate the efficiency of this method and indicate that it is competitive to some state-of-the-art algorithms in the literature, such as FISTA and FTVd.